Calculus: AP Edition, 2nd edition


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Calculus AP Edition, 2e ©2018 NASTA SE + 3yr MMLS w/etext  FL ONLY
ISBN13: 9780136174189
Hardcover

Overview
For courses in Calculus.
Covers the most recent AP exam guidelines, including the new Mathematical Practices for AP Calculus
In Calculus: AP Edition, 2nd Edition, wellknown authors Briggs and Cochran apply their proven approach to the most recent changes in the AP Exam guidelines, including the new Mathematical Practices for AP Calculus (MPACs). The writing maintains just the right balance of mathematical formality and conversational tone, keeping students’ attention and making collegelevel calculus something that they truly can grasp. Examples are steppedout in detail and thoughtfully annotated to encourage independent learning. Figures are a step above other texts in both quality and scope, building a foundation of geometric intuition that leads to true understanding of the key concepts. Exercises feature remarkable breadth and variety, providing ample opportunities for students to practice the MPACs.
Table of contents
Preface
Guide to AP Calculus
Guide to Mathematical Practices for AP Calculus (MPACs)
AP Calculus Pacing Guide
1. Functions
1.1 Review of Functions
1.2 Representing Functions
1.3 Inverse, Exponential, and Logarithmic Functions
1.4 Trigonometric Functions and Their Inverses
Review Exercises
AP Practice Questions
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
AP Practice Questions
3. Derivatives
3.1 Introducing the Derivative
3.2 Working with Derivatives
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 Derivatives of Logarithmic and Exponential Functions
3.10 Derivatives of Inverse Trigonometric Functions
3.11 Related Rates
Review Exercises
AP Practice Questions
4. Applications of the Derivative
4.1 Maxima and Minima
4.2 What Derivatives Tell Us
4.3 Graphing Functions
4.4 Optimization Problems
4.5 Linear Approximation and Differentials
4.6 Mean Value Theorem
4.7 L’Hôpital’s Rule
4.8 Newton’s Method
Review Exercises
AP Practice Questions
5. Integration
5.1 Antiderivatives
5.2 Approximating Areas under Curves
5.3 Definite Integrals
5.4 Fundamental Theorem of Calculus
5.5 Properties of Integrals and Average Value
5.6 Substitution Rule
5.7 Numerical Integration
Review Exercises
AP Practice Questions
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 Physical Applications
Review Exercises
AP Practice Questions
7. Integration Techniques
7.1 Basic Approaches
7.2 Integration by Parts
7.3 Partial Fractions
7.4 Improper Integrals
7.5 Trigonometric Substitutions
Review Exercises
AP Practice Questions
8. Differential Equations
8.1 Basic Ideas
8.2 Slope Fields and Euler’s Method
8.3 Separable Differential Equations
8.4 Exponential Models
Review Exercises
AP Practice Questions
9. Sequences and Infinite Series
9.1 An Overview
9.2 Sequences
9.3 Infinite Series
9.4 The Divergence and Integral Tests
9.5 The Ratio, Root, and Comparison Tests
9.6 Alternating Series
Review Exercises
AP Practice Questions
10. Power Series
10.1 Approximating Functions with Polynomials
10.2 Properties of Power Series
10.3 Taylor Series
10.4 Working with Taylor Series
Review Exercises
AP Practice Questions
11. Parametric, Polar, and Vector Curves
11.1 Parametric Equations
11.2 Calculus with Parametric Equations
11.3 Polar Coordinates
11.4 Calculus in Polar Coordinates
11.5 Vectors in the Plane
11.6 Calculus of VectorValued Functions
11.7 TwoDimensional Motion
Review Exercises
AP Practice Questions
Appendix A. Algebra Review
Appendix B. Conic Sections
Appendix C. Proofs of Selected Theorems
Answers
Credits
Index
Table of Integrals
Published by AddisonWesley (April 11th 2017)  Copyright © 2018