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by Chris Monahan
Calculus II
Cover
Title Page
Copyright Page
Contents
Introduction
Part 1: Review of Pre-Calculus and Calculus I
1 Pre-Calculus Topics Used in Calculus II
Trigonometry
Exponents and Logarithms
Parametric Equations
Polar Coordinates
Geometric Sequences and Series
Partial Fractions
2 Limits, Derivatives, and Basic Integration
Limits
Derivatives
Implicit Differentiation
Mean Value Theorem
Relative Extremes and Concavity
Applications of the Derivative
Related Rates
3 Definite and Indefinite Integrals
Indefinite Integrals
u-Substitutions
Fundamental Theorem of Calculus
Numerical Approximation
Part 2: Length, Area, and Volumes
4 Areas and Approximations
Riemann Sums
From Numerical Approximations to the True Area
Average Value of a Function
Area Between Two Curves
Simpson’s Rule
5 Volumes and Areas of Solids of Revolutions
Volumes of Solids with Defined Cross Sections
Disks and Washers
Cylindrical Shell Method
Arc Length
Surface Area
Part 3: More Definite and Indefinite Integrals
6 More Integration Techniques
Integration by Parts
Polynomials and Transcendentals
Two Transcendentals
7 Integration with Trigonometric Functions
Trigonometric Substitutions
Case I: a2+x2
Case II: x2-a2
Case III: a2-x2
Integrals of the Form sinn(x) cosm(x) (When Either m or n Is Odd)
Case I: Both m and n Are Odd
Case II: Both m and n Are Even
Case III: Either m or n Is Odd
Integrals with Integrands of the Form tann(x) secm(x) (m Is Even)
Integrals with Integrands of the Form tann(x) secm(x) (m Is Odd, n Is Even)
8 Integration with Fractions
Completing the Square
Integration by Partial Fractions
Nonrepeating Linear Factors
Repeated Linear Factors
Irreducible Quadratic Factors
Part 4: The Infinite Series and More
9 To Infinity and Beyond
Improper Integrals
Infinite Limits of Integration
Discontinuities in the Integrand
Comparison Test for Improper Integrals
10 Parametric Equations
First and Second Derivatives of Parametric Curves
Arc Length of a Parametric Curve
11 Polar Coordinates
Slope of the Tangent Line
Length of an Arc of a Polar Curve
Area Under a Curve
12 Introduction to Vectors
Scalars and Vectors
Displacement, Velocity, and Acceleration
13 Differential Equations
Separable Differential Equations
Linear Approximations
Euler’s Method
Slope Fields
First Order Linear Differential Equations
14 Infinite Sequences
Convergence and Divergence of Sequences
Squeeze Theorem
Increasing, Decreasing, and Monotonic Sequences
15 Infinite Series
Infinite Geometric Series
Tests of Convergence
Alternating Series
Estimating the Sum of Alternating Series
16 Power Series
Power Series
MacLaurin Series
Taylor Series
Error Estimates for the MacLaurin and Taylor Series
17 Calculus II Final Exam
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Chapter 13
Chapter 14
Chapter 15
Chapter 16
Solutions
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Chapter 13
Chapter 14
Chapter 15
Chapter 16
Appendixes
A Solutions to “You’ve Got Problems”
B Integration Practice Problems and Solutions
C Glossary
About the Author
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