NIRMA UNIVERSITY
Institute of Technology
(B. Tech. in All)
(Semester I)
| L | T | P | C |
| 3 | 1 | 0 | 4 |
| Course Code | MA101 |
| Course Title | Calculus |
Course Learning Outcomes (CLO):
At the end of the course, student will able to-
- find higher order derivatives and hence represent function in power series of (x-a)
- apply the knowledge of function of several variables and its derivatives in engineering problems
- employ the knowledge of special functions (Gamma, Beta, Elliptic, Error) and its application in engineering problems
- use the knowledge of multiple integration and its application for solving engineering problems
Syllabus:
| Differential Calculus Teaching hours: 15 | |
| Review of limits, continuity and differentiability, Successive differentiation, Leibnitz theorem (without proof), Indeterminate forms, Taylor’s and Maclaurin’s expansion of single variable, Partial Differentiation, Total derivative, Chain Rule, Implicit function, Euler’s theorem and its applications, Taylor’s and Maclaurin’s expansion of function of several variables, Maxima and Minima of function of several variables, Lagrange’s method of undetermined multipliers, Jacobian. | |
| Integral Calculus Teaching hours: 30 | |
| Review of proper and improper integrals, Reduction formulae, Beta-Gamma functions, Error function, Tracing of curves, Rectification, Quadrature, Volume of solid of revolution, Area of surface of revolution, Double integral and evaluation, Change of order of integration, Change of variable, Triple integral and evaluation, Area using double integration, Volume as double and triple integration, Volume of solid by double integration. | |
Suggested Readings:
- Thomas, G.B. (2008) Thomas’ Calculus. Chennai: Pearson Publication.
- Thomas, G. B. and Finney, R. L. (1996) Calculus and Analytic Geometry. Delhi: Narosa Publication
- Stewart, J (2008) Calculus. Belmont, California: Thomson Learning.
- Grewal, B. S. (2005) Higher Engineering Mathematics. Delhi: Khanna Publication
- Sharma and Yeolekar (2009) Engineering Mathematics Vol. I. New Delhi: PHI
- Kachot, K. R. (2013) Higher Engineering Mathematics Vol. I. Ahmedabad, Gujarat: Mahajan Publication
L = Lecture, T = Tutorial, P = Practical, C = Credit
Calculus 