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Calculus
Single Variable
Wai Yan Pong
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Front Matter
I
Calculus I
1
Differentiation
1.1
Differentiability
1.2
Derivatives
1.2.1
Rules of Differentiation
1.2.2
Implicit Differentiation
1.3
Derivatives of Elementary Functions
1.3.1
Derivatives of Algebraic Functions
1.3.2
Derivatives of Exponential and Logarithmic Functions
1.3.3
Derivatives of trigonometric functions and their inverses
1.4
Exercises
2
Integration
2.1
Anti-derivatives
2.2
Integration by Substitution
2.3
Fundamental Theorem of Calculus
2.4
Exercises
II
Calculus II
3
Techniques of Integration
3.1
Integration by Parts
3.2
Trigonometric Integrals
3.2.1
Products of Trigonometric Functions
3.2.2
Powers of Trigonometric Functions
3.2.3
Half-Angle Substitution
3.3
Trigonometric Substitutions
3.4
Integrals of Rational Functions
3.4.1
Partial Fraction Decomposition
3.4.2
The reduced cases
3.5
Exercises
4
Improper Integrals
4.1
Definitions and Examples
4.2
Comparison Test for Integrals
4.3
Exercises
5
Sequence and Series
5.1
Sequences
5.1.1
The Basics
5.1.2
Algebraic Operations on Sequences
5.1.3
Convergence of Sequence
5.2
Convergence Tests for Sequences
5.3
Series
5.4
Convergence Tests for Series
5.5
Power Series
5.5.1
Applications to summing series
5.6
Taylor Series
5.7
Exercises
Back Matter
A
Algebra Basics
A.1
Polynomial Division
A.2
Completing the Square
A.3
Factoring Quadratics
A.4
System of Linear Equations
B
Trigonometric Identities
C
Some Important Limits
D
Power Series of Some Common Analytic Functions
E
Binomial Series
F
Hints and Selected Answers
References
Index
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Website
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©2020–2025 Wai Yan Pong
This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License. To view a copy of this license, visit
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