Calculus Books

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Book SynopsisTrade Review"...if you use this book frequently it’s definitely worth getting the new edition…" --MAA.org, November 2014 "The integrals are very useful, but this book includes many other features that will be helpful to the reader, especially graduate students. The sections on Hermite and Legendre polynomials are especially helpful for students of Electricity and Magnetism, Quantum Mechanics, and Mathematical physics (they won't have to hunt in several books to find what they need)." --Barry Simon, California Institute of Technology "This book is to the CRC Mathematical Tables as the unabridged Oxford English Dictionary is to Webster's Collegiate. Besides being big, it's easy to find things in, because of the way the integrals are organized into classes...It really helped me through grad school." --Phil Hobbs, Amazon ReviewTable of Contents1. Elementary Functions 2. Indefinite Integrals of Elementary Functions 3. Definite Integrals of Elementary Functions 4. Combinations Involving Trigonometric and Hyperbolic Functions and Power 5. Indefinite Integrals of Special Functions 6. Definite Integrals of Special Functions 7. Associated Legendre Functions 8. Special Functions 9. Hypergeometric Functions 10. Vector Field Theory 11. Algebraic Inequalities 12. Integral Inequalities 13. Matrices and Related Result 14. Determinants 15. Norms 16. Ordinary Differential Equations 17. Fourier, Laplace, and Mellin Transforms 18. The Z-transform

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Book SynopsisFor three-semester undergraduate-level courses in Calculus. This text combines traditional mainstream calculus with the most flexible approach to new ideas and calculator/computer technology. It contains superb problem sets and a fresh conceptual emphasis flavored by new technological possibilities. The Calculus II portion now has a new focus on differential equations.Table of Contents1. Functions, Graphs, and Models. Functions and Mathematical Modeling. Graphs of Equations and Functions. Polynomials and Algebraic Functions. Transcendental Functions. Preview: What Is Calculus? 2. Prelude to Calculus. Tangent Lines and Slope Predictors. The Limit Concept. More about Limits. The Concept of Continuity. 3. The Derivative. The Derivative and Rates of Change. Basic Differentiation Rules. The Chain Rule. Derivatives of Algebraic Functions. Maxima and Minima of Functions on Closed Intervals. Applied Optimization Problems. Derivatives of Trigonometric Functions. Successive Approximations and Newton's Method. 4. Additional Applications of the Derivative. Implicit Functions and Related Rates. Increments, Differentials, and Linear Approximation. Increasing and Decreasing Functions and the Mean Value Theorem. The First Derivative Test and Applications. Simple Curve Sketching. Higher Derivatives and Concavity. Curve Sketching and Asymptotes. 5. The Integral. Introduction. Antiderivatives and Initial Value Problems. Elementary Area Computations. Riemann Sums and the Integral. Evaluation of Integrals. The Fundamental Theorem of Calculus. Integration by Substitution. Areas of Plane Regions. Numerical Integration. 6. Applications of the Integral. Riemann Sum Approximations. Volumes by the Method of Cross Sections. Volumes by the Method of Cylindrical Shells. Arc Length and Surface Area of Revolution. Force and Work. Centroids of Plane Regions and Curves. 7. Calculus of Transcendental Functions. Exponential and Logarithmic Functions. Indeterminate Forms and L'Hopîtal's Rule. More Indeterminate Forms. The Logarithm as an Integral. Inverse Trigonometric Functions. Hyperbolic Functions. 8. Techniques of Integration. Introduction. Integral Tables and Simple Substitutions. Integration by Parts. Trigonometric Integrals. Rational Functions and Partial Fractions. Trigonometric Substitutions. Integrals Involving Quadratic Polynomials. Improper Integrals. 9. Differential Equations. Simple Equations and Models. Slope Fields and Euler's Method. Separable Equations and Applications. Linear Equations and Applications. Population Models. Linear Second-Order Equations. Mechanical Vibrations. 10. Polar Coordinates and Parametric Curves. Analytic Geometry and the Conic Sections. Polar Coordinates. Area Computations in Polar Coordinates. Parametric Curves. Integral Computations with Parametric Curves. Conic Sections and Applications. 11. Infinite Series. Introduction. Infinite Sequences. Infinite Series and Convergence. Taylor Series and Taylor Polynomials. The Integral Test. Comparison Tests for Positive-Term Series. Alternating Series and Absolute Convergence. Power Series. Power Series Computations. Series Solutions of Differential Equations. 12. Vectors, Curves, and Surfaces in Space. Vectors in the Plane. Three-Dimensional Vectors. The Cross Product of Vectors. Lines and Planes in Space. Curves and Motions in Space. Curvature and Acceleration. Cylinders and Quadric Surfaces. Cylindrical and Spherical Coordinates. 13. Partial Differentiation. Introduction. Functions of Several Variables. Limits and Continuity. Partial Derivatives. Multivariable Optimization Problems. Increments and Linear Approximation. The Multivariable Chain Rule. Directional Derivatives and the Gradient Vector. Lagrange Multipliers and Constrained Optimization. Critical Points of Functions of Two Variables. 14. Multiple Integrals. Double Integrals. Double Integrals over More General Regions. Area and Volume by Double Integration. Double Integrals in Polar Coordinates. Applications of Double Integrals. Triple Integrals. Integration in Cylindrical and Spherical Coordinates. Surface Area. Change of Variables in Multiple Integrals. 15. Vector Calculus. Vector Fields. Line Integrals. The Fundamental Theorem and Independence of Path. Green's Theorem. Surface Integrals. The Divergence Theorem. Stokes' Theorem. Appendices. Answers. Index.

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Book SynopsisJoel Hass received his PhD from the University of California Berkeley. He is currently a professor of mathematics at the University of California Davis. He has coauthored widely used calculus texts as well as calculus study guides. He is currently on the editorial board of several publications, including the Notices of the American Mathematical Society. He has been a member of the Institute for Advanced Study at Princeton University and of the Mathematical Sciences Research Institute, and he was a Sloan Research Fellow. Hass's current areas of research include the geometry of proteins, three dimensional manifolds, applied math, and computational complexity. In his free time, Hass enjoys kayaking. Christopher Heil received his PhD from the University of Maryland.  He is currently a professor of mathematics at the Georgia Institute of TechnolTable of ContentsTable of Contents Functions 1.1 Functions and Their Graphs 1.2 Combining Functions; Shifting and Scaling Graphs 1.3 Trigonometric Functions 1.4 Graphing with Software Limits and Continuity 2.1 Rates of Change and Tangent Lines to Curves 2.2 Limit of a Function and Limit Laws 2.3 The Precise Definition of a Limit 2.4 One-Sided Limits 2.5 Continuity 2.6 Limits Involving Infinity; Asymptotes of Graphs Derivatives 3.1 Tangent Lines and the Derivative at a Point 3.2 The Derivative as a Function 3.3 Differentiation Rules 3.4 The Derivative as a Rate of Change 3.5 Derivatives of Trigonometric Functions 3.6 The Chain Rule 3.7 Implicit Differentiation 3.8 Related Rates 3.9 Linearization and Differentials Applications of Derivatives 4.1 Extreme Values of Functions on Closed Intervals 4.2 The Mean Value Theorem 4.3 Monotonic Functions and the First Derivative Test 4.4 Concavity and Curve Sketching 4.5 Applied Optimization 4.6 Newton’S Method 4.7 Antiderivatives Integrals 5.1 Area and Estimating with Finite Sums 5.2 Sigma Notation and Limits of Finite Sums 5.3 The Definite Integral 5.4 The Fundamental Theorem of Calculus 5.5 Indefinite Integrals and the Substitution Method 5.6 Definite Integral Substitutions and the Area Between Curves Applications of Definite Integrals 6.1 Volumes Using Cross-Sections 6.2 Volumes Using Cylindrical Shells 6.3 Arc Length 6.4 Areas of Surfaces of Revolution 6.5 Work and Fluid Forces 6.6 Moments and Centers of Mass Transcendental Functions 7.1 Inverse Functions and Their Derivatives 7.2 Natural Logarithms 7.3 Exponential Functions 7.4 Exponential Change and Separable Differential Equations 7.5 Indeterminate Forms and L’Hôpital's Rule 7.6 Inverse Trigonometric Functions 7.7 Hyperbolic Functions 7.8 Relative Rates of Growth Techniques of Integration 8.1 Using Basic Integration Formulas 8.2 Integration by Parts 8.3 Trigonometric Integrals 8.4 Trigonometric Substitutions 8.5 Integration of Rational Functions by Partial Fractions 8.6 Integral Tables and Computer Algebra Systems 8.7 Numerical Integration 8.8 Improper Integrals 8.9 Probability First-Order Differential Equations 9.1 Solutions, Slope Fields, and Euler’s Method 9.2 First-Order Linear Equations 9.3 Applications 9.4 Graphical Solutions of Autonomous Equations 9.5 Systems of Equations and Phase Planes Infinite Sequences and Series 10.1 Sequences 10.2 Infinite Series 10.3 The Integral Test 10.4 Comparison Tests 10.5 Absolute Convergence; The Ratio and Root Tests 10.6 Alternating Series and Conditional Convergence 10.7 Power Series 10.8 Taylor and Maclaurin Series 10.9 Convergence of Taylor Series 10.10 Applications of Taylor Series Parametric Equations and Polar Coordinates 11.1 Parametrizations of Plane Curves 11.2 Calculus with Parametric Curves 11.3 Polar Coordinates 11.4 Graphing Polar Coordinate Equations 11.5 Areas and Lengths in Polar Coordinates 11.6 Conic Sections 11.7 Conics in Polar Coordinates Vectors and the Geometry of Space 12.1 Three-Dimensional Coordinate Systems 12.2 Vectors 12.3 The Dot Product 12.4 The Cross Product 12.5 Lines and Planes in Space 12.6 Cylinders and Quadric Surfaces Vector-Valued Functions and Motion in Space 13.1 Curves in Space and Their Tangents 13.2 Integrals of Vector Functions; Projectile Motion 13.3 Arc Length in Space 13.4 Curvature and Normal Vectors of a Curve 13.5 Tangential and Normal Components of Acceleration 13.6 Velocity and Acceleration in Polar Coordinates Partial Derivatives 14.1 Functions of Several Variables 14.2 Limits and Continuity in Higher Dimensions 14.3 Partial Derivatives 14.4 The Chain Rule 14.5 Directional Derivatives and Gradient Vectors 14.6 Tangent Planes and Differentials 14.7 Extreme Values and Saddle Points 14.8 Lagrange Multipliers 14.9 Taylor’s Formula for Two Variables 14.10 Partial Derivatives with Constrained Variables Multiple Integrals 15.1 Double and Iterated Integrals over Rectangles 15.2 Double Integrals over General Regions 15.3 Area by Double Integration 15.4 Double Integrals in Polar Form 15.5 Triple Integrals in Rectangular Coordinates 15.6 Applications 15.7 Triple Integrals in Cylindrical and Spherical Coordinates 15.8 Substitutions in Multiple Integrals Integrals and Vector Fields 16.1 Line Integrals of Scalar Functions 16.2 Vector Fields and Line Integrals: Work, Circulation, and Flux 16.3 Path Independence, Conservative Fields, and Potential Functions 16.4 Green’s Theorem in the Plane 16.5 Surfaces and Area 16.6 Surface Integrals 16.7 Stokes' Theorem 16.8 The Divergence Theorem and a Unified Theory Second-Order Differential Equations (Online at www.goo.gl/MgDXPY) 17.1 Second-Order Linear Equations 17.2 Nonhomogeneous Linear Equations 17.3 Applications 17.4 Euler Equations 17.5 Power-Series Solutions Appendices Real Numbers and the Real Line Mathematical Induction Lines, Circles, and Parabolas Proofs of Limit Theorems Commonly Occurring Limits Theory of the Real Numbers Complex Numbers The Distributive Law for Vector Cross Products The Mixed Derivative Theorem and the Increment Theorem

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Book SynopsisTable of ContentsTable of Contents Functions 1.1 Functions and Their Graphs 1.2 Combining Functions; Shifting and Scaling Graphs 1.3 Trigonometric Functions 1.4 Graphing with Software 1.5 Exponential Functions 1.6 Inverse Functions and Logarithms Limits and Continuity 2.1 Rates of Change and Tangent Lines to Curves 2.2 Limit of a Function and Limit Laws 2.3 The Precise Definition of a Limit 2.4 One-Sided Limits 2.5 Continuity 2.6 Limits Involving Infinity; Asymptotes of Graphs Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Derivatives 3.1 Tangent Lines and the Derivative at a Point 3.2 The Derivative as a Function 3.3 Differentiation Rules 3.4 The Derivative as a Rate of Change 3.5 Derivatives of Trigonometric Functions 3.6 The Chain Rule 3.7 Implicit Differentiation 3.8 Derivatives of Inverse Functions and Logarithms 3.9 Inverse Trigonometric Functions 3.10 Related Rates 3.11 Linearization and Differentials Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Applications of Derivatives 4.1 Extreme Values of Functions on Closed Intervals 4.2 The Mean Value Theorem 4.3 Monotonic Functions and the First Derivative Test 4.4 Concavity and Curve Sketching 4.5 Indeterminate Forms and L’Hôpital’s Rule 4.6 Applied Optimization 4.7 Newton’s Method 4.8 Antiderivatives Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Integrals 5.1 Area and Estimating with Finite Sums 5.2 Sigma Notation and Limits of Finite Sums 5.3 The Definite Integral 5.4 The Fundamental Theorem of Calculus 5.5 Indefinite Integrals and the Substitution Method 5.6 Definite Integral Substitutions and the Area Between Curves Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Applications of Definite Integrals 6.1 Volumes Using Cross-Sections 6.2 Volumes Using Cylindrical Shells 6.3 Arc Length 6.4 Areas of Surfaces of Revolution 6.5 Work 6.6 Moments and Centers of Mass Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Integrals and Transcendental Functions 7.1 The Logarithm Defined as an Integral 7.2 Exponential Change and Separable Differential Equations 7.3 Hyperbolic Functions Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Techniques of Integration 8.1 Integration by Parts 8.2 Trigonometric Integrals 8.3 Trigonometric Substitutions 8.4 Integration of Rational Functions by Partial Fractions 8.5 Integral Tables and Computer Algebra Systems 8.6 Numerical Integration 8.7 Improper Integrals Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Infinite Sequences and Series 9.1 Sequences 9.2 Infinite Series 9.3 The Integral Test 9.4 Comparison Tests 9.5 Absolute Convergence; The Ratio and Root Tests 9.6 Alternating Series and Conditional Convergence 9.7 Power Series 9.8 Taylor and Maclaurin Series 9.9 Convergence of Taylor Series 9.10 Applications of Taylor Series Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Parametric Equations and Polar Coordinates 10.1 Parametrizations of Plane Curves 10.2 Calculus with Parametric Curves 10.3 Polar Coordinates 10.4 Graphing Polar Coordinate Equations 10.5 Areas and Lengths in Polar Coordinates Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Vectors and the Geometry of Space 11.1 Three-Dimensional Coordinate Systems 11.2 Vectors 11.3 The Dot Product 11.4 The Cross Product 11.5 Lines and Planes in Space 11.6 Cylinders and Quadric Surfaces Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Vector-Valued Functions and Motion in Space 12.1 Curves in Space and Their Tangents 12.2 Integrals of Vector Functions; Projectile Motion 12.3 Arc Length in Space 12.4 Curvature and Normal Vectors of a Curve 12.5 Tangential and Normal Components of Acceleration 12.6 Velocity and Acceleration in Polar Coordinates Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Partial Derivatives 13.1 Functions of Several Variables 13.2 Limits and Continuity in Higher Dimensions 13.3 Partial Derivatives 13.4 The Chain Rule 13.5 Directional Derivatives and Gradient Vectors 13.6 Tangent Planes and Differentials 13.7 Extreme Values and Saddle Points 13.8 Lagrange Multiplier Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Multiple Integrals 14.1 Double and Iterated Integrals over Rectangles 14.2 Double Integrals over General Regions 14.3 Area by Double Integration 14.4 Double Integrals in Polar Form 14.5 Triple Integrals in Rectangular Coordinates 14.6 Applications 14.7 Triple Integrals in Cylindrical and Spherical Coordinates 14.8 Substitutions in Multiple Integrals Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Integrals and Vector Fields 15.1 Line Integrals of Scalar Functions 15.2 Vector Fields and Line Integrals: Work, Circulation, and Flux 15.3 Path Independence, Conservative Fields, and Potential Functions 15.4 Green’s Theorem in the Plane 15.5 Surfaces and Area 15.6 Surface Integrals 15.7 Stokes’ Theorem 15.8 The Divergence Theorem and a Unified Theory Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises First-Order Differential Equations (online at bit.ly/2pzYlEq) 16.1 Solutions, Slope Fields, and Euler’s Method 16.2 First-Order Linear Equations 16.3 Applications 16.4 Graphical Solutions of Autonomous Equations 16.5 Systems of Equations and Phase Planes Second-Order Differential Equations (online at bit.ly/2IHCJyE) 17.1 Second-Order Linear Equations 17.2 Non-homogeneous Linear Equations 17.3 Applications 17.4 Euler Equations 17.5 Power-Series Solutions Appendix A.1 Real Numbers and the Real Line A.2 Mathematical Induction A.3 Lines and Circles A.4 Conic Sections A.5 Proofs of Limit Theorems A.6 Commonly Occurring Limits A.7 Theory of the Real Numbers A.8 Complex Numbers A.9 The Distributive Law for Vector Cross Products A.10 The Mixed Derivative Theorem and the increment Theorem Additional Topics (online at bit.ly/2IDDl8w) B.1 Relative Rates of Growth B.2 Probability B.3 Conics in Polar Coordinates B.4 Taylor’s Formula for Two Variables B.5 Partial Derivatives with Constrained Variables Odd Answers

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Book Synopsis

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Book Synopsis

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Book SynopsisAbout our authors Joel Hass received his PhD from the University of California - Berkeley. He is currently a professor of mathematics at the University of California - Davis. He has coauthored 6 widely used calculus texts as well as 2 calculus study guides. He is currently on the editorial board of?Geometriae Dedicata and Media-Enhanced Mathematics. He has been a member of the Institute for Advanced Study at Princeton University and of the Mathematical Sciences Research Institute, and he was a Sloan Research Fellow. Hass's current areas of research include the geometry of proteins, 3-dimensional manifolds, applied math and computational complexity. In his free time, Hass enjoys kayaking. Christopher Heil received his PhD from the University of Maryland. He is currently a professor of mathematics at the Georgia Institute of Technology. He is the author of a graduate text on analysis and a number of highly cited research survey articleTable of ContentsTable of Contents Functions 1.1 Functions and Their Graphs 1.2 Combining Functions; Shifting and Scaling Graphs 1.3 Trigonometric Functions 1.4 Graphing with Software 1.5 Exponential Functions 1.6 Inverse Functions and Logarithms Limits and Continuity 2.1 Rates of Change and Tangent Lines to Curves 2.2 Limit of a Function and Limit Laws 2.3 The Precise Definition of a Limit 2.4 One-Sided Limits 2.5 Continuity 2.6 Limits Involving Infinity; Asymptotes of Graphs Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Derivatives 3.1 Tangent Lines and the Derivative at a Point 3.2 The Derivative as a Function 3.3 Differentiation Rules 3.4 The Derivative as a Rate of Change 3.5 Derivatives of Trigonometric Functions 3.6 The Chain Rule 3.7 Implicit Differentiation 3.8 Derivatives of Inverse Functions and Logarithms 3.9 Inverse Trigonometric Functions 3.10 Related Rates 3.11 Linearization and Differentials Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Applications of Derivatives 4.1 Extreme Values of Functions on Closed Intervals 4.2 The Mean Value Theorem 4.3 Monotonic Functions and the First Derivative Test 4.4 Concavity and Curve Sketching 4.5 Indeterminate Forms and L’Hôpital’s Rule 4.6 Applied Optimization 4.7 Newton’s Method 4.8 Antiderivatives Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Integrals 5.1 Area and Estimating with Finite Sums 5.2 Sigma Notation and Limits of Finite Sums 5.3 The Definite Integral 5.4 The Fundamental Theorem of Calculus 5.5 Indefinite Integrals and the Substitution Method 5.6 Definite Integral Substitutions and the Area Between Curves Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Applications of Definite Integrals 6.1 Volumes Using Cross-Sections 6.2 Volumes Using Cylindrical Shells 6.3 Arc Length 6.4 Areas of Surfaces of Revolution 6.5 Work 6.6 Moments and Centers of Mass Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Integrals and Transcendental Functions 7.1 The Logarithm Defined as an Integral 7.2 Exponential Change and Separable Differential Equations 7.3 Hyperbolic Functions Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Techniques of Integration 8.1 Integration by Parts 8.2 Trigonometric Integrals 8.3 Trigonometric Substitutions 8.4 Integration of Rational Functions by Partial Fractions 8.5 Integral Tables and Computer Algebra Systems 8.6 Numerical Integration 8.7 Improper Integrals Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Infinite Sequences and Series 9.1 Sequences 9.2 Infinite Series 9.3 The Integral Test 9.4 Comparison Tests 9.5 Absolute Convergence; The Ratio and Root Tests 9.6 Alternating Series and Conditional Convergence 9.7 Power Series 9.8 Taylor and Maclaurin Series 9.9 Convergence of Taylor Series 9.10 Applications of Taylor Series Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Parametric Equations and Polar Coordinates 10.1 Parametrizations of Plane Curves 10.2 Calculus with Parametric Curves 10.3 Polar Coordinates 10.4 Graphing Polar Coordinate Equations 10.5 Areas and Lengths in Polar Coordinates Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Vectors and the Geometry of Space 11.1 Three-Dimensional Coordinate Systems 11.2 Vectors 11.3 The Dot Product 11.4 The Cross Product 11.5 Lines and Planes in Space 11.6 Cylinders and Quadric Surfaces Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Vector-Valued Functions and Motion in Space 12.1 Curves in Space and Their Tangents 12.2 Integrals of Vector Functions; Projectile Motion 12.3 Arc Length in Space 12.4 Curvature and Normal Vectors of a Curve 12.5 Tangential and Normal Components of Acceleration 12.6 Velocity and Acceleration in Polar Coordinates Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Partial Derivatives 13.1 Functions of Several Variables 13.2 Limits and Continuity in Higher Dimensions 13.3 Partial Derivatives 13.4 The Chain Rule 13.5 Directional Derivatives and Gradient Vectors 13.6 Tangent Planes and Differentials 13.7 Extreme Values and Saddle Points 13.8 Lagrange Multiplier Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Multiple Integrals 14.1 Double and Iterated Integrals over Rectangles 14.2 Double Integrals over General Regions 14.3 Area by Double Integration 14.4 Double Integrals in Polar Form 14.5 Triple Integrals in Rectangular Coordinates 14.6 Applications 14.7 Triple Integrals in Cylindrical and Spherical Coordinates 14.8 Substitutions in Multiple Integrals Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Integrals and Vector Fields 15.1 Line Integrals of Scalar Functions 15.2 Vector Fields and Line Integrals: Work, Circulation, and Flux 15.3 Path Independence, Conservative Fields, and Potential Functions 15.4 Green’s Theorem in the Plane 15.5 Surfaces and Area 15.6 Surface Integrals 15.7 Stokes’ Theorem 15.8 The Divergence Theorem and a Unified Theory Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises First-Order Differential Equations (online at bit.ly/2pzYlEq) 16.1 Solutions, Slope Fields, and Euler’s Method 16.2 First-Order Linear Equations 16.3 Applications 16.4 Graphical Solutions of Autonomous Equations 16.5 Systems of Equations and Phase Planes Second-Order Differential Equations (online at bit.ly/2IHCJyE) 17.1 Second-Order Linear Equations 17.2 Non-homogeneous Linear Equations 17.3 Applications 17.4 Euler Equations 17.5 Power-Series Solutions Appendix A.1 Real Numbers and the Real Line A.2 Mathematical Induction A.3 Lines and Circles A.4 Conic Sections A.5 Proofs of Limit Theorems A.6 Commonly Occurring Limits A.7 Theory of the Real Numbers A.8 Complex Numbers A.9 The Distributive Law for Vector Cross Products A.10 The Mixed Derivative Theorem and the increment Theorem Additional Topics (online at bit.ly/2IDDl8w) B.1 Relative Rates of Growth B.2 Probability B.3 Conics in Polar Coordinates B.4 Taylor’s Formula for Two Variables B.5 Partial Derivatives with Constrained Variables Odd Answers

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Book SynopsisMarvin Bittinger has been teaching math at the university level for more than thirty-eight years. Since 1968, he has been employed at Indiana University Purdue University Indianapolis, and is now professor emeritus of mathematics education. Professor Bittinger has authored over 250 publications on topics ranging from basic mathematics to algebra and trigonometry to applied calculus. He received his BA in mathematics from Manchester College and his PhD in mathematics education from Purdue University. Special honors include Distinguished Visiting Professor at the United States Air Force Academy and his election to the Manchester College Board of Trustees from 1992 to 1999. His hobbies include hiking in Utah, baseball, golf, and bowling. Professor Bittinger has also had the privilege of speaking at many mathematics conventions, most recently giving a lecture entitled Baseball and Mathematics. In addition, he also has an interest in philosophy and theology,Table of ContentsTable of Contents Preface Prerequisite Skills Diagnostic Test Functions, Graphs, and Models R.1 Graphs and Equations R.2 Functions and Models R.3 Finding Domain and Range R.4 Slope and Linear Functions R.5 Nonlinear Functions and Models R.6 Exponential and Logarithmic Functions R.7 Mathematical Modeling and Curve Fitting Chapter Summary Chapter Review Exercises Chapter Test Extended Technology Application: Average Price of a Movie Ticket Differentiation 1.1 Limits: A Numerical and Graphical Approach 1.2 Algebraic Limits and Continuity 1.3 Average Rates of Change 1.4 Differentiation Using Limits and Difference Quotients 1.5 Leibniz Notation and the Power and Sum—Difference Rules 1.6 The Product and Quotient Rules 1.7 The Chain Rule 1.8 Higher-Order Derivatives Chapter Summary Chapter Review Exercises Chapter Test Extended Technology Application: Path of a Baseball: The Tale of the Tape Exponential and Logarithmic Functions 2.1 Exponential and Logarithmic Functions of the Natural Base, e 2.2 Derivatives of Exponential (Base-e) Functions 2.3 Derivatives of Natural Logarithmic Functions 2.4 Applications: Uninhibited and Limited Growth Models 2.5 Applications: Exponential Decay231 2.6 The Derivatives of ax and loga x Chapter Summary Chapter Review Exercises Chapter Test Extended Technology Application: The Business of Motion Picture Revenue and DVD Release Applications of Differentiation 3.1 Using First Derivatives to Classify Maximum and Minimum Values and Sketch Graphs 3.2 Using Second Derivatives to Classify Maximum and Minimum Values and Sketch Graphs 3.3 Graph Sketching: Asymptotes and Rational Functions 3.4 Optimization: Finding Absolute Maximum and Minimum Values 3.5 Optimization: Business, Economics, and General Applications 3.6 Marginals, Differentials, and Linearization 3.7 Elasticity of Demand 3.8 Implicit Differentiation and Logarithmic Differentiation 3.9 Related Rates Chapter Summary Chapter Review Exercises Chapter Test Extended Technology Application: Maximum Sustainable Harvest Integration 4.1 Antidifferentiation 4.2 Antiderivatives as Areas 4.3 Area and Definite Integrals 4.4 Properties of Definite Integrals: Additive Property, Average Value, and Moving Average 4.5 Integration Techniques: Substitution 4.6 Integration Techniques: Integration by Parts 4.7 Numerical Integration Chapter Summary Chapter Review Exercises Chapter Test Extended Technology Application: Business and Economics: Distribution of Wealth Applications of Integration 5.1 Consumer and Producer Surplus; Price Floors, Price Ceilings, and Deadweight Loss 5.2 Integrating Growth and Decay Models 5.3 Improper Integrals 5.4 Probability 5.5 Probability: Expected Value; the Normal Distribution 5.6 Volume 5.7 Differential Equations Chapter Summary Chapter Review Exercises Chapter Test Extended Technology Application: Curve Fitting and Volumes of Containers Functions of Several Variables 6.1 Functions of Several Variables 6.2 Partial Derivatives 6.3 Maximum—Minimum Problems 6.4 An Application: The Least-Squares Technique 6.5 Constrained Optimization: Lagrange Multipliers and the Extreme-Value Theorem 6.6 Double Integrals Chapter Summary Chapter Review Exercises Chapter Test Extended Technology Application: Minimizing Employees’ Travel Time in a Building Trigonometric Functions 7.1 Basics of Trigonometry 7.2 Derivatives of Trigonometric Functions 7.3 Integration of Trigonometric Functions 7.4 Inverse Trigonometric Functions and Applications Chapter Summary Chapter Review Exercises Chapter Test Extended Technology Application Differential Equations 8.1 Direction Fields, Autonomic Forms, and Population Models 8.2 Applications: Inhibited Growth Models 8.3 First-Order Linear Differential Equations 8.4 Higher-Order Differential Equations and a Trigonometry Connection Chapter Summary Chapter Review Exercises Chapter Test Extended Technology Application Sequences and Series 9.1 Arithmetic Sequences and Series 9.2 Geometric Sequences and Series 9.3 Simple and Compound Interest 9.4 Annuities and Amortization 9.5 Power Series and Linearization 9.6 Taylor Series and a Trigonometry Connection Chapter Summary Chapter Review Exercises Chapter Test Extended Technology Application Probability Distributions 10.1 A Review of Sets 10.2 Theoretical Probability 10.3 Discrete Probability Distributions 10.4 Continuous Probability Distributions: Mean, Variance, and Standard Deviation Chapter Summary Chapter Review Exercises Chapter Test Extended Technology Application Systems and Matrices (online only) 11.1 Systems of Linear Equations 11.2 Gaussian Elimination 11.3 Matrices and Row Operations 11.4 Matrix Arithmetic: Equality, Addition, and Scalar Multiples 11.5 Matrix Multiplication, Multiplicative Identities, and Inverses 11.6 Determinants and Cramer’s Rule 11.7 Systems of Linear Inequalities and Linear Programming Chapter Summary Chapter Review Exercises Chapter Test Extended Technology Application Combinatorics and Probability (online only) 12.1 Compound Events and Odds 12.2 Combinatorics: The Multiplication Principle and Factorial Notation 12.3 Permutations and Distinguishable Arrangements 12.4 Combinations and the Binomial Theorem 12.5 Conditional Probability and the Hypergeometric Probability Distribution Model 12.6 Independent Events, Bernoulli Trials, and the Binomial Probability Model 12.7 Bayes Theorem Chapter Summary Chapter Review Exercises Chapter Test Extended Technology Application Cumulative Review Appendix A: Review of Basic Algebra Appendix B: Indeterminate Forms and l’Hôpital’s Rule Appendix C: Regression and Microsoft Excel Appendix D: Areas for a Standard Normal Distribution Appendix E: Using Tables of Integration Formulas Answers Index of Applications Index

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Book SynopsisThis manual provides detailed solutions to odd-numbered exercises in the text.   0135166136 / 9780135166130 STUDENT SOLUTIONS MANUAL SINGLE VARIABLE FOR UNIVERSITY CALCULUS: EARLY TRANSCENDENTALS, 4/e Table of ContentsTable of Contents Functions 1.1 Functions and Their Graphs 1.2 Combining Functions; Shifting and Scaling Graphs 1.3 Trigonometric Functions 1.4 Graphing with Software 1.5 Exponential Functions 1.6 Inverse Functions and Logarithms Limits and Continuity 2.1 Rates of Change and Tangent Lines to Curves 2.2 Limit of a Function and Limit Laws 2.3 The Precise Definition of a Limit 2.4 One-Sided Limits 2.5 Continuity 2.6 Limits Involving Infinity; Asymptotes of Graphs Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Derivatives 3.1 Tangent Lines and the Derivative at a Point 3.2 The Derivative as a Function 3.3 Differentiation Rules 3.4 The Derivative as a Rate of Change 3.5 Derivatives of Trigonometric Functions 3.6 The Chain Rule 3.7 Implicit Differentiation 3.8 Derivatives of Inverse Functions and Logarithms 3.9 Inverse Trigonometric Functions 3.10 Related Rates 3.11 Linearization and Differentials Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Applications of Derivatives 4.1 Extreme Values of Functions on Closed Intervals 4.2 The Mean Value Theorem 4.3 Monotonic Functions and the First Derivative Test 4.4 Concavity and Curve Sketching 4.5 Indeterminate Forms and L’Hôpital’s Rule 4.6 Applied Optimization 4.7 Newton’s Method 4.8 Antiderivatives Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Integrals 5.1 Area and Estimating with Finite Sums 5.2 Sigma Notation and Limits of Finite Sums 5.3 The Definite Integral 5.4 The Fundamental Theorem of Calculus 5.5 Indefinite Integrals and the Substitution Method 5.6 Definite Integral Substitutions and the Area Between Curves Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Applications of Definite Integrals 6.1 Volumes Using Cross-Sections 6.2 Volumes Using Cylindrical Shells 6.3 Arc Length 6.4 Areas of Surfaces of Revolution 6.5 Work 6.6 Moments and Centers of Mass Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Integrals and Transcendental Functions 7.1 The Logarithm Defined as an Integral 7.2 Exponential Change and Separable Differential Equations 7.3 Hyperbolic Functions Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Techniques of Integration 8.1 Integration by Parts 8.2 Trigonometric Integrals 8.3 Trigonometric Substitutions 8.4 Integration of Rational Functions by Partial Fractions 8.5 Integral Tables and Computer Algebra Systems 8.6 Numerical Integration 8.7 Improper Integrals Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Infinite Sequences and Series 9.1 Sequences 9.2 Infinite Series 9.3 The Integral Test 9.4 Comparison Tests 9.5 Absolute Convergence; The Ratio and Root Tests 9.6 Alternating Series and Conditional Convergence 9.7 Power Series 9.8 Taylor and Maclaurin Series 9.9 Convergence of Taylor Series 9.10 Applications of Taylor Series Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Parametric Equations and Polar Coordinates 10.1 Parametrizations of Plane Curves 10.2 Calculus with Parametric Curves 10.3 Polar Coordinates 10.4 Graphing Polar Coordinate Equations 10.5 Areas and Lengths in Polar Coordinates Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Vectors and the Geometry of Space 11.1 Three-Dimensional Coordinate Systems 11.2 Vectors 11.3 The Dot Product 11.4 The Cross Product 11.5 Lines and Planes in Space 11.6 Cylinders and Quadric Surfaces Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Vector-Valued Functions and Motion in Space 12.1 Curves in Space and Their Tangents 12.2 Integrals of Vector Functions; Projectile Motion 12.3 Arc Length in Space 12.4 Curvature and Normal Vectors of a Curve 12.5 Tangential and Normal Components of Acceleration 12.6 Velocity and Acceleration in Polar Coordinates Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Partial Derivatives 13.1 Functions of Several Variables 13.2 Limits and Continuity in Higher Dimensions 13.3 Partial Derivatives 13.4 The Chain Rule 13.5 Directional Derivatives and Gradient Vectors 13.6 Tangent Planes and Differentials 13.7 Extreme Values and Saddle Points 13.8 Lagrange Multiplier Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Multiple Integrals 14.1 Double and Iterated Integrals over Rectangles 14.2 Double Integrals over General Regions 14.3 Area by Double Integration 14.4 Double Integrals in Polar Form 14.5 Triple Integrals in Rectangular Coordinates 14.6 Applications 14.7 Triple Integrals in Cylindrical and Spherical Coordinates 14.8 Substitutions in Multiple Integrals Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Integrals and Vector Fields 15.1 Line Integrals of Scalar Functions 15.2 Vector Fields and Line Integrals: Work, Circulation, and Flux 15.3 Path Independence, Conservative Fields, and Potential Functions 15.4 Green’s Theorem in the Plane 15.5 Surfaces and Area 15.6 Surface Integrals 15.7 Stokes’ Theorem 15.8 The Divergence Theorem and a Unified Theory Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises First-Order Differential Equations (online at bit.ly/2pzYlEq) 16.1 Solutions, Slope Fields, and Euler’s Method 16.2 First-Order Linear Equations 16.3 Applications 16.4 Graphical Solutions of Autonomous Equations 16.5 Systems of Equations and Phase Planes Second-Order Differential Equations (online at bit.ly/2IHCJyE) 17.1 Second-Order Linear Equations 17.2 Non-homogeneous Linear Equations 17.3 Applications 17.4 Euler Equations 17.5 Power-Series Solutions Appendix A.1 Real Numbers and the Real Line A.2 Mathematical Induction A.3 Lines and Circles A.4 Conic Sections A.5 Proofs of Limit Theorems A.6 Commonly Occurring Limits A.7 Theory of the Real Numbers A.8 Complex Numbers A.9 The Distributive Law for Vector Cross Products A.10 The Mixed Derivative Theorem and the increment Theorem Additional Topics (online at bit.ly/2IDDl8w) B.1 Relative Rates of Growth B.2 Probability B.3 Conics in Polar Coordinates B.4 Taylor’s Formula for Two Variables B.5 Partial Derivatives with Constrained Variables Odd Answers

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Book SynopsisThis manual provides detailed solutions to odd-numbered exercises in the text. 0135166632 / 0135166632 STUDENT SOLUTIONS MANUAL MULTIVARIABLE FOR UNIVERSITY CALCULUS, EARLY TRANSCENDENTALS, 4/e  Table of ContentsTable of Contents Functions 1.1 Functions and Their Graphs 1.2 Combining Functions; Shifting and Scaling Graphs 1.3 Trigonometric Functions 1.4 Graphing with Software 1.5 Exponential Functions 1.6 Inverse Functions and Logarithms Limits and Continuity 2.1 Rates of Change and Tangent Lines to Curves 2.2 Limit of a Function and Limit Laws 2.3 The Precise Definition of a Limit 2.4 One-Sided Limits 2.5 Continuity 2.6 Limits Involving Infinity; Asymptotes of Graphs Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Derivatives 3.1 Tangent Lines and the Derivative at a Point 3.2 The Derivative as a Function 3.3 Differentiation Rules 3.4 The Derivative as a Rate of Change 3.5 Derivatives of Trigonometric Functions 3.6 The Chain Rule 3.7 Implicit Differentiation 3.8 Derivatives of Inverse Functions and Logarithms 3.9 Inverse Trigonometric Functions 3.10 Related Rates 3.11 Linearization and Differentials Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Applications of Derivatives 4.1 Extreme Values of Functions on Closed Intervals 4.2 The Mean Value Theorem 4.3 Monotonic Functions and the First Derivative Test 4.4 Concavity and Curve Sketching 4.5 Indeterminate Forms and L’Hôpital’s Rule 4.6 Applied Optimization 4.7 Newton’s Method 4.8 Antiderivatives Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Integrals 5.1 Area and Estimating with Finite Sums 5.2 Sigma Notation and Limits of Finite Sums 5.3 The Definite Integral 5.4 The Fundamental Theorem of Calculus 5.5 Indefinite Integrals and the Substitution Method 5.6 Definite Integral Substitutions and the Area Between Curves Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Applications of Definite Integrals 6.1 Volumes Using Cross-Sections 6.2 Volumes Using Cylindrical Shells 6.3 Arc Length 6.4 Areas of Surfaces of Revolution 6.5 Work 6.6 Moments and Centers of Mass Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Integrals and Transcendental Functions 7.1 The Logarithm Defined as an Integral 7.2 Exponential Change and Separable Differential Equations 7.3 Hyperbolic Functions Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Techniques of Integration 8.1 Integration by Parts 8.2 Trigonometric Integrals 8.3 Trigonometric Substitutions 8.4 Integration of Rational Functions by Partial Fractions 8.5 Integral Tables and Computer Algebra Systems 8.6 Numerical Integration 8.7 Improper Integrals Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Infinite Sequences and Series 9.1 Sequences 9.2 Infinite Series 9.3 The Integral Test 9.4 Comparison Tests 9.5 Absolute Convergence; The Ratio and Root Tests 9.6 Alternating Series and Conditional Convergence 9.7 Power Series 9.8 Taylor and Maclaurin Series 9.9 Convergence of Taylor Series 9.10 Applications of Taylor Series Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Parametric Equations and Polar Coordinates 10.1 Parametrizations of Plane Curves 10.2 Calculus with Parametric Curves 10.3 Polar Coordinates 10.4 Graphing Polar Coordinate Equations 10.5 Areas and Lengths in Polar Coordinates Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Vectors and the Geometry of Space 11.1 Three-Dimensional Coordinate Systems 11.2 Vectors 11.3 The Dot Product 11.4 The Cross Product 11.5 Lines and Planes in Space 11.6 Cylinders and Quadric Surfaces Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Vector-Valued Functions and Motion in Space 12.1 Curves in Space and Their Tangents 12.2 Integrals of Vector Functions; Projectile Motion 12.3 Arc Length in Space 12.4 Curvature and Normal Vectors of a Curve 12.5 Tangential and Normal Components of Acceleration 12.6 Velocity and Acceleration in Polar Coordinates Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Partial Derivatives 13.1 Functions of Several Variables 13.2 Limits and Continuity in Higher Dimensions 13.3 Partial Derivatives 13.4 The Chain Rule 13.5 Directional Derivatives and Gradient Vectors 13.6 Tangent Planes and Differentials 13.7 Extreme Values and Saddle Points 13.8 Lagrange Multiplier Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Multiple Integrals 14.1 Double and Iterated Integrals over Rectangles 14.2 Double Integrals over General Regions 14.3 Area by Double Integration 14.4 Double Integrals in Polar Form 14.5 Triple Integrals in Rectangular Coordinates 14.6 Applications 14.7 Triple Integrals in Cylindrical and Spherical Coordinates 14.8 Substitutions in Multiple Integrals Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Integrals and Vector Fields 15.1 Line Integrals of Scalar Functions 15.2 Vector Fields and Line Integrals: Work, Circulation, and Flux 15.3 Path Independence, Conservative Fields, and Potential Functions 15.4 Green’s Theorem in the Plane 15.5 Surfaces and Area 15.6 Surface Integrals 15.7 Stokes’ Theorem 15.8 The Divergence Theorem and a Unified Theory Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises First-Order Differential Equations (online at bit.ly/2pzYlEq) 16.1 Solutions, Slope Fields, and Euler’s Method 16.2 First-Order Linear Equations 16.3 Applications 16.4 Graphical Solutions of Autonomous Equations 16.5 Systems of Equations and Phase Planes Second-Order Differential Equations (online at bit.ly/2IHCJyE) 17.1 Second-Order Linear Equations 17.2 Non-homogeneous Linear Equations 17.3 Applications 17.4 Euler Equations 17.5 Power-Series Solutions Appendix A.1 Real Numbers and the Real Line A.2 Mathematical Induction A.3 Lines and Circles A.4 Conic Sections A.5 Proofs of Limit Theorems A.6 Commonly Occurring Limits A.7 Theory of the Real Numbers A.8 Complex Numbers A.9 The Distributive Law for Vector Cross Products A.10 The Mixed Derivative Theorem and the increment Theorem Additional Topics (online at bit.ly/2IDDl8w) B.1 Relative Rates of Growth B.2 Probability B.3 Conics in Polar Coordinates B.4 Taylor’s Formula for Two Variables B.5 Partial Derivatives with Constrained Variables Odd Answers

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