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 1.1-13, 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, linear and nonlinear equations, exact equations and inegrating factors)
• Week 3: Section 2.8,  ( Existence and uniqueness theorem, Picard’ iterations, Second order ODE’s with constant coefficients)
• Week 4   Section 3.2  (Linear  homogeneous equations. Existence and uniqueness theorem.  Wronskian. Abel’s theorem and applications)
• Week 5   Section 3.3  ( Review of Calculus topics. Complex roots of characteristic equation)
• Week 6   Section  3.4 (Repeated roots, reduction of order)
• Week 7  Section   3.5  (Non-homogeneous equations. Metod of variation of parameters)
• Week 8 Section   3..6  (Metod of variation of parameters. Resonance effect.)
• Week 9 Section    5.1, 5.2 . (Review of power series. Series solutions near ordinary point)
• Week 10 Section    6.1, 6.2 . (Laplace transform. Solution of Cauchy problems)
• Week 11 Section    6.3, 6.4, .6.6 (ODE’s with discontinuous forcing. Convolution Integral)
• .Week 12 Section   7.3- – 7.6  (Systems of ODE’s:)
• Weak  13 Sections   7.7  – 7.9   (Fundamental Matrix. Non-homogeneous systems)
• Weak  14 Sections   10.1 -10.4   (Fourier Series)
• Week  15  Sections   10-5-10.7   (Heat equation. Wave equation)