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, 2.2 (Introduction, basic matheatical models, solutions od some ODE’s, classication of ODEs, first order linear ODEs, separable equations)
• Week 2: Sections 2.4, 2.6, 2.8 (Nonlinear first order equations Bernoulli equation, exact equations and integrating factors, the existence and uniqueness theorem)
• Week 3: Sections 2.8, 3.1, 3.2 (Existence and uniqueness theorem, homogeneous linear, the Wronskian, second order ODEs, Abel’s theorem)
• Week 4: Sections 3.2, 3.3, 3.4 Euler’s equation, complex roots of chatacteristic equation, repeated roots and reduction of order.
• Week 5: Sections 3.6, 3.8 Method of variation of parameters, forced periodic vibrations.
• Week 6: Sections 5.1 -5.2 Review of power series, series solutions near an ordinary point.
• Week 7: Sections 5.3, 6.1 Series solutions near an ordinary point, Laplace transform and its roperties.
• Week 8: Sections 6.2-6.4 Solution of initial value problems by using the Laplace transform, step functions, Differential equations wth discontinuous forsing functions
• Week 9: Sections 6.6, 7.1, 7.2 The convolution integral, Introduction to systems of first order ODEs, Matrices, Systems of linear algebraic equations.
• Week 10: Sections 7.3-7.5 Systems of linear algebraic equations, Eigenvalue problems, Basic theorey of systems of first order linear ODEs, Homogeneous linear systems.
• Week 11: Sections 7.6- 7.8 Complex – valued eigenvalues, Exponential of a matrix, Fundamental Matrix, Repeated eigenvalues.
• Week 12: Sections 7.9, 10.1, 10.2 Nonhomogeneous linear systems, Two-point boundary value problems, Fourier series.
• Week 13: Sections 10.3, 10.4, 10.5 The Fourier convergence theorem, even and odd functions, Separation of variables, heat equation.
• Week 14: 10.6 Other heat conduction problems.