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The focus of this course is to analyze the functions of a complex variable and the calculus of residues. Along with these it also covers subjects such as ordinary differential equations, partial differential equations, Bessel and Legendre functions, and the Sturm-Liouville theory. If you are keen to gather some knowledge about Calculus then this course is the perfect diploma course for you.  

Assessment

This course does not involve any written exams. Students need to answer 5 assignment questions to complete the course, the answers will be in the form of written work in pdf or word. Students can write the answers in their own time. Each answer needs to be 200 words (1 Page). Once the answers are submitted, the tutor will check and assess the work.

Certification

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Course Credit: MIT

Course Curriculum

Module 01
lecture1 Number Systems and Algebra of Complex Numbers 00:10:00
lecture2 Elementary Complex Functions, Part 1 00:10:00
lecture3 Elementary Complex Functions, Part 2 00:10:00
lecture4 Branch Points and Branch Cuts 00:10:00
lecture5 Analytic Functions 00:15:00
lecture6 Complex Integrals 00:10:00
lecture7 Cauchy’s Formula, Properties of Analytic Functions 00:05:00
lecture8 Taylor Series, Laurent Series 00:10:00
lecture9 Laurent Series (cont.) 00:10:00
lecture10 Properties of Laurent Series, Singularities 00:10:00
lecture11 Singularities (cont.) 00:10:00
lecture12 Residue Theorem 00:10:00
Module 02
lecture13 Evaluation of Real Definite Integrals, Case I 00:20:00
lecture14 Evaluation of Real Definite Integrals, Case II 00:10:00
lecture15 Evaluation of Real Definite Integrals, Case III 00:10:00
lecture16 Evaluation of Real Definite Integrals, Case IV 00:15:00
lecture17 Theorems for Contour Integration 00:05:00
lecture18 Series and Convergence 00:05:00
lecture19 Ordinary Differential Equations 00:15:00
lecture20 Singular Points of Linear Second-order ODEs 00:10:00
lecture21 Frobenius Method 00:10:00
lecture22 Frobenius Method – Examples 00:10:00
lecture23 Frobenius Method (cont.) and a particular type of ODE 00:15:00
lecture24 Bessel Functions 00:15:00
Module 03
lecture25 Properties of Bessel Functions 00:05:00
lecture26 Modified Bessel Functions 00:05:00
lecture27 Differential Equations Satisfied by Bessel Functions 00:10:00
lecture28 Introduction to Boundary-Value Problems 00:05:00
lecture29 Eigenvalues, Eigenfunctions, Orthogonality of Eigenfunctions 00:10:00
lecture30 Boundary Value Problems for Nonhomogeneous PDEs 00:15:00
lecture31 Sturm-Liouville Problem 00:10:00
lecture32 Fourier Series 00:15:00
lecture33 Fourier Sine and Cosine Series 00:15:00
lecture34 Complete Fourier Series 00:15:00
lecture35 Review of Boundary Value Problems for Nonhomogeneous PDEs 00:15:00
Assessment
Submit Your Assignment 00:00:00
Certification 00:00:00

Course Reviews

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