by Colin Adams, Abigail Thompson and Joel Hass

ISBN13: 978-0716731603

ISBN10: 0716731606

Cover type:

Edition/Copyright: 98

Publisher: Henry Holt and Co.

Published: 1998

International: No

ISBN10: 0716731606

Cover type:

Edition/Copyright: 98

Publisher: Henry Holt and Co.

Published: 1998

International: No

- Witty, clever, and pedagogically solid explanations of the basic concepts of calculus
- Survival skills cover choosing the professor, taking notes, studying, and taking exams
- Numerous relevant examples and analogies based on the author's own classroom experiences
- Flexible organization allows students to use the guide with any traditional or reform-based calculus text
- Well-known and respected author team
- An appendix serves as a quick reference guide to the most frequently used formulas

**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 **

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 **

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

Differentiating the Natural Log

Working with Other Bases

Integrals and the Natural Log

**26. Logarithmic Differentiation: Making the Hard Stuff Easy **

**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 **

Glossary: A Quick Guide to Mathematical Jargon

Index

Quick Reference Guide

Colin Adams, Abigail Thompson and Joel Hass

ISBN13: 978-0716731603ISBN10: 0716731606

Cover type:

Edition/Copyright: 98

Publisher: Henry Holt and Co.

Published: 1998

International: No

- Witty, clever, and pedagogically solid explanations of the basic concepts of calculus
- Survival skills cover choosing the professor, taking notes, studying, and taking exams
- Numerous relevant examples and analogies based on the author's own classroom experiences
- Flexible organization allows students to use the guide with any traditional or reform-based calculus text
- Well-known and respected author team
- An appendix serves as a quick reference guide to the most frequently used formulas

Table 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 **

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 **

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

Differentiating the Natural Log

Working with Other Bases

Integrals and the Natural Log

**26. Logarithmic Differentiation: Making the Hard Stuff Easy **

**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 **

Glossary: A Quick Guide to Mathematical Jargon

Index

Quick Reference Guide

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