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Contents
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| Week 1: |
Some geometrical and physical problems reducing to ordinary differential equations (ODE), basic concepts and definations, isoclines |
| Week 2: |
Equations with separated variables, homogeneous equations |
| Week 3: |
Linear, Bernoulli and Riccati equations |
| Week 4: |
Exact equations, integrating factors |
| Week 5: |
Euler lines, Arzela’s lemma, Peano’s existence theorem |
| Week 6: |
Osgood’s uniqueness theorem, Lipschitz condition, Gronwall’s integral inequality |
| Week 7: |
Cauchy-Picard existence and uniqueness theorem, method of successive approximations |
| Week 8: |
Midterm exam I. First order ODE not solved by derivative , existence and uniqueness theorem for Cauchy problem |
| Week 9: |
Method adding parameter, Lagrange and Clairaut equations |
| Week 10: |
Singular solutions and methods to find them |
| Week 11: |
Linear systems of ODE, properties of solutions of homogeneous linear systems |
| Week 12: |
Midterm exam II. Fundamental system of solutions, Wronskian, Liouville-Ostrogradski-Jakoby formula |
| Week 13: |
General solution of homogenous linear systems with constant coefficients |
| Week 14: |
Method of variation of constants, general solution of homogenous high order linear equations with constant coefficients. |
| Week 15*: |
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| Week 16*: |
Final exam. |
| Textbooks and materials: |
Ordinary Differential Equations (I. G. Petrovski) |
| Recommended readings: |
An Introduction to Ordinary Differential Equations (Earl A. Coddington)
Differential Equations (S. L. Ross)
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* Between 15th and 16th weeks is there a free week for students to prepare for final exam.
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