Mathematical Methods I

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

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

Prerequisites: Class XII Mathematics.

Overview:  In this course we study multi-variable calculus. Concepts of derivatives and integration will be developed for higher dimensional spaces. This course has direct applications in most engineering applications. 

Detailed Syllabus:

1. Review of high school calculus.
2. Parametric curves (Vector functions): plotting, tangent, arc-length, polar coordinates, derivatives and integrals.                                                                    
3. Functions of several variables: level curves and surfaces, differentiation of functions of several variables, gradient, unconstrained and constrained optimization.
4. Double and triple integrals: integrated integrals, polar coordinates, cylindrical and spherical coordinates, change of variables.
5. Vector fields, divergence and curl, Line and surface integrals, Fundamental Theorems of Green, Stokes and Gauss.

References:

1. A Banner, The Calculus Lifesaver, Princeton University Press.
2. James Stewart, Essential Calculus – Early Transcendentals, Cengage.
3. G B Thomas and R L Finney, Calculus and Analytic Geometry, Addison-Wesley.
4. Erwin Kreyszig, Advanced Engineering Mathematics, Wiley.

Past Instructors: Ajit Kumar, Sneh Lata