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This course analyzes the functions of a complex variable and the calculus of residues.
FREE
This course includes
Hours of videos
972 years, 1 month
Units & Quizzes
35
Unlimited Lifetime access
Access on mobile app
Certificate of Completion
It also covers subjects such as ordinary differential equations, partial differential equations, Bessel and Legendre functions, and the Sturm-Liouville theory.
Course Currilcum
- Number Systems and Algebra of Complex Numbers Unlimited
- Elementary Complex Functions, Part 1 Unlimited
- Elementary Complex Functions, Part 2 Unlimited
- Branch Points and Branch Cuts Unlimited
- Analytic Functions Unlimited
- Complex Integrals Unlimited
- Cauchy’s Formula, Properties of Analytic Functions Unlimited
- Taylor Series, Laurent Series Unlimited
- Laurent Series (cont.) Unlimited
- Properties of Laurent Series, Singularities Unlimited
- Singularities (cont.) Unlimited
- Residue Theorem Unlimited
- Evaluation of Real Definite Integrals, Case I Unlimited
- Evaluation of Real Definite Integrals, Case II Unlimited
- Evaluation of Real Definite Integrals, Case III Unlimited
- Evaluation of Real Definite Integrals, Case IV Unlimited
- Theorems for Contour Integration Unlimited
- Series and Convergence Unlimited
- Ordinary Differential Equations Unlimited
- Singular Points of Linear Second-order ODEs Unlimited
- Frobenius Method Unlimited
- Frobenius Method – Examples Unlimited
- Frobenius Method (cont.) and a “particular type” of ODE Unlimited
- Bessel Functions Unlimited
- Properties of Bessel Functions Unlimited
- Modified Bessel Functions Unlimited
- Differential Equations Satisfied by Bessel Functions Unlimited
- Introduction to Boundary-Value Problems Unlimited
- Eigenvalues, Eigenfunctions, Orthogonality of Eigenfunctions Unlimited
- Boundary Value Problems for Nonhomogeneous PDEs Unlimited
- Sturm-Liouville Problem Unlimited
- Fourier Series Unlimited
- Fourier Sine and Cosine Series Unlimited
- Complete Fourier Series Unlimited
- Review of Boundary Value Problems for Nonhomogeneous PDEs Unlimited
