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Advanced Analytic Methods in Science and Engineering is a comprehensive treatment of the advanced methods of applied mathematics. It was designed to strengthen the mathematical abilities of graduate students and train them to think on their own. Topics will cover such as series solutions of linear homogeneous ODE and Discussion of how to make expansions around irregular and regular singular points.

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
The Differential Operator 00:12:00
Complex Analysis 00:10:00
First-Order Partial Differential Equations 00:10:00
Second-Order Partial Differential Equations 00:10:00
Module: 02
Separation of Variables 00:10:00
Singular Points of Ordinary Differential Equations 00:10:00
Regular Singular Points of Ordinary Differential Equations 00:10:00
Irregular Singular Points of Ordinary Differential Equations 00:12:00
The WKB Approximation 00:10:00
Turning Point 00:08:00
Module: 03
The Laplace Method 00:10:00
Method of Stationary Phase 00:10:00
Asymptotic Expansions of Integrals 00:10:00
Boundary Layers and Singular Perturbation 00:20:00
Interior Turning Points 00:10:00
Assessment
Submit Your Assignment 00:00:00
Certification 00:00:00

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