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UNIT I |
PROBABILITY AND RANDOM VARIABLES |
9 |
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Axioms of probability – Conditional probability – Total probability – Baye᎙s theorem- Discrete and continuous random variables ᎓ Moments ᎓ Moment generating functions and their properties. |
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UNIT II |
TESTING OF HYPOTHESIS |
9 |
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Sampling distributions ᎓ Tests for single mean, proportion and difference of means (large and small samples) ᎓ Tests for single variance and equality of variances ᎓ Chi square test for goodness of fit ᎓ Independence of attributes. |
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UNIT III |
SOLUTIONS OF EQUATIONS |
9 |
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Newton Raphson method ᎓ Solution of linear system of equations ᎓ Gauss elimination method ᎓ Pivoting Gauss Jordan methods ᎓ Iterative methods of Gauss Jacobi and Gauss Seidal. |
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UNIT IV |
INTERPOLATION, NUMERICAL DIFFERENTIATION AND NUMERICAL INTEGRATION |
9 |
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Lagrange᎙s interpolation ᎓ Newton᎙s forward and backward difference interpolation ᎓ Approximation of derivatives using interpolation polynomials ᎓ Numerical single integration using Trapezoidal and Simpson᎙s 1/3 rules. |
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UNIT V |
NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS |
9 |
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Single step methods: Taylor᎙s series method ᎓ Euler᎙s method ᎓ Modified Euler᎙s Method ᎓ Fourth order Runge-Kutta method for solving first order equations ᎓ Multi step methods: Milne᎙s predictor-corrector methods for solving first order equations. |
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L:45 |
T:0 |
P: 0 |
Total: 45 Periods |
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TEXT BOOKS |
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T1 |
Johnson, R.A., Miller, I and Freund J., Miller and Freund᎙s Probability and statistics for Engineers, Pearson Education Asia, 9th Edition, 2018. |
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T2 |
Grewal, B.S and Grewal, J.S, Numerical methods in Engineering and Science, 10th Edition, Khanna Publishers, New Delhi, 2015 |
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REFERENCES |
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R1 |
Walpole. R.E., Myers. R.H., Myers. S.L., and Ye. K., Probability and Statistics for Engineers and Scientists,9th Edition, Pearson Education, Asia, 2010. |
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R2 |
Burden, R.L and Faires, J.D, “Numerical Analysis”, 9 th Edition, Cengage Learning, 2016. |
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R3 |
Devore. J.L., “Probability and Statistics for Engineering and the Sciences”, Cengage Learning, New Delhi, 8 th Edition, 2014. |
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R4 |
Gerald. C.F. and Wheatley. P.O. “Applied Numerical Analysis” Pearson Education, Asia, New Delhi, 7th Edition, 2007. |
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R5 |
Spiegel,M.R., Schiller, J. and Srinivasan,R.A., “Schaum᎙s Outlines on Probability and Statistics, Tata McGraw Hill edition, 4th Edition, 2012. |
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COURSE OUTCOMES At the end of the course students should be able to |
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CO 1 |
Revise fundamental knowledge of the concepts of probability distributions which can describe real life phenomenon. |
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CO 2 |
Apply the statistical concepts and tools for engineering applications and to use different types of research methodology techniques for decision making under uncertainty. |
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CO 3 |
Compute the algebraic equations representing steady state models formed in engineering problems. |
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CO 4 |
Demonstrate the numerical techniques of interpolation in various intervals and apply the numerical techniques of differentiation and integration for engineering problems. |
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CO 5 |
Predict the system dynamic behaviour through solution of ODEs modelling the system. |
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