Calculus, 3rd edition

William L. Briggs
, Lyle Cochran
, Bernard Gillett
, Eric Schulz

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Calculus builds from a foundation of strong exercise sets, then draws you into the narrative through writing that reflects an instructor's voice. Examples are stepped out and thoroughly annotated, and figures are designed carefully to work with the content. The 3rd Edition introduces important advances and refinements while retaining its proven hallmark features. Extensively revised exercise sets are rearranged and relabeled, with some modified and other new ones added. Chapter Review exercises are thoroughly revised to provide more exercises (more than 26% are new), more intermediate-level problems, and more opportunities to choose a strategy of solution.

ISBN-13: 9780136880639

Subject: Calculus

Category: Calculus

1. Functions

1.1 Review of Functions
1.2 Representing Functions
1.3 Trigonometric Functions
Review Exercises

2. Limits

2.1 The Idea of Limits
2.2 Definitions of Limits
2.3 Techniques for Computing Limits
2.4 Infinite Limits
2.5 Limits at Infinity
2.6 Continuity
2.7 Precise Definitions of Limits
Review Exercises

3. Derivatives

3.1 Introducing the Derivative
3.2 The Derivative as a Function
3.3 Rules of Differentiation
3.4 The Product and Quotient Rules
3.5 Derivatives of Trigonometric Functions
3.6 Derivatives as Rates of Change
3.7 The Chain Rule
3.8 Implicit Differentiation
3.9 Related Rates
Review Exercises

4. Applications of the Derivative

4.1 Maxima and Minima
4.2 Mean Value Theorem
4.3 What Derivatives Tell Us
4.4 Graphing Functions
4.5 Optimization Problems
4.6 Linear Approximation and Differentials
4.7 L'Hôpital's Rule
4.8 Newton's Method
4.9 Antiderivatives
Review Exercises

5. Integration

5.1 Approximating Areas under Curves
5.2 Definite Integrals
5.3 Fundamental Theorem of Calculus
5.4 Working with Integrals
5.5 Substitution Rule
Review Exercises

6. Applications of Integration

6.1 Velocity and Net Change
6.2 Regions Between Curves
6.3 Volume by Slicing
6.4 Volume by Shells
6.5 Length of Curves
6.6 Surface Area
6.7 Physical Applications
Review Exercises

7. Logarithmic and Exponential Functions

7.1 Inverse Functions
7.2 The Natural Logarithmic and Exponential Functions
7.3 Logarithmic and Exponential Functions with Other Bases
7.4 Exponential Models
7.5 Inverse Trigonometric Functions
7.6 L' Hôpital's Rule and Growth Rates of Functions
7.7 Hyperbolic Functions
Review Exercises

8. Integration Techniques

8.1 Basic Approaches
8.2 Integration by Parts
8.3 Trigonometric Integrals
8.4 Trigonometric Substitutions
8.5 Partial Fractions
8.6 Integration Strategies
8.7 Other Methods of Integration
8.8 Numerical Integration
8.9 Improper Integrals
Review Exercises

9. Differential Equations

9.1 Basic Ideas
9.2 Direction Fields and Euler's Method
9.3 Separable Differential Equations
9.4 Special First-Order Linear Differential Equations
9.5 Modeling with Differential Equations
Review Exercises

10. Sequences and Infinite Series

10.1 An Overview
10.2 Sequences
10.3 Infinite Series
10.4 The Divergence and Integral Tests
10.5 Comparison Tests
10.6 Alternating Series
10.7 The Ratio and Root Tests
10.8 Choosing a Convergence Test
Review Exercises

11. Power Series

11.1 Approximating Functions with Polynomials
11.2 Properties of Power Series
11.3 Taylor Series
11.4 Working with Taylor Series
Review Exercises

12. Parametric and Polar Curves

12.1 Parametric Equations
12.2 Polar Coordinates
12.3 Calculus in Polar Coordinates
12.4 Conic Sections
Review Exercises

13. Vectors and the Geometry of Space

13.1 Vectors in the Plane
13.2 Vectors in Three Dimensions
13.3 Dot Products
13.4 Cross Products
13.5 Lines and Planes in Space
13.6 Cylinders and Quadric Surfaces
Review Exercises

14. Vector-Valued Functions

14.1 Vector-Valued Functions
14.2 Calculus of Vector-Valued Functions
14.3 Motion in Space
14.4 Length of Curves
14.5 Curvature and Normal Vectors
Review Exercises

15. Functions of Several Variables

15.1 Graphs and Level Curves
15.2 Limits and Continuity
15.3 Partial Derivatives
15.4 The Chain Rule
15.5 Directional Derivatives and the Gradient
15.6 Tangent Planes and Linear Approximation
15.7 Maximum/Minimum Problems
15.8 Lagrange Multipliers
Review Exercises

16. Multiple Integration

16.1 Double Integrals over Rectangular Regions
16.2 Double Integrals over General Regions
16.3 Double Integrals in Polar Coordinates
16.4 Triple Integrals
16.5 Triple Integrals in Cylindrical and Spherical Coordinates
16.6 Integrals for Mass Calculations
16.7 Change of Variables in Multiple Integrals
Review Exercises

17. Vector Calculus

17.1 Vector Fields
17.2 Line Integrals
17.3 Conservative Vector Fields
17.4 Green's Theorem
17.5 Divergence and Curl
17.6 Surface Integrals
17.7 Stokes' Theorem
17.8 Divergence Theorem
Review Exercises

D2 Second-Order Differential Equations ONLINE

D2.1 Basic Ideas
D2.2 Linear Homogeneous Equations
D2.3 Linear Nonhomogeneous Equations
D2.4 Applications
D2.5 Complex Forcing Functions
Review Exercises