Tentative Course Outline

Textbook: W. E. Boyce , R. C. DiPrima and D.B. Meade, Elementary Differential Equations and Boundary Value Problems, Global Edition (John Wiley & Sons, New York). :

• Week 1: Sections 1.1-1.3, 2.1 (Introduction, basic matheatical models, solutions of some ODE’s, classication of ODEs, first order linear ODEs)
• Week 2: Sections 2.2, 2.4, 2.6 (Separable equations, Diffrence between linear and nonlinear equations, Exact equations and integrating factors)
• Week 3: Sections 2.8, 3.1 (Bernoulli’s equation, The existence and uniqueness theorem, Second order equations with constant coefficients
• Week 4: Section 3.2 (Existence and uniqueness of solutions to the Cauchy problem for second order linear ODE’s. Abel’s theorem
• Week 5: Sections 3.3, 3.4 (Complex roots of the characteristic equation. Repeated roots.
• Week 6: Sections 3.6, 3.8  (Non-homogeneous equations. Method of variation of parameters. Forced periodic vibrations)
• Week 7: Sections 5.1 , 5.2 (Review of power series. Series solutions of ODE’s
• Week 8: Sections 5.3, 6.1 ( Series solutions near ordinary points. Laplace transform)
• Week 9:  Sections   6.2, 6.3 (Initial value problems.  Step functions)
• Week 10: Sections   6.4, 6.6 ( ODE’s with discontinuous forcing function. The  convolution integral)
• Week 11: Sections   Sections 7.1,-7.3 (Review of systems of algebraic equations, vector – functions, matrices)
• Week 12: Sections   7.4 -7.6 , 7.8(Systems of first order ODE’s. Abel’s Theorem. Homogeneous systems with constant coefficients. Complex – valued roots, Repeated  eigenvalues)
• Week 13: Sections  7.7 , 7.9, 10.1 Non-homogeneous systems of first order ODE’s. Two-point boundary value prblems
• Week 14: Sections   10.1- 10.5  Fourier series. Heat equation