Mathematical Methods II

Core course for all B.Tech. Programs. Optional for B.Sc. (Research) Chemistry. Not available as UWE.

Credits (Lec:Tut:Lab)= 3:1:0 (3 lectures and 1 tutorial weekly)

Prerequisites: Class XII Mathematics

Overview:  We will study Ordinary Differential Equations which are a powerful tool for solving many science and engineering problems. This course also covers some basic linear algebra which is needed for systems of ODEs.

Detailed Syllabus:

1. First order ODEs: separable, exact, linear
2. Second order ODEs: homogeneous and nonhomogeneous linear, linear with constant coefficients, Wronskian, undetermined coefficients, variation of parameters
3. Laplace transform: definition and inverse, linearity, shift, derivatives, integrals, initial value problems, time shift, Dirac’s delta function and partial fractions, convolution, differentiation and integration of transform
4. Matrices: operations, inverse, determinant, eigenvalues and eigenvectors, diagonalization
5. Systems of ODEs: superposition principle, Wronskian, constant coefficient systems, phase plane, critical points, stability

References:

1. James Stewart, Essential Calculus – Early Transcendentals, Cengage.
2. Erwin Kreyszig, Advanced Engineering Mathematics, Wiley.

Past Instructors: Ajit Kumar, Neha Gupta