Advanced Analysis II: Functions and Equations

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Related lectures (27)

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Existence of y: Proofs and EDO Resolution

Covers the proof of the existence of y and the resolution of EDOs with practical examples.

Solutions of Differential Equations

Explores finding solutions of differential equations, emphasizing maximal solutions and general solutions with constants.

Cauchy Problem: Differential Equations and Initial Conditions

Covers the Cauchy problem, focusing on differential equations and the role of initial conditions in determining unique solutions.

Linear First Order Differential Equations

Covers linear first order differential equations, separation of variables, particular solutions, uniqueness, and coefficients application.

Advanced Analysis II: Solving Separable Differential Equations

Covers the theory and methods for solving separable differential equations, focusing on existence, uniqueness, and the construction of solutions through integration.

Advanced Analysis II: Cauchy Problem and Differential Equations

Covers the Cauchy problem in differential equations, focusing on initial conditions and their impact on solution uniqueness.

Products and Convolution of Transforms

Covers the definition and properties of convolution of two functions and explores radioactive material decay rates.

Differential Equations: Initial Conditions and Solutions

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

Advanced Analysis: Differential Equations Overview

Covers the fundamentals of differential equations, their properties, and methods for finding solutions through various examples.

Differential Forms on Manifolds

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.