Course Contents at a Glance

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The following list shows a summary of the topics covered in this course. To see all of the course pages, visit the Table of Contents.

Module 1: Integration

  • Approximating Areas
  • The Definite Integral
  • The Fundamental Theorem of Calculus
  • Integration Formulas and the Net Change Theorem
  • Substitution
  • Integrals Involving Exponential and Logarithmic Functions
  • Integrals Resulting in Inverse Trigonometric Functions

Module 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
  • Moments and Centers of Mass
  • Integrals, Exponential Functions, and Logarithms
  • Exponential Growth and Decay
  • Calculus of the Hyperbolic Functions

Module 3: Techniques of Integration

  • Integration by Parts
  • Trigonometric Integrals
  • Trigonometric Substitution
  • Partial Fractions
  • Other Strategies for Integration
  • Numerical Integration
  • Improper Integrals

Module 4: Introduction to Differential Equations

  • Basics of Differential Equations
  • Direction Fields and Numerical Methods
  • Separable Equations
  • The Logistic Equation
  • First-order Linear Equations

Module 5: Sequences and Series

  • Sequences
  • Infinite Series
  • The Divergence and Integral Tests
  • Comparison Tests
  • Alternating Series
  • Ratio and Root Tests

Module 6: Power Series

  • Power Series and Functions
  • Properties of Power Series
  • Taylor and Maclaurin Series
  • Working with Taylor Series

Module 7: Parametric Equations and Polar Coordinates

  • Parametric Equations
  • Calculus of Parametric Curves
  • Polar Coordinates
  • Area and Arc Length in Polar Coordinates
  • Conic Sections