Multivariable Calculus

  1. Multiple Integrals
    1. Double Integrals over Rectangles
      1. Riemann Sums for Functions of Two Variables
        1. Definition of Double Integrals
          1. Properties of Double Integrals
            1. Iterated Integrals
              1. Fubini's Theorem
                1. Statement and Conditions
                  1. Applications of Fubini's Theorem
                2. Double Integrals over General Regions
                  1. Type I Regions
                    1. Definition and Setup
                      1. Integration over Type I Regions
                      2. Type II Regions
                        1. Definition and Setup
                          1. Integration over Type II Regions
                          2. Changing Order of Integration
                            1. Properties of Double Integrals over General Regions
                            2. Applications of Double Integrals
                              1. Area of Plane Regions
                                1. Volume under Surfaces
                                  1. Mass of Laminas
                                    1. Constant Density
                                      1. Variable Density
                                      2. Center of Mass and Centroid
                                        1. Moments of Inertia
                                          1. Average Value of Functions
                                          2. Double Integrals in Polar Coordinates
                                            1. Polar Coordinate System Review
                                              1. Coordinate Transformations
                                                1. Jacobian for Polar Coordinates
                                                  1. Setting Up Double Integrals in Polar Coordinates
                                                    1. Applications in Polar Coordinates
                                                    2. Triple Integrals
                                                      1. Definition and Properties
                                                        1. Triple Integrals over Rectangular Boxes
                                                          1. Triple Integrals over General Regions
                                                            1. Order of Integration
                                                              1. Applications of Triple Integrals
                                                                1. Volume of Solids
                                                                  1. Mass of Solids
                                                                    1. Center of Mass of Solids
                                                                      1. Moments of Inertia for Solids
                                                                    2. Triple Integrals in Cylindrical Coordinates
                                                                      1. Cylindrical Coordinate System
                                                                        1. Coordinate Transformations
                                                                          1. Jacobian for Cylindrical Coordinates
                                                                            1. Setting Up Triple Integrals in Cylindrical Coordinates
                                                                              1. Applications in Cylindrical Coordinates
                                                                              2. Triple Integrals in Spherical Coordinates
                                                                                1. Spherical Coordinate System
                                                                                  1. Coordinate Transformations
                                                                                    1. Jacobian for Spherical Coordinates
                                                                                      1. Setting Up Triple Integrals in Spherical Coordinates
                                                                                        1. Applications in Spherical Coordinates
                                                                                        2. Change of Variables in Multiple Integrals
                                                                                          1. General Transformations
                                                                                            1. The Jacobian Matrix
                                                                                              1. Definition and Computation
                                                                                                1. Geometric Interpretation
                                                                                                2. Change of Variables Formula
                                                                                                  1. Double Integrals
                                                                                                    1. Triple Integrals
                                                                                                    2. Applications of Change of Variables

                                                                                                  Previous

                                                                                                  5. Optimization of Multivariable Functions

                                                                                                  Go to top

                                                                                                  Next

                                                                                                  7. Vector Calculus