Exact Differential Equations

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Related lectures (26)

Page 2 of 3

Introduces the basics of ordinary differential equations, exploring existence, uniqueness, higher dimensions, Lipschitz functions, and solution finding.

Functions with Values in R^m

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

Homogeneous Differential Equations

Explores solving first-order homogeneous differential equations through variable changes and delves into the Bernoulli differential equation.

Numerical Analysis: Stability in ODEs

Covers the stability analysis of ODEs using numerical methods and discusses stability conditions.

Ordinary Differential Equations: Definitions and Examples

Covers ordinary differential equations, including orders, solutions, and separable equations, with a focus on examples and general solutions.

Implicit Functions Theorem

Explores the Implicit Functions Theorem, demonstrating how to find solutions to equations like x²+y²=1 through implicit differentiation and function properties.

Implicit Functions

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

Differential Equations: Initial Conditions and Solutions

Discusses ordinary differential equations, focusing on initial conditions and methods for finding solutions.

Canonical Transformations: Hamilton-Jacobi Equation

Explores canonical transformations, the Hamilton-Jacobi equation, symplectic groups, and differential equations in physics.

Linear Approximation and Derivative Parametric

Covers linear approximation, parametric derivatives, and differentiability conditions on intervals.