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Week 1 |
| First order ordinary differential equations: Definition and classification of differential equations. Basic ideas; solutions of differential equations, initial and boundary value problems. Solving separable and linear equations. |
Week 2 |
| Methods of solution of homogeneous equations, exact equations, Bernoulli equations and other substitutions. |
Week 3 |
| Applications such as law of cooling , the free fall and chemical reactions. |
Week 4 |
| Linear second order ordinary differential equations with constant coefficients: Second order homogeneous differential equations. Solution of nonhomogenous equations. Method of undetermined coefficients. |
Week 5 |
| Method of variation of parameters. Solving higher order ODE’s up to fourth order using method of the undetermined coefficients. |
Week 6 |
| Applications of second order differential equations: mechanical vibrations, damped and undamped free vibrations, and electrical circuits, circuits with and without impedance/resistance. |
Week 7 |
| Laplace transforms: Definition of Laplace transforms, derivation of Laplace transforms for standard elementary functions. Linearity property, first shifting theorem, multiplication by t^n. Test 1 (15%) |
Week 8 |
| Laplace transforms of unit step functions, Laplace transforms of Delta Dirac functions, Second shifting Theorem, Laplace transforms of the derivatives. |
Week 9 |
| Inverse Laplace transforms and Convolution theorem. |
Week 10 |
| Solving initial value problems ( IVP), boundary value problems (BVP) and system of differential equation using Laplace transform. |
Week 11 |
| Fourier series: Graph sketching of periodic functions, even and odd functions. Fourier series for periodic functions. |
Week 12 |
| Fourier series for even and odd functions, Half-range Fourier series. Test 2 (20%) |
Week 13 |
| Partial differential equations. Basic concepts, classifications. Method of d’Alembert for solving wave equations. |
Week 14 |
| Method of separation of variables for solving heat equation (consolidation theory), wave equations.Method of separation of variables for solving Laplace equations. |
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