Yet Another Calculus Book

Contents 
Acknowledgements 
Preface 

1 Functions 
1.1 Some Vocabulary & Notation 
1.2 Finding the Domain 
1.3 A Word on Continuity 
1.4 Combining Functions 
1.5 Practice Problems 
1.6 Answers to Chapter Questions 

2 Limits 
2.1 Intro to Limits 
2.2 The Graph 
2.3 The Equation
2.4 Plug In 
2.5 When You Get ∞ 
2.6 Piece-Wise Defined Functions 
2.7 Practice Problems 
2.8 Answers to Chapter Questions 

3 Derivatives 
3.1 Finding the Units 
3.2 Get the Picture 
3.3 Oogy Definition 
3.4 Some General Derivatives 
3.5 Differentiable 
3.6 Derivatives of sin(x) and cos(x) 
3.7 Practice Problems 
3.8 Answers to Chapter Questions 

4 Shortcuts 
4.1 Power Rule 
4.2 Product Rule 
4.3 Quotient Rule 
4.4 Chain Rule 
4.5 Implicit Differentiation 
4.6 Practice Problems 
4.7 Answers to Chapter Questions 
4.8 Proofs 

5 More Functions 
5.1 Exponential Functions 
5.2 Logarithmic Functions 
5.3 Trigonometric Functions 
5.4 Inverse Trigonometric Functions 
5.5 Practice Problems 
5.6 Answers to Chapter Questions 
5.7 Proofs 

6 More Limits 
6.1 To Infinity 
6.2 l’Hôpital’s Rule 
6.3 What about 0 · ∞? 
6.4 What about ∞ − ∞? 
6.5 What about 0⁰, 1^∞, or ∞⁰? 
6.6 Practice Problems 
6.7 Answers to Chapter Questions 

7 Shape of Graphs 
7.1 Intercepts 
7.2 The Ups and Downs: The First Derivative 
7.3 Curviness 
7.4 All Together Now 
7.5 Practice Problems 
7.6 Answers to Chapter Questions 

8 Motion 
8.1 Linear Motion
8.2 Non-linear Motion 
8.3 Practice Problems 
8.4 Answers to Chapter Questions 

9 Optimization 
9.1 Don’t Fence Me In 
9.2 That Is Going to Cost How Much? 
9.3 Funkier Optimization Problems 
9.4 Practice Problems 
9.5 Answers to Chapter Questions 

10 Related Rates 
10.1 Setting up the Problem 
10.2 Practice Problems 
10.3 Answers to Chapter Questions 

11 Baby Integration 
11.1 Antiderivative 
11.2 The Formulas 
11.3 Integration by Substitution 
11.4 Differential Equations 
11.5 Practice Problems 
11.6 Answers to Chapter Questions 

Appendices 

A Solutions 
A.1 Chapter 1 
A.2 Chapter 2 
A.3 Chapter 3 
A.4 Chapter 4 
A.5 Chapter 5 
A.6 Chapter 6 
A.7 Chapter 7 
A.8 Chapter 8 
A.9 Chapter 9 
A.10 Chapter 10
A.11 Chapter 11 

B Remember This Stuff? 
B.1 PEMDAS 
B.2 Multiplying Polynomials 
B.3 Pascal’s Triangle 
B.4 Factoring 
B.5 Synthetic Division 
B.6 Completing the Square 
B.7 Interval Notation 

C Basic Functions: A (Somewhat) Quick Review 

C.1 Power Functions 
Definitions 
Graphs

C.2 Polynomials 
Definitions 
Graphs 

C.3 Rational Functions 
Definitions 
Graphs 

C.4 Exponential Functions 
Definitions 
Graphs 
Manipulations

C.5 Logarithmic Functions 
Definitions 
Graphs 
Manipulations 

C.6 Trigonometric Functions 
Definitions 
Graphs 
Manipulations 

C.7 Arctrigonometric Functions 
Definitions 
Graphs 
Manipulations