Lectures related to Exact Differential Equations

Explores tangent planes, implicit functions, and directional derivatives in relation to graphs of functions.

Explores the geometric interpretation of derivatives and properties of derivable functions.

Implicit Function Theorem: Tangent Planes and Derivatives

Discusses the Implicit Function Theorem and its application to tangent planes and derivatives.

Differential Equations: Implicit Function Theorem Applications

Discusses the reduction of higher-order differential equations to first-order systems using the implicit function theorem.

Canonical Transformations: Existence and Equations

Explores canonical transformations, focusing on existence, equations, simplicity, and differential equations' theory.

Differential Equations: Speed Variation Analysis

Covers the analysis of speed variation using differential equations and small time intervals.

Differential Equations: Implicit Solutions

Explores implicit solutions for differential equations and their applications in different scenarios.

Implicit Functions Theorem

Covers the Implicit Functions Theorem, explaining how equations can define functions implicitly.

Partial Derivatives and Differential Equations

Covers partial derivatives, differentiability, differential equations, sets properties, and local extrema verification.

Ordinary Differential Equations: Basics

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.