Lectures in course MATH-207(d): Analysis IV

Explores partial differential equations, focusing on chapter 6 equations and their solutions through Fourier series and variable separation methods.

Covers heat equations, Fourier transforms, and variable separation methods.

Explores integral equations, Laplace transform methods, and problem-solving techniques.

Covers Cauchy and Laurent series in complex analysis.

Focuses on understanding how to use example 5.12 to distinguish when to close a curve to the left or right.

Focuses on solving second order differential equations with examples and conditions, including Fourier series and Sturm-Liouville theory.