How to Ace Calculus : The Streetwise Guide

1. Introduction

2. Exactly Who and What is Your Instructor?

Choosing an Instructor
What to Expect From Your Instructor
How To Deal With Your Instructor

3. The General Principles of Acing Calculus

4. Good and Bad Questions

Why Ask Questions?
Some Sample Questions
Questions Not To Ask

5. Are You Ready? Calc Prereqs

What You Think You Learned
What You Really Need to Know on the First Day of Class
Computers and Calculators-Our 2-Bit Friends

6. How to Handle the Exam

What Will Be on the Exam
How to Study
How Not to Study for the Exam
Taking the Exam

7. Lines, Circles, and Their Friends

Cartesian Plane
General Graphing Tricks: The Parable of the Parabola
Lines
Circles
Ellipses, Parabolas, and Hyperbolas

8. Limits: You Gotta Have Them

Basic Idea
General Procedures for Taking a Limit
One-Sided Limits
Limits of Weird Functions
Calculators and Limits

9. Continuity or Why You Shouldn't Ski Down Discontinuous Slopes

The Idea
Three Conditions for Continuity

10. What is the Derivative? Change is Good

11. The Limit Definition of the Derivative: Finding Derivatives the Hard Way

Defining the Derivative
Other Forms for the Limit Definition of the Derivative

12. Derivatives: How to Find Them the Easy Way

Basic Rules of Differentiation
Power Rule
Product Rule
Quotient Rule
Derivatives of Trig Functions
Second Derivatives, Third Derivatives, and so on

13. Velocity: Put the Pedal to the Metal

Velocity as a Derivative
Position and Velocity of a Car
Velocity of a Falling Object

14. Chain Rule: S&M Made Easy

15. Graphing: How to Doodle Like an Expert

Graphing Functions
Tricky Graphs That Can Trip You Up
The Second Derivative Test
Concavity

16. Maxima and Minima: The Bread and Butter Section

Maxima and Minima over Closed Intervals
Applied Max-Min Problems

17. Implicit Differentiation: Let's Be Oblique

18. Related Rates: You Change, I Change

19. Differential: Estimating Your Way to Fame and Glory

20. Intermediate Value Theorem and Mean Value Theorem

Intermediate Value Theorem: It Ain't a Sandwich Unless There's Something Between the Bread
Mean Value Theorem: Steep is Steep

21. Integration: Doing It All Backward

Indefinite Integral
Integration Method: The Easy Ones
Integration Method: Substitution
Integration Method: The Eyeball Technique
Integration Method: Tables
Integration Method: Computers and Calculators

22. The Definite Integral

How to Find the Definite Integral
Area
Fundamental Theorem of Calculus
Some Basic Rules for Definite Integrals
Integration Method: Numerical Approximation
The Riemann Sum-With Nitty Gritty Details

23. Modeling: From Toy Planes to the Runway

Real-Life Problem

24. Exponents and Logarithms: A Review of All That "e" Hoopla

Exponents
Logarithms

25. Doing That Calc Thing to Exponents and Logs

Differentiating e^x and Its Friends
Integrating e^x and Its Friends
Differentiating the Natural Log
Working with Other Bases
Integrals and the Natural Log

26. Logarithmic Differentiation: Making the Hard Stuff Easy

27. Exponential Growth and Decay: The Rise and Fall of Slime

28. Fancy-Pants Techniques of Integration

Integration Method: Integration by Parts
Integration Method: Trigonometric Substitution
Method of Finding an Integral: Partial Fractions

29. The Twenty Most Common Exam Mistakes

30. What's Going to be on the Final?

Glossary: A Quick Guide to Mathematical Jargon
Index
Quick Reference Guide