by Colin Adams, Abigail Thompson and Joel Hass
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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
Colin Adams, Abigail Thompson and Joel Hass
ISBN13: 978-0716731603Table of Contents
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