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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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