|
Week - 1 |
First-order differential equations: Basic definitions and concepts of differential equations, integrals as general and particular solutions. |
|
Week - 2 |
Slope fields and solution curves. Separable equations and applications. |
|
Week - 3 |
Linear first-order equations. Substitution methods and exact equations. |
|
Week - 4 |
Linear equations of higher order. Second-order linear equations. |
|
Week - 5 |
General solutions of linear equations. |
|
Week - 6 |
Homogeneous equations with constant coefficients. |
|
Week - 7 |
Nonhomogeneous equations and undetermined coefficients. |
|
Week - 8 |
Undetermined coefficients. Variation of parameters. |
|
Week - 9 |
Electrical circuit applications. |
|
Week - 10 |
Laplace transform methods. Laplace transforms and inverse transforms. |
|
Week - 11 |
Transformation of initial-value problems. Translation and partial fractions. |
|
Week - 12 |
Derivatives, integrals and products of transforms. Convolution theorem. |
|
Week - 13 |
Periodic and piecewise continuous input functions. Impulse (delta) functions. Impulse response and transfer function. |
|
Week - 14 |
Linear systems of differential equations: The matrix exponential. |