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Notes for Math 220,
Calculus 2
Brenton LeMesurier
Contents
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Contents
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Front Matter
Copyright Page
1
Integration (review from first semester calculus)
Approximating Areas (and Distance Traveled)
The Definite Integral
The Fundamental Theorem of Calculus
Integration Formulas and the Net Change Theorem
Substitution
Integrals Involving Exponential and Logarithmic Functions — Summary
Integrals Resulting in Inverse Trigonometric Functions — Summary
2
Applications of Integration
Areas between Curves
Determining Volumes by Slicing
Volumes of Revolution: Cylindrical Shells
Arc Length of a Curve and Surface Area
Physical Applications (omitted)
Moments and Centers of Mass (omitted)
Integrals, Exponential Functions, and Logarithms (omitted)
Exponential Growth and Decay (omitted)
Hyperbolic Functions
3
Techniques of Integration
Integration by Parts
Trigonometric Integrals
Trigonometric Substitution
Partial Fractions
Other Strategies for Integration
Numerical Integration
Improper Integrals
4
Introduction to Differential Equations
Basics of Differential Equations
Direction Fields and Numerical Methods (omitted)
Separable Equations
The Logistic Equation (omitted)
First-order Linear Equations
5
Sequences and Series
Sequences
Infinite Series
The Divergence and Integral Tests
Comparison Tests
Alternating Series (and Conditional vs. Absolute Convergence)
Ratio and Root Tests
6
Power Series
Power Series and Functions
Properties of Power Series
Taylor and Maclaurin Series
Working with Taylor Series
7
Parametric Equations and Polar Coordinates
Parametric Equations
Calculus of Parametric Curves
Polar Coordinates
Area and Arc Length in Polar Coordinates
Appendices
A
Rules for Derivatives and Integrals
Rules for Derivatives
Rules for Integrals
B
Calculus Formula Checklists
Derivatives Checklist
Integrals Checklist
C
Reduction Formulas For Integrals
Integrals Involving Exponential or Trigonometric Functions
Integrals Involving Inverse Trigonometric Functions
Integrals Involving
\(\sqrt{a + bu}\)
D
Some Taylor Series
Authored in PreTeXt
Appendix
B
Calculus Formula Checklists
B.1
Derivatives Checklist
B.2
Integrals Checklist