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Understanding Calculus

This is a complete, free, online Calculus textbook/course.
The materials in green give unlimited online practice and/or supplement the text.
If you've gone through my online curriculum through Precalculus,
then you should be able to jump right into Chapter 3.
The first two chapters review essential material and introduce new readers to math language concepts.
This link is for the COMPLETE book (a pdf file, about 47 MB).
It's a BIG file, and will take time to load into your browser—so you may prefer individual sections below.
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)
STUDENT'S COMPLETE SOLUTION MANUAL:
solutions (showing all steps) to ALL in-section and end-of-section exercises, sample tests
TITLE PAGE
TABLE OF CONTENTS (i–ii)
SECTION SOLUTIONS:
Chapter 1: 1.1 1.2 1.3 1.4 1.5  
Chapter 2: 2.1 2.2 2.3 2.4  
Sample Test, Chapters 1 and 2
(scanned pages, hand-written solutions)
Zoom to enlarge (as needed):
page 40     page 41     page 42     page 43    
Chapter 3: 3.1 3.2 3.3 3.4 3.5 3.6 3.7  
Sample Test, Chapter 3
(scanned pages, hand-written solutions)
Zoom to enlarge (as needed):
page 74     page 75     page 76    
Chapter 4: 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9
Sample Test, Chapter 4
(scanned pages, hand-written solutions)
Zoom to enlarge (as needed):
page 123     page 124     page 125    
Chapter 5: 5.1 5.2 5.3 5.4 5.5 5.6  
Sample Test, Chapter 5
(scanned pages, hand-written solutions)
Zoom to enlarge (as needed):
page 158     page 159     page 160    
Chapter 6: 6.1 6.2 6.3 6.4 6.5 6.6  
Sample Test, Chapter 6
(scanned pages, hand-written solutions)
Zoom to enlarge (as needed):
page 185     page 186     page 187    
Chapter 7: 7.1 7.2 7.3 7.4 7.5 7.6 7.7  
Sample Test, Chapter 7
(scanned pages, hand-written solutions)
Zoom to enlarge (as needed):
page 207     page 208     page 209