Differential Calculus and Numerical Methods (1BMATC201)

Differential Calculus and Numerical Methods

Course Code 1BMATC201 
CIE Marks 50
Teaching Hours/Week (L:T:P: S) 3:2:0:0 
SEE Marks 50
Total Hours of Pedagogy 40Hours Theory + 20Hours Tutorials 
Total Marks 100
Credits 4 
Exam Hours 3 
Examination type (SEE) Theory

Module-1: Integral Calculus

Multiple Integrals: 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: Partial Differential Equations (PDE) 

Formation of PDEs by elimination of arbitrary constants and functions. Solution of nonhomogeneous PDE by direct integration. Homogeneous PDEs involving derivatives with respect

to one independent variable only. Method of Separation of variables. Application of PDE:

Derivation of one-dimensional heat equation and wave equation.

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, Statements of Green’s theorem

and Stoke’s theorem, problems without verification.

Textbook -1. Chapter -8.4-8.14

Module-4: Numerical Methods - 1 

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

methods, problems.

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's 1/3rd and 3/8th rules.

Text Book -1. Chapter -28.1-28.2, 29.1-30.8

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 method and Adams-Bashforth predictor-corrector method.

Textbook -1. Chapter -28.1-30.8

Suggested Learning Resources:

Textbooks:

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

2. E. Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons, 10thEd., 2018.

3. 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. B.V. Ramana, Higher Engineering Mathematics, McGraw-Hill Education, 11th Ed., 2017

2. Srimanta Pal & Subodh C.Bhunia, Engineering Mathematics, Oxford University Press, 3rd Ed., 2016.

3. N. P. Bali and Manish Goyal, A Textbook of Engineering Mathematics, Laxmi Publications, 10th Ed.,

2022.

4. H. K. Dass and Er. Rajnish Verma, Higher Engineering Mathematics, S. Chand Publication,

3rd Ed., 2014.

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

Scientists, McGraw-Hill, 3rd Ed., 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, 5th Ed., 2012.