Calculus Concepts and Contexts Enhanced 4th Edition by James Stewart ISBN 1337687669 9781337687669

Chapter 1: Functions and Models

1.1: Four Ways to Represent a Function

1.2: Mathematical Models: A Catalog of Essential Functions

1.3: New Functions from Old Functions

1.4: Graphing Calculators and Computers

1.5: Exponential Functions

1.6: Inverse Functions and Logarithms

1.7: Parametric Curves

Chapter 2: Limits and Derivatives

2.1: The Tangent and Velocity Problems

2.2: The Limit of a Function

2.3: Calculating Limits Using the Limit Laws

2.4: Continuity

2.5: Limits Involving Infinity

2.6: Derivatives and Rates of Change

2.7: The Derivative as a Function

2.8: What Does f’ Say About f ?

Chapter 3: Differentiation Rules

3.1: Derivatives of Polynomials and Exponential Functions

3.2: The Product and Quotient Rules

3.3: Derivatives of Trigonometric Functions

3.4: The Chain Rule

3.5: Implicit Differentiation

3.6: Inverse Trigonometric Functions and Their Derivatives

3.7: Derivatives of Logarithmic Functions

3.8: Rates of Change in the Natural and Social Sciences

3.9: Linear Approximations and Differentials

Chapter 4: Applications of Differentiation

4.1: Related Rates

4.2: Maximum and Minimum Values

4.3: Derivatives and the Shapes of Curves

4.4: Graphing with Calculus and Calculators

4.5: Indeterminate Forms and l’Hospital’s Rule

4.6: Optimization Problems

4.7: Newton’s Method

4.8: Antiderivatives

Chapter 5: Integrals

5.1: Areas and Distances

5.2: The Definite Integral

5.3: Evaluating Definite Integrals

5.4: The Fundamental Theorem of Calculus

5.5: The Substitution Rule

5.6: Integration by Parts

5.7: Techniques of Integration

5.8: Integration Using Tables and Computer Algebra Systems

5.9: Approximate Integration

5.10: Improper Integrals

Chapter 6: Applications of Integration

6.1: More About Areas

6.2: Volumes

6.3: Volumes by Cylindrical Shells

6.4: Arc Length

6.5: Average Value of a Function

6.6: Applications to Physics and Engineering

6.7: Applications to Economics and Biology

6.8: Probability

Chapter 7: Differential Equations

7.1: Modeling with Differential Equations

7.2: Direction Fields and Euler’s Method

7.3: Separable Equations

7.4: Exponential Growth and Decay

7.5: The Logistic Equation

7.6: Predator-Prey Systems

Chapter 8: Infnite Sequences and Series

8.1: Sequences

8.2: Series

8.3: The Integral and Comparison Tests; Estimating Sums

8.4: Other Convergence Tests

8.5: Power Series

8.6: Representations of Functions as Power Series

8.7: Taylor and Maclaurin Series

8.8: Applications of Taylor Polynomials

Chapter 9: Vectors and the Geometry of Space

9.1: Three-Dimensional Coordinate Systems

9.2: Vectors

9.3: The Dot Product

9.4: The Cross Product

9.5: Equations of Lines and Planes

9.6: Functions and Surfaces

9.7: Cylindrical and Spherical Coordinates

Chapter 10: Vector Functions

10.1: Vector Functions and Space Curves

10.2: Derivatives and Integrals of Vector Functions

10.3: Arc Length and Curvature

10.4: Motion in Space: Velocity and Acceleration

10.5: Parametric Surfaces

Chapter 11: Partial Derivatives

11.1: Functions of Several Variables

11.2: Limits and Continuity

11.3: Partial Derivatives

11.4: Tangent Planes and Linear Approximations

11.5: The Chain Rule

11.6: Directional Derivatives and the Gradient Vector

11.7: Maximum and Minimum Values

11.8: Lagrange Multipliers

Chapter 12: Multiple Integrals

12.1: Double Integrals over Rectangles

12.2: Iterated Integrals

12.3: Double Integrals over General Regions

12.4: Double Integrals in Polar Coordinates

12.5: Applications of Double Integrals

12.6: Surface Area

12.7: Triple Integrals

12.8: Triple Integrals in Cylindrical and Spherical Coordinates

12.9: Change of Variables in Multiple Integrals

Chapter 13: Vector Calculus

13.1: Vector Fields

13.2: Line Integrals

13.3: The Fundamental Theorem for Line Integrals

13.4: Green’s Theorem

13.5: Curl and Divergence

13.6: Surface Integrals

13.7: Stokes’ Theorem

13.8: The Divergence Theorem

13.9: Summary