Description

Book Synopsis


Table of Contents
Table of Contents
  1. 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
  2. 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
  3. 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
  4. 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
  5. 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
  6. 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
  7. 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
  8. 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
  9. 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
  10. 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
  11. 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
  12. 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
  13. 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
  14. 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
  15. 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
  16. 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
  17. 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

University Calculus

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    A Paperback / softback by Joel Hass, Christopher Heil, Maurice Weir

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      Book details

      Publisher Pearson Education (US)
      Published 1 January 2019
      ISBN-13 9780134995540
      978-0134995540
      ISBN-10 0134995546
      Also in:
      Calculus

      Description

      Book Synopsis


      Table of Contents
      Table of Contents
      1. 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
      2. 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
      3. 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
      4. 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
      5. 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
      6. 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
      7. 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
      8. 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
      9. 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
      10. 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
      11. 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
      12. 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
      13. 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
      14. 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
      15. 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
      16. 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
      17. 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
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