MTech Mathematical Modeling In Engineering syllabus for 1 Sem 2020 scheme 20MAP11

Module-1 Model fitting 0 hours

Model fitting

Introduction, Fitting models to data graphically - Analytic methods of model fitting - Chebyshev Approximation Criterion, Minimizing the Sum of the Absolute Deviations, Least-Squares Criterion, Relating the Criteria. Applying the least squares criterion- Fitting a Straight Line, Fitting a Power Curve, Transformed Least Squares Fit, Example: Vehicular stopping distance

Module-2 Modelling with a differential equations 0 hours

Modelling with a differential equations

Introduction- Population growth, Prescribing Drug Dosage, Breaking distance revisited. Graphical solutions of Autonomous differential equations, Example: Drawing a phase line and sketching solution curves, Numerical approximation methods - First-Order Initial Value Problems, Approximating Solutions to Initial Value Problems: Example 1: Using Euler’s method, Example 2: A saving certificate revisited.

A d v e r t i s e m e n t
Module-3 Ordinary Differential Equations 0 hours

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.

Module-4 Partial Differential Equations 0 hours

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.

Module-5 Sampling Theory 0 hours

Sampling Theory:

Testing of hypothesis using t and 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:

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

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

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

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

5. 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 A First course in Mathematical modeling Frank.R.Giordano, Maurice.D.Weir, Willium.P.Fox China machine press 2003

2 Numerical methods for Scientific and Engg computation M K Jain, S.R.K Iyengar, R K. Jain New Age International 2003

 

Reference Books

1 Higher Engineering Mathematics B.S. Grewal Khanna Publishers 2017

2 Probability and Statistics for Engineers and Scientists R.E, Walpole, R.H.Myres, S.L.Myres and Keying Ye Pearson 2012

3 Probability and Statistics in Engineering William W.H., Douglas C.M., David M.G.and Connie M.B Wiley 2008

4 Advanced Engineering Mathematics C. Ray Wylie and Louis C Barrett McGraw-Hill 1995

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