Course

MATH-202(c): Analysis III

Lectures in this course (37)

Poisson Problem: Fourier Transform Approach

Explores solving the Poisson problem using Fourier transform, discussing source terms, boundary conditions, and solution uniqueness.

Fourier Transformation: Solving Differential Equations

Explores using Fourier transformation to solve differential equations, focusing on a specific example and deriving the solution formula step by step.

Gradient: Scalar Field

Explores gradient in scalar fields, directional derivatives, and level sets.

Summary using nabla symbol

Covers the concept of nabla symbol, vector scalar, divergence, and cross product in 3D.

Curl in 2D: Understanding Vector Field Rotation

Explores the concept of curl in 2D vector fields and its practical applications.

Curl in 3D

Covers the concept of curl in 3D, a vector operator describing rotation.

Laplacian: Basics and Examples

Covers the basics of the Laplacian operator applied to scalar fields and its importance in mathematical models.

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Fluid Dynamics: Navier-Stokes

Covers the Navier-Stokes equations in fluid dynamics and elasticity equations.

Introduction: Lightboard 0-1

Serves as a helpful review for vector calculus topics before the final exam.

Solving Poisson Problem: Fourier Transform Approach

Explores using Fourier transform to simplify solving the Poisson problem, transforming convolutions into multiplications for an explicit solution.

Poisson Problem: Periodic Boundary Conditions

Explores the Poisson problem with periodic boundary conditions and the application of Fourier series in mathematical modeling.

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Divergence and Stokes' Theorems

Introduces the divergence and Stokes' theorems, comparing surface and volume integrals, and explains parameterization of surfaces and boundaries.

Fourier Transform: Concepts and Applications

Covers the Fourier transform, its properties, and applications in signal processing and differential equations, demonstrating its importance in mathematical analysis.

Maxwell's Equations: Basics

Covers the basics of Maxwell's equations, describing the behavior of electric and magnetic fields.

Laplace Poisson Equation

Covers the Laplace and Poisson equations, the heat equation, and the wave equation in physics.

Vector Analysis: Basics and Applications

Explores the importance of vector analysis in physics and engineering, showcasing its application in various laws and relationships.

Divergence Examples

Explores examples of divergence in vector fields and their physical meanings.