Calculus

  1. Applications of Integration
    1. Area Between Curves
      1. Setting Up Integrals for Area
        1. Area with Respect to x
          1. Area with Respect to y
            1. Choosing the Appropriate Variable
            2. Volumes of Solids
              1. Volumes by Cross-Sections
                1. Method of Cross-Sections
                  1. Common Cross-Sectional Shapes
                  2. Volumes of Revolution
                    1. Disk Method
                      1. Washer Method
                        1. Shell Method
                        2. Choosing the Best Method
                        3. Arc Length and Surface Area
                          1. Arc Length of Curves
                            1. Arc Length Formula
                              1. Parametric and Polar Cases
                              2. Surface Area of Revolution
                                1. Surfaces Generated by Rotation About x-axis
                                  1. Surfaces Generated by Rotation About y-axis
                                2. Applications in Physics and Engineering
                                  1. Work
                                    1. Work Done by Variable Force
                                      1. Work in Pumping Liquids
                                      2. Fluid Pressure and Force
                                        1. Hydrostatic Pressure
                                          1. Force Against Submerged Surfaces
                                          2. Center of Mass and Centroids
                                            1. Center of Mass of Thin Rods
                                              1. Centroids of Plane Regions
                                                1. Pappus's Theorems
                                                2. Moments of Inertia
                                                  1. Definition and Applications
                                                3. Differential Equations
                                                  1. Introduction to Differential Equations
                                                    1. Classification by Order and Linearity
                                                      1. General and Particular Solutions
                                                      2. Separable Differential Equations
                                                        1. Method of Separation of Variables
                                                          1. Applications to Growth and Decay
                                                          2. First-Order Linear Differential Equations
                                                            1. Standard Form
                                                              1. Integrating Factor Method
                                                              2. Applications of Differential Equations
                                                                1. Population Models
                                                                  1. Cooling and Heating
                                                                    1. Mixing Problems

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                                                                7. Techniques of Integration

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                                                                9. Infinite Sequences and Series