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MATH-202(c): Analysis III

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Lectures in this course (46)

Fourier Transform: Concepts and Applications Log in to Mediaspace to watch this video

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

Curl in 2D: Understanding Vector Field Rotation Log in to Mediaspace to watch this video

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

Divergence Examples Log in to Mediaspace to watch this video

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

Scalar fields and level sets Log in to Mediaspace to watch this video

Covers scalar fields and level sets, focusing on the level set { x ∈ R³ | x² + x² + x₃ = 1}.

Fourier Series: Periodic Functions and Calculations Log in to Mediaspace to watch this video

Covers Fourier series for periodic functions and calculations involving Fourier coefficients.

Maxwell's Equations: Basics Log in to Mediaspace to watch this video

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

Introduction: Lightboard 0-1 Log in to Mediaspace to watch this video

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

Curve Integrals: Gauss/Green Theorem Log in to Mediaspace to watch this video

Explores the application of the Gauss/Green theorem to calculate curve integrals along simple closed curves.

Divergence Explained: Lightboard 2-4 Log in to Mediaspace to watch this video

Explores how sources and sinks affect the divergence of vector fields.

General Surfaces: Definition and Examples Log in to Mediaspace to watch this video

Introduces general surfaces, explaining parameterizations, regularity, and integrals with examples like cylinder shells and spheres.

Poisson Problem: Periodic Boundary Conditions Log in to Mediaspace to watch this video

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

Curve Integrals: Parameterizations and Riemann Sums Log in to Mediaspace to watch this video

Explores curve integrals, emphasizing parameterizations, geometric curves, and Riemann sums.

Laplacian: Basics and Examples Log in to Mediaspace to watch this video

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

Vector Analysis: Fundamentals and Applications Log in to Mediaspace to watch this video

Covers fundamental concepts of vector analysis and their applications in science and engineering.

Fluid Dynamics: Navier-Stokes Log in to Mediaspace to watch this video

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

Poisson Problem: Fourier Transform Approach Log in to Mediaspace to watch this video

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

Vector Analysis: Basics and Applications Log in to Mediaspace to watch this video

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

Curve Integrals of Vector Fields Log in to Mediaspace to watch this video

Explores curve integrals of vector fields, energy calculations, potential functions, and tangential vectors, with a focus on line integrals and domains.

Gradient: Scalar Field Log in to Mediaspace to watch this video

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

Fourier Transformation: Solving Differential Equations Log in to Mediaspace to watch this video

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

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