

Contents


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: 
CauchyPicard 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, LiouvilleOstrogradskiJakoby 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*: 
 
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)


* Between 15th and 16th weeks is there a free week for students to prepare for final exam.

