The Calculus Lifesaver

All the Tools You Need to Excel at Calculus

Adrian Banner

• Publisher: Princeton University Press
• Year: 2009
• Print ISBN: 9780691130880, 9780691131535
• eBook ISBN: 9781400835782
• Topic: Mathematics
• Subtopic: Calculus
• Index: Mathematics

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.



The Calculus Lifesaver combines ease of use and readability with the depth of content and mathematical rigor of the best calculus textbooks. It is an indispensable volume for any student seeking to master calculus.

• Serves as a companion to any single-variable calculus textbook


• Informal, entertaining, and not intimidating


• Informative videos that follow the book--a full forty-eight hours of Banner's Princeton calculus-review course--is available at Adrian Banner lectures
  


• More than 475 examples (ranging from easy to hard) provide step-by-step reasoning


• Theorems and methods justified and connections made to actual practice


• Difficult topics such as improper integrals and infinite series covered in detail


• Tried and tested by students taking freshman calculus

Table of contents

• Cover
• Contents
• 1 Functions, Graphs, and Lines
• 2 Review of Trigonometry
• 3 Introduction to Limits
• 4 How to Solve Limit Problems Involving Polynomials
• 5 Continuity and Dierentiability
• 6 How to Solve Dierentiation Problems
• 7 Trig Limits and Derivatives
• 8 Implicit Dierentiation and Related Rates
• 9 Exponentials and Logarithms
• 10 Inverse Functions and Inverse Trig Functions
• 11 The Derivative and Graphs
• 12 Sketching Graphs
• 13 Optimization and Linearization
• 14 L'H^opital's Rule and Overview of Limits
• 15 Introduction to Integration
• 16 Denite Integrals
• 17 The Fundamental Theorems of Calculus
• 18 Techniques of Integration, Part One
• 19 Techniques of Integration, Part Two
• 20 Improper Integrals: Basic Concepts
• 21 Improper Integrals: How to Solve Problems
• 22 Sequences and Series: Basic Concepts
• 23 How to Solve Series Problems
• 24 Taylor Polynomials, Taylor Series, and Power Series
• 25 How to Solve Estimation Problems
• 26 Taylor and Power Series: How to Solve Problems
• 27 Parametric Equations and Polar Coordinates
• 28 Complex Numbers
• 29 Volumes, Arc Lengths, and Surface Areas
• 30 Dierential Equations
• Appendix A Limits and Proofs
• Appendix B Estimating Integrals