The aim of this course is to cover same material as Differential Equations (18.03) with more emphasis on the theory. In addition to that, it treats mathematical aspects of ordinary differential equations such as existence theorems. If students are interested to get a diploma in Differential Equations then this course is the perfect for the students. Topics includes Terminology and implicit solutions and Integration and solutions.
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 | |||
| lec00 Terminology and implicit solutions | 00:10:00 | ||
| lec01 Integration and solutions | 00:20:00 | ||
| lec02 Fundamental principles | 00:25:00 | ||
| lec03 First-order linear equations | 00:20:00 | ||
| lec04 Separable equations | 00:20:00 | ||
| lec05 Linear fractional equations | 00:20:00 | ||
| lec06 Second-order linear equations | 00:20:00 | ||
| lec07 Mechanical oscillation | 00:20:00 | ||
| lec08 Uniqueness and the wronskian | 00:20:00 | ||
| lec09 Separation and comparison theorems | 00:20:00 | ||
| lec10 The maximum principle | 00:20:00 | ||
| lec11 Higher-order linear equations | 00:10:00 | ||
| lec12 Solution bases | 00:20:00 | ||
| lec13 Inhomogeneous equations | 00:20:00 | ||
| Module 02 | |||
| lec14 Stability | 00:20:00 | ||
| lec15 Laplace transform | 00:20:00 | ||
| lec16 Transform and differential equations generalized solutions, application to ODEs | 00:20:00 | ||
| lec17 Step functions | 00:20:00 | ||
| lec18 Convolution | 00:15:00 | ||
| lec19 The dirac distribution | 00:20:00 | ||
| lec20 The transfer function and the pole diagram | 00:20:00 | ||
| lec21 Linear systems | 00:20:00 | ||
| lec22 Eigenvalues and eigenvectors | 00:20:00 | ||
| lec23 Complex solutions and the fundamental matrix | 00:20:00 | ||
| lec24 Repeated eigenvalues and the matrix exponential | 00:20:00 | ||
| lec25 Phase planes I | 00:25:00 | ||
| lec26 Phase planes II | 00:15:00 | ||
| lec27 The Poincare-Bendixson theorem | 00:25:00 | ||
| Assessment | |||
| Submit Your Assignment | 00:00:00 | ||
| Certification | 00:00:00 | ||
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