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One Mathematical Cat, Please!
Understanding Calculus

(read for free at the bottom of this page)


Complete Solution Manual
print version
digital version
Curious about Calculus?
Want honest content, but a bit ‘slower and kinder’
than traditional Calculus books?
Like the way I explain things in Algebra I, Geometry, Algebra II, and Precalculus?
Then, this book is for you.

It's a complete Calculus course.
Selected solutions are part of the main text.
For ALL the solutions, I offer:

One Mathematical Cat, Please!
Understanding Calculus
COMPLETE SOLUTION MANUAL

PRINT VERSION
(at Amazon)

The print version is for those of us
who like to highlight, write in margins,
feel the paper between our fingers.

DIGITAL VERSION
(pdf file, 42 MB)
$3.33

The digital version is identical to
the paper version, but without the paper.

When you buy the digital version,
you'll receive an email with a download link.
(So, check your email after checking out!)

I use SendOwl
for my secure ‘Buy Now’ button.
I also offer a set of Calculus Index Cards:
Hold the entire course in the palm of your hand!

READ THE BOOK

Gone through my online curriculum through Precalculus?
Then, jump right into Chapter 3.

Haven't been using my lessons? No problem.
The first two chapters review essential material
and introduce you to all the math language concepts you'll need.
This link is for the COMPLETE book (a pdf file, about 47 MB).
It's a BIG file, and may take time to load into your browser.
So, you may prefer individual sections below.
However, it's certainly easier to search for stuff when it's all in one place.
The materials in green give unlimited online practice and/or supplement the text.
TABLE OF CONTENTS (i–ii)
PREFACE (iii–v)
ACKNOWLEDGEMENTS (vi)
STUDY STRATEGIES for Students of Mathematics (vii)
TABLE OF SYMBOLS (viii–ix)
CHAPTER 1. ESSENTIAL PRELIMINARIES
1.1 The Language of Mathematics—Expressions versus Sentences (1–11)
1.2 The Role of Variables (12–21)
1.3 Sets and Set Notation (22–28)
1.4 Mathematical Equivalence (29–38)
1.5 Graphs (39–53)
CHAPTER 2. FUNCTIONS
2.1 Functions and Function Notation (54–68)
2.2 Graphs of Functions (69–81)
2.3 Composite Functions (82–91)
2.4 One-to-One Functions and Inverse Functions (92–103)
SAMPLE TEST, Chapters 1 and 2 (104–107)
      Prerequisites for Precalculus (with solutions): also needed for Calculus!
      Average Rate of Change (great practice with function notation)
CHAPTER 3. LIMITS AND CONTINUITY
3.1 Limits—The Idea (108–119)
      Introduction to Limits
3.2 Limits—Making it Precise (120–132)
3.3 Properties of Limits (133–144)
3.4 Continuity (145–153)
3.5 Indeterminate Forms (154–159)
3.6 The Intermediate Value Theorem (160–170)
3.7 The Max-Min Theorem (171–178)
SAMPLE TEST, Chapter 3 (179–181)
CHAPTER 4. THE DERIVATIVE
4.1 Tangent Lines (182–192)
4.2 The Derivative (193–203)
4.3 Some Very Basic Differentiation Formulas (194–219)
      Basic Differentiation Shortcuts (differentiating constants and linear functions; the Simple Power Rule)
4.4 Instantaneous Rates of Change (220–227)
4.5 The Chain Rule (Differentiating Composite Functions) (228–238)
4.6 Differentiating Products and Quotients (239–248)
      Differentiation Formula Practice
      Mixed Differentiation Practice
      Mixed Differentiation Practice (strict parentheses version)
4.7 Higher Order Derivatives (249–256)
4.8 Implicit Differentiation (optional) (257–265)
4.9 The Mean Value Theorem (266–272)
SAMPLE TEST, Chapter 4 (273–275)
CHAPTER 5. USING THE INFORMATION GIVEN BY THE DERIVATIVE
5.1 Increasing and Decreasing Functions (276–286)
5.2 Local Maxima and Minima—Critical Points (287–298)
5.3 The Second Derivative—Inflection Points (299–308)
5.4 Graphing Functions—Some Basic Techniques (309–319)
5.5 More Graphing Techniques (320–329)
5.6 Asymptotes—Checking Behavior at Infinity (330–338)
SAMPLE TEST, Chapter 5 (339–341)
CHAPTER 6. ANTIDIFFERENTIATION
6.1 Antiderivatives (342–353)
6.2 Some Basic Antidifferentiation Formulas (354–361)
6.3 Analyzing a Falling Object (optional) (362–375)
6.4 The Substitution Technique for Antidifferentiation (376–384)
6.5 More on Substitution (385–390)
6.6 Integration By Parts (391–397)
SAMPLE TEST, Chapter 6 (398–400)
CHAPTER 7. THE DEFINITE INTEGRAL
7.1 Using Antiderivatives to Find Area (401–407)
7.2 The Definite Integral (408–417)
7.3 The Definite Integral as the Limit of Riemann Sums (418–422)
7.4 The Substitution Technique applied to Definite Integrals (423–427)
      Mixed Integration Practice
7.5 The Area Between Two Curves (428–435)
7.6 Finding the Volume of a Solid of Revolution—Disks (436–443)
7.7 Finding the Volume of a Solid of Revolution—Shells (444–449)
SAMPLE TEST, Chapter 7 (450–452)
ABBREVIATED SOLUTIONS: Odd-Numbered End-of-Section Exercises and Quick Quiz Problems
Chapter 1 (453–457)
Chapter 2 (458–462)
Chapter 3 (463–469)
Chapter 4 (470–476)
Chapter 5 (477–479)
Chapter 6 (480–482)
Chapter 7 (483–486)
INDEX (487–497)