NUMERICAL METHODS (1BMATS201)

NUMERICAL METHODS

Course Code 1BMATS201 
Semester 2
CIE Marks 50
Teaching Hours/Week (L: T: P: S) 3:2:0:0 
SEE Marks 50
Total Hours of Pedagogy 40Hours Theory + 20Hours Tutorial 
Total Marks 100
Credits 4 
Exam Hours 3 hrs
Examination type (SEE) Theory

Module-1: Introduction to Numerical Methods 

Errors and their computation: Round off error, Truncation error, Absolute error, Relative error and

Percentage error.

Solution of algebraic and transcendental equations: Bisection, Regula-Falsi, Secant and

Newton-Raphson methods.

Textbook-1: Chapter-1: section 1.3, Chapter-2: sections 2.1-2.3.

Module-2: Numerical solutions for system of linear equations 

Norms: Vector norms and Matrix norms-L1, L2 and L∞, Ill conditioned linear system, condition

number.

Solution of system of linear equations: Gauss Seidel method and LU-decomposition method.

Eigenvalues and Eigen vectors: Rayleigh power method, Jacobi’s method.

Textbook-1: Chapter-3: sections 3.3-3.4, 3.7, 3.11

Module-3: Interpolation 

Finite differences, interpolation using Newton Gregary forward and Newton Gregary backward

difference formulae, Newton’s divided difference. Lagrange interpolation formulae, piecewise

interpolation-linear and quadratic.

Textbook-1: Chapter-4: sections 4.1-4.4, 4.6

Module-4: Differential Equations of First and Higher Order 

Linear and Bernoulli`s differential equations. Exact and reducible to exact differential equations

with integrating factors on

Homogeneous and non-homogeneous

Differential equations of higher order with constant coefficients. Inverse differential operators -

eax, sin(ax+b), cos(ax+b) and xn

Textbook-3: Chapter-11: Sections 11.9-11.12 Chapter-13: Sections 13.1-13.7

Module-5: Numerical Integration and Numerical Solution of Differential Equations

Numerical integration: Trapezoidal, Simpson's 1/3rd, Simpson’s 3/8th rule and Weddle’s rule.

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 and Milne’s

predictor-corrector method.

Textbook-1: Chapter-5: Sections 5.6, 5.7. Chapter-6: Sections 6.3, 6.4, 6.7

Textbook-3: Chapter-30: Sections 30.4-30.10, Chapter-32: Sections 32.3-32.9,

Suggested Learning Resources: 

Textbooks:

1. M.K. Jain, S.R.K. Iyengar and R.K. Jain, Numerical Methods for Scientific and Engineering Computation,

New Age International Publishers, 8thEd., 2022.

2. David C Lay, Linear Algebra and its Applications, Pearson Publishers, 5th Ed., 2023.

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

Reference books:

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

2. N. P. Bali and Manish Goyal, A Textbook of Engineering Mathematics, Laxmi Publications,

10th Ed., 2022.

3. S. S. Sastry, Introductory Methods of Numerical Analysis, PHI Learning Private Limited, 5th Ed. 2012.

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

Scientists, McGraw-Hill, 3rd Ed., 2011.

5. Richard L. Burden, Douglas J. Faires, A. M. Burden, Numerical Analysis, 10th Edition.,2010, Cengage

Publishers.