Multivariable Calculus and Numerical Methods (1BMATM201)

Multivariable Calculus and Numerical Methods

Course Code 1BMATM201 
CIE Marks 50
Teaching Hours/Week (L:T:P: S) 3:2:0:0 
SEE Marks 50
Total Hours of Pedagogy 40Hours Theory + 20-24Hours Tutorials 
Total Marks 100
Credits 4 
Exam Hours 3 Hours
Examination type (SEE) Theory

Module-1: Integral Calculus

Multiple Integrals: Definition, Evaluation of double and triple integrals, evaluation of double

integrals by change of order of integration, changing into polar coordinates. Applications to find

Area and Volume by double integral.

Beta and Gamma functions: Definitions, properties, relation between Beta and Gamma functions.

Textbook 1: Chapter:7.1-7.16

Module-2: Ordinary Differential Equations of Higher Order

Higher-order ordinary differential equations with constant coefficients, homogeneous and nonhomogeneous equations-eax, sin(ax+b), cos(ax+b), xn

only, Method of variation of parameters,

Cauchy’s and Legendre’s homogeneous differential equations. Applications: mass spring model.

Textbook 1: Chapter 17.8-17.12, Chapter 13.4-13.9(1,2), Chapter 14:14.2,

Textbook 2: Chapter 9: 9.13

Module-3: Vector Calculus 

Scalar and vector fields. Gradient, directional derivative, divergence and curl-physical

interpretation, solenoidal vector fields, irrotational vector fields and scalar potential.

Vector Integration: Line integrals, work done by a force and flux. Statement of Green’s theorem

and Stoke’s theorem and problems without verifications.

Textbook 1: Chapter 8 :8.4,8.5,8.6,8.7(1,2),8.9,8.18(1),8.11,8.13,8.14,8.17

Module-4: Numerical Methods- 1

Solution of algebraic and transcendental equations: Regula-Falsi and Newton-Raphson methods.

Interpolation: Finite differences, Interpolation using Newton’s forward and backward difference

formulae, Newton’s divided difference formula and Lagrange’s interpolation formula.

Numerical integration: Trapezoidal, Simpson's1/3rd and 3/8thrules.

Textbook1:Chapter28: Chapter29:29.1-29.12,Chapter 30:30.2-,30.8

Module-5: Numerical Methods– 2 

Numerical solution of ordinary differential equations of first order and first degree: Taylor’s series

method, Modified Euler’s method, Runge-Kutta method of fourth order, Milne’s predictorcorrector formula and Adams-Bashforth predictor-corrector method.

Textbook 1: Chapter 32 :32.3- 32.10

Suggested Learning Resources:

Textbooks:

1. B.S. Grewal, Higher Engineering Mathematics, Khanna Publishers,44nd Ed., 2021.

2. B.V.Ramana, HigherEngineeringMathematics,McGraw-HillEducation,11thEd., 2017

3. E.Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons,10th Ed.,2018.

4. M.K. Jain, S.R.K. Iyengar and R.K. Jain:Numerical Methods for Scientific and Engineering

Computation, New Age International Publishers, 8thEd., 2022.

Reference books:

1. Srimanta Pal & Subodh C.Bhunia, Engineering Mathematics, Oxford University Press, 3rd

Ed., 2016.

2. N. P.Baliand ManishGoyal, A Text book of Engineering Mathematics, Laxmi

Publications,10thEd.,2022.

3. H.K.Dassand Er.RajnishVerma, Higher Engineering Mathematics, S.Chand Publication, 3rd

Ed., 2014.

4. Ray Wylie, Louis C.Barrett, Advanced Engineering Mathematics, McGrawHill Book Co.,

New York, 6th Ed., 2017.

5. Steven V. Chapra and Raymond P. Canale, Applied Numerical Methods with Matlab for

Engineers and Scientists, Mc Graw-Hill,3rdEd., 2011.

6. Richard L. Burden, Douglas J. Faires and A. M. Burden, Numerical Analysis, 10th Ed.,2010,

Cengage Publishers.

7. S.S. Sastry,“Introductory Methods of Numerical Analysis”,PHI Learning Private Limited,

5thEd.,2012.