Calculus Lifesaver All the Tools You Need to Excel at Calculus Princeton Lifesaver Study Guides 1st editon by Adrian Banner 0691131538 9780691131535

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Product details:

ISBN 10: 0691131538
ISBN 13: 9780691131535
Author: Adrian Banner

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:

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

13.1 Optimization

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

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