MTH132: Calculus with Analytic Geometry II

Unit 1 - Techniques of Integration

• Chapter 8

  • 8.1 - Integration Using Substitution

  • 8.4 - Integration by Parts

  • 8.5 - Integration Using Linear Partial Fractions

Unit 2 - Applications of Integration

• Chapter 9

  • 9.1 - Area Between Curves

  • 9.3 - Volume

  • 9.4 - Average Value of a Function

  • 9.7 - Improper Integrals

Unit 3 - Polar Coordinates, Parametric Equations

• Chapter 10

  • 10.1 - Polar Coordinates (NOTE: The video also includes parametric equations.)

  • 10.2 - Slopes in Polar Coordinates

    • Supplementary Video: https://youtu.be/rkfO3xbIQA8

  • 10.3 - Areas in Polar Coordinates

    • Conceptual Video: https://youtu.be/FrEwNMCV-DI

    • Example Problem Video: https://youtu.be/eZR-6JKFXic

  • 10.4 - Parametric Equations (NOTE: This is the same video as 10.1.)

  • 10.5 - Calculus with Parametric Equations

Unit 4 - Sequences and Series

• Chapter 11

  • Convergent/Divergent Series/Geometric Series/Representing Functions as Power Series

  • Taylor Series and Taylor Polynomials

  • Convergence Tests

  • 11.2 - Series

  • 11.3 - The Integral Test

  • 11.4 - Alternating Series

  • 11.5 - Comparison Tests

  • 11.6 - Absolute Convergence

  • 11.7 - The Ratio and Root Tests

  • 11.8 - Power Series

  • 11.9 - Calculus with Power Series

  • 11.10 - Taylor Series

  • 11.11 - Taylor's Theorem