Multivariable Calculus

  1. Optimization of Multivariable Functions
    1. Critical Points and Local Extrema
      1. Critical Points
        1. Definition and Finding Critical Points
          1. Types of Critical Points
          2. Second Derivative Test
            1. Discriminant Test
              1. Classification of Critical Points
                1. Local Maxima
                  1. Local Minima
                    1. Saddle Points
                2. Absolute Extrema
                  1. Extreme Value Theorem for Multivariable Functions
                    1. Finding Absolute Extrema on Closed Bounded Sets
                      1. Boundary Analysis
                        1. Applications to Optimization Problems
                        2. Constrained Optimization
                          1. Lagrange Multipliers Method
                            1. Single Constraint Problems
                              1. Multiple Constraint Problems
                              2. Geometric Interpretation of Lagrange Multipliers
                                1. Applications of Constrained Optimization
                                  1. Economic Applications
                                    1. Engineering Applications
                                      1. Geometric Applications

                                  Previous

                                  4. Partial Derivatives

                                  Go to top

                                  Next

                                  6. Multiple Integrals