First order ODE : Ordinary Differential Equations – Basic concepts, modelling, first order ODEs, exact ODEs, integrating factors. ( 5 hrs )
Second order ODE : , homogeneous linear ODEs, Euler-Cauchy equations, existence and uniqueness of solution, Wronskian, non-homogeneous ODEs, variation of parameters. Modelling of free and forced oscillations of spring-mass system, resonance. ( 1 3 hrs )
Higher order ODEs, homogeneous and nonhomogeneous linear ODEs. System of ODEs – Phase space, velocity field, flow, fixed points, stability of fixed points. Qualitative methods for ODEs. ( 1 2 hrs )
Fourier Series, arbitrary period, even and odd expressions, half range expressions, Fourier Integral, Fourier transforms. Laplace transform, transform of derivatives and integrals, solution of initial value problems by Laplace transform. ( 1 5 hrs )
Partial differential equations – Basics of PDEs. Modelling of vibrating string, wave equation, solution by separation of variables, D’Alembert’s solution, Heat flow modelling, heat equation, solution of heat equation by Fourier series, heat equation in very long bars, solution by Fourier transforms, Laplace’s equation and its solution. ( 1 5 hrs )
Course Evaluation Pattern:
Test-1 -15 marks (two hour test)
CA - 20 marks (Quizzes / assignments / lab practice) Test – 2- 15 marks (two-hour test)
End semester- 50 marks. Total - 100 marks.
Supplementary exam for this course will be conducted as a three-hour test for 50 marks.