2HS101 : Calculus

Learning Outcomes: 
Upon completion of this course, students will be able to:
Understand all basic fundamentals of Differentiation and Integration.
Prepare him/her for finding Area and Volume.
Apply mathematical formulas in various subjects of his/her branch.
Syllabus: 
Unit NoTopics
Differential Calculus

Review of the prerequisites such as limits of sequences and functions, continuity, uniform continuity and differentiability. Successive differentiation, Leibniz’s theorem (without proof), Taylor's & Maclaurin's expansions of single variable, Indeterminate forms.

Partial differentiation and its applications

Partial and total differential coefficient, Euler’s theorem, Transformations, Geometrical interpretation of partial derivatives, Tangent plane and Normal line, Jacobians, Taylor’s expansion for two variables, Errors and approximations,Maxima and Minima of functions of two variables,Lagrange method of undetermined multipliers to determine stationary values.

Integral Calculus

Reduction Formulae: Reduction formulae of the type ò sinn xdx,ò cosn x dx, ò sinmxcosnxdx ,ò tannxdxandò cotnxdx.Beta&Gammafunction,Error function, Elliptic integrals. Application of integration- Length of a curve,  for Cartesian, parametric & polarform.

Multiple integrals

Double integral, change of order of integration, transformation of variables by Jacobian only for double integration, change into polar co-ordinates in double integrals only ,Triple integral

Text Books: 
Name : 
Higher Engineering Mathematics
Author: 
Dr. B. S. Grewal
Reference Books: 
Name: 
Higher Engineering Mathematics
Author: 
Dr. K. R. Kachot
Name: 
Calculus and analytical geometry
Author: 
G. B. Thomas and R. L. Finney
Syllabus PDF: 
AttachmentSize
PDF icon 2HS101 calculas.pdf159.54 KB
branch: 
CBA
BDA
MA
Course: 
2014
Stream: 
B.Tech