MTech Advanced Mathematical Methods In Engineering syllabus for 1 Sem 2020 scheme 20MAU11

Errors and Simple Mathematical modelling:

Error definition, round off errors and truncation errors. Mathematical modelling and Engineering problem solving: Simple mathematical model, Conservation Laws of Engineering. Engineering Applications on : Deflection of Beams, Whirling of shafts, Terminal velocity of a freely falling body

Roots of Equations by Numerical Methods:

Newton- Raphson method, Horner’s Method. Muller’s method ,Barstow’s (or Lin’s method) , Graeffe’s roots squaring method

Ordinary Differential Equations:

Solving ODE”s using: Picard’s method, Runge-Kutta fourth order, Runge-Kutta Fehlberg method, Stiffness of ODE using shooting method, Boundary value problems.

Partial Differential Equations:

Classification of second order Partial Differential Equations. Solution of One dimensional wave equation,(Schmidt`s explicit formula), One dimensional heat equation by Schmidt method, Crank- Nicholson method, and Du Fort-Frankel method

Sampling Theory:

Testing of hypothesis using t and 𝜒 2 test, Goodness of fit, F-test, Analysis of Variance: One – way with/without interactions, problems related to ANOVA, Design of experiments, RBD.

Course outcomes:

At the end of the course the student will be able to:

CO1: Acquire the idea of significant figures, types of errors during numerical computation.

CO2: Develop the mathematical models of thermal system using ODE’s and PDE’s.

CO3: Learn the deterministic approach for statistical problems by using probability distributions.

CO4: Demonstrate the validity of the hypothesis for the given sampling distribution using standard tests and understand the randomization on design of experiments.

CO5: Classify and analyze mathematical tools applied to thermal engineering study cases

Question paper pattern:

The SEE question paper will be set for 100 marks and the marks scored will be proportionately reduced to 60.

• The question paper will have ten full questions carrying equal marks.
• Each full question is for 20 marks.
• There will be two full questions (with a maximum of four sub questions) from each module.
• Each full question will have sub question covering all the topics under a module.
• The students will have to answer five full questions, selecting one full question from each module.

Textbook/ Textbooks

(1)M K Jain, S.R.K Iyengar, R K. Jain, Numerical methods for Scientific and engg computation, New Age International, 2003

(2) B.S. Grewal: Higher Engineering Mathematics, Khanna Publishers, 44th Ed., 2017 (

3) 3. Steven C Chapra and Raymond P Canale, “Numerical Methods for Engineers,” 7th Ed., cGraw-Hill Edition, 2015.

Reference Books

(1) William W.H., Douglas C.M., David M.G.and Connie M.B., “Probability and Statistics in Engineering, 4th Edition, Willey Student edition, 2008

(2) Dr. B.S. Grewal, “Numerical Methods in Engineering and Science”, Khanna Publishers, 1999.

(3)K Shankar Rao, “Introduction to Partial Differential Equations” Prentice - Hall of India Pvt. Lt. , 1995 Edition.

(4) C. Ray Wylie and Louis C Barrett, “Advanced Engineering Mathematics”. 6th edition, McGraw-Hill, 1995.