Supplements: Test Bank｜Power point｜Solutions Manual
Author
Adrian Banner, Princeton University
Description
For many students, calculus can be the most mystifying and frustrating course they will ever take. The Calculus Lifesaver provides students with the essential tools they need not only to learn calculus, but to excel at it.
All of the material in this user-friendly study guide has been proven to get results. The book arose from Adrian Banner's popular calculus review course at Princeton University, which he developed especially for students who are motivated to earn A's but get only average grades on exams. The complete course will be available for free on the Web in a series of videotaped lectures. This study guide works as a supplement to any single-variable calculus course or textbook. Coupled with a selection of exercises, the book can also be used as a textbook in its own right. The style is informal, non-intimidating, and even entertaining, without sacrificing comprehensiveness. The author elaborates standard course material with scores of detailed examples that treat the reader to an "inner monologue"--the train of thought students should be following in order to solve the problem--providing the necessary reasoning as well as the solution. The book's emphasis is on building problem-solving skills. Examples range from easy to difficult and illustrate the in-depth presentation of theory.
Table of Contents
Ch 1: Functions, Graphs, and Lines
Ch 2: Review of Trigonometry
Ch 3: Introduction to Limits
Ch 4: How to Solve Limit Problems Involving Polynomials
Ch 5: Continuity and Differentiability
Ch 6: How to Solve Differentiation Problems
Ch 7: Trig Limits and Derivatives
Ch 8: Implicit Differentiation and Related Rates
Ch 9: Exponentials and Logarithms
Ch 10: Inverse Functions and Inverse Trig Functions
Ch11: The Derivative and Graphs
Ch 12: Sketching Graphs
Ch13: Optimization and Linearization
Ch 14: L'Hôpital's Rule and Overview of Limits
Ch 15: Introduction to Integration
Ch 16: Definite Integrals
Ch 17: The Fundamental Theorems of Calculus
Ch 18: Techniques of Integration, Part One
Ch 19: Techniques of Integration, Part Two
Ch 20: Improper Integrals: Basic Concepts
Ch 21: Improper Integrals: How to Solve Problems
Ch 22: Sequences and Series: Basic Concepts
Ch 23: How to Solve Series Problems
Ch 24: Taylor Polynomials, Taylor Series, and Power Series
Ch 25: How to Solve Estimation Problems
Ch 26: Taylor and Power Series: How to Solve Problems
Ch 27: Parametric Equations and Polar Coordinates
Ch 28: Complex Numbers
Ch 29: Volumes, Arc Lengths, and Surface Areas
Ch 30: Differential Equations
Appendix A Limits and Proofs
Appendix B Estimating Integrals
List of Symbols
Index
