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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    View other formats and editions of University Calculus by Joel Hass

    Publisher: Pearson Education (US)
    Publication Date: 01/01/2019
    ISBN13: 9780134995540, 978-0134995540
    ISBN10: 0134995546
    Also in:
    Mathematics 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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