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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.


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.


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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
Submit Your Assignment 00:00:00
Certification 00:00:00

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