MA4112 Mathematics for Plastic Technology Syllabus:

MA4112 Mathematics for Plastic Technology Syllabus – Anna University PG Syllabus Regulation 2021

COURSE OBJECTIVES :

 To understand the basic concept of numerical methods in solving ordinary differential equations.
 To understand the basic concept of numerical methods in solving partial differential equations.
 To understand the basics of random variables with emphases on the standard discrete and continuous distributions.
 To introduce the basic concept of Markovian Queueing Systems.
 To apply small and large sample tests through tests of hypothèses.

UNIT I NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS

Solution of first order ordinary differential equation – Taylor’s method – Euler’s method – Runge – Kutta method of fourth order – Predictor – Corrector Methods – Milne’s and Adam’s – Bashforth methods – Introduction to numeric use of the above techniques in plastics engineering and calculations.

UNIT II NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS

Classification of second order linear partial differential equations – Elliptic equations – Solution of Laplace equations – Solution of Poisson’s equation – Parabolic equations – Solution of one – dimensional heat equation – Hyperbolic equations – Solution of wave equation.

UNIT III PROBABILITY AND STATISTICS

Probability – Addition theorem – Multiplication theorem – Conditional probability – Baye’s theorem – Distribution functions – Binomial distribution – Poisson distribution – Normal distribution – Uniform distribution – Curve fitting – Fitting a straight line and second degree curve – Fitting a non linear curve – Correlation and regression.

UNIT IV QUEUEING MODELS

Poisson process – Markovian queues – Single and multiserver models – Little’s formula – Steady state analysis – Self service queue.

UNIT V TESTING OF HYPOTHESIS

Sampling distribution – Large sample and small samples – Testing of null hypothesis – Type I and Type II errors – “t” test and Chi square test – Goodness of fit – Fisher’s “F” test.

TOTAL : 60 PERIODS

COURSE OUTCOMES:

At the end of the course, students will be able to
CO1 Develop a good understanding of the various methods used for the numerical solution of scientific problems.
CO2 Learn various numerical methods of solving partial differential equations.
CO3 Analyze the performance in terms of probabilities and distributions achieved by the determined solutions.
CO4 Formulate the various kinds of Non-Markovian, MarkovianQueueing Models.
CO5 Apply the basic principles underlying statistical inference.(estimation and hypothesis testing)

REFERENCES:

1. Burden, R. C. and Faires, J. D., “Numerical Analysis”, 9th Edition, Cengage Learning, 2016.
2. Johnson, R.A., Miller, I and Freund J., “Miller and Freund’s Probability and Statistics for Engineers”, 9th Edition, Pearson Education, Asia, 2016.
3. Gupta, S. C. and Kapoor, Y. K., “Fundamentals of Mathematical Statistics”, 12th Edition, Sultan Chand and Sons, 2020.
4. Gross, D., Shortle, J.F., Thomson, J. M. and Harris, C. M., “Fundamentals of Queuing Theory “, 4th Edition, Wiley, 2014.