Calculus II

Book description

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Table of contents

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

Product information

  • Title: Calculus II
  • Author(s): Chris Monahan
  • Release date:
  • Publisher(s): Alpha
  • ISBN: None