Multivariable Calculus

  1. Partial Derivatives
    1. Introduction to Partial Derivatives
      1. Definition of Partial Derivatives
        1. Notation for Partial Derivatives
          1. Computing First Partial Derivatives
            1. Geometric Interpretation
              1. Slopes of Tangent Lines
                1. Rate of Change
              2. Higher-Order Partial Derivatives
                1. Second Partial Derivatives
                  1. Mixed Partial Derivatives
                    1. Clairaut's Theorem
                      1. Higher-Order Derivatives
                      2. The Total Differential
                        1. Definition of Differentials
                          1. Linear Approximation
                            1. Error Estimation
                              1. Applications of Differentials
                              2. The Chain Rule for Multivariable Functions
                                1. Chain Rule with One Independent Variable
                                  1. Chain Rule with Multiple Independent Variables
                                    1. Tree Diagrams
                                      1. Applications of the Chain Rule
                                      2. Implicit Differentiation
                                        1. Implicit Functions of Two Variables
                                          1. Implicit Functions of Three Variables
                                          2. Directional Derivatives
                                            1. Definition of Directional Derivatives
                                              1. Computing Directional Derivatives
                                                1. Properties of Directional Derivatives
                                                  1. Maximum Rate of Change
                                                  2. The Gradient Vector
                                                    1. Definition of the Gradient
                                                      1. Properties of the Gradient
                                                        1. Gradient as Direction of Steepest Ascent
                                                          1. Gradient and Level Curves
                                                            1. Gradient and Normal Vectors
                                                            2. Tangent Planes and Normal Lines
                                                              1. Tangent Planes to Surfaces
                                                                1. Equation of Tangent Plane
                                                                  1. Finding Tangent Planes
                                                                  2. Normal Lines to Surfaces
                                                                    1. Linear Approximation of Functions

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                                                                  3. Functions of Several Variables

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                                                                  5. Optimization of Multivariable Functions