Tangent Planes and Implicit Functions

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Functions with Values in R^m

Explores functions with values in R^m, gradients, derivatives, and the Jacobian matrix in multiple dimensions.

Directional Derivatives and Tangent Planes

Explores directional derivatives, tangent planes, and function differentiability in multivariable calculus.

Exact Differential Equations

Revisits exact differential equations, discussing implicit function theorem and factors integrants.

Linear Transformations: Matrices and Kernels

Covers linear transformations, matrices, kernels, and properties of invertible matrices.

Advanced Analysis II: Tangent Plan and Differentiability

Explores tangent planes and differentiability in advanced analysis, emphasizing the properties of tangent planes and the conditions for differentiability.

Functions: Definitions and Notations

Covers the generalities of functions, including the definition of an application between sets and the uniqueness of elements in the image set.

Derivative: Application Examples

Explores examples of using derivatives to find tangent lines and points on graphs.

Graph Sketching: Motion Analysis

Explores motion graph analysis, focusing on function study and derivative interpretation.

Differential Calculation: Trigonometric Derivatives

Explores trigonometric derivatives, composition of functions, and inflection points in differential calculation.

Implicit Functions

Covers directional derivatives, implicit functions, and the concept of the maximum.