First Order Differential Equation: Formation. Methods of the solution: Separating the variables, homogeneous, linear and exact. Initial value problem. Applications: Growth population, Newton’s Law of Cooling, linear motion, simple electric circuit.
Second-Order Linear Differential Equation with Constant Coefficients: Methods of the solution: Method of undetermined coefficients and method of variation of parameters. Applications in mechanical motions include free oscillations and force oscillations.
Laplace Transforms: Linearity. First shift theorem. Multiplying by t. Unit step functions. Delta functions. Second shift theorem. Inverse Laplace transforms; Definition and its properties. Convolution theorem. Solving an initial and boundary value problems for linear differential equations with constant coefficients which involve unit step functions, Dirac Delta functions and periodic functions.
Fourier Series: Fourier series in the interval (–l, l). Odd and even functions. Half range Fourier series.
Partial Differential Equation: Heat equations. Wave equations.
What You Will Learn
Course Learning Outcomes
At the end of the course, students will be able to:
Identify the appropriate techniques to find the solution of first and second-order differential equations.
Apply the Laplace transform to solve initial and boundary value problems.
Produce the Fourier series of the given function.
Solve partial differential equations using the method of separation of the variable.
Independently proceeds lifelong learning in a guided PBL assignment/projects.