BT 401-Mathematics III

BT401 Mathematics-III   3L-1T-0P 4 Credits

Module 1: Numerical Methods – 1: (8 hours): Solution of polynomial and transcendental equations – Bisection method, Newton-Raphson method and Regula- Falsi method. Finite differences, Relation between operators, Interpolation using Newton’s forward and backward difference formulae. Interpolation with unequal intervals: Newton’s divided difference and Lagrange’s formulae.

AD-401_Mathematics III_UNIT-1_Notes

AD-401_Mathematics III_Assignment_Unit-1

Module 2: Numerical Methods – 2: (6 hours): Numerical Differentiation, Numerical integration: Trapezoidal rule and Simpson’s 1/3rd and 3/8 rules. Solution of Simultaneous Linear Algebraic Equations by Gauss’s Elimination, Gauss’s Jordan, Crout’s methods, Jacobi’s, Gauss-Seidal, and Relaxation method.

AD-401_Mathematics III_UNIT-2_Notes

AD-401_Mathematics III_Assignment_Unit-2

Module 3: Numerical Methods – 3: (10 hours): Ordinary differential equations: Taylor’s series, Euler and modified Euler’s methods. Runge Kutta method of fourth order for solving first and second order equations. Milne’s and Adam’s predicator- corrector methods. Partial differential equations: Finite difference solution two dimensional Laplace equation and Poission equation, Implicit and explicit methods for one dimensional heat equation (Bender- Schmidt and Crank-Nicholson methods), Finite difference explicit method for wave equation.

AD-401_Mathematics III_UNIT-3_Notes

AD-401_Mathematics III_Assignment_Unit-3

Module 4: Transform Calculus: (8 hours): Laplace Transform, Properties of Laplace Transform, Laplace transform of periodic functions. Finding inverse Laplace transform by different methods, convolution theorem. Evaluation of integrals by Laplace transform, solving ODEs by Laplace Transform method, Fourier transforms.

AD-401_Mathematics III_UNIT-4_Notes

AD-401_Mathematics III_Assignment_Unit-4

Module 5: Concept of Probability: (8 hours): Probability Mass function, Probability Density Function, Discrete Distribution: Binomial, Poisson’s, Continuous Distribution: Normal Distribution, Exponential Distribution.

AD-401_Mathematics III_UNIT-5_Notes 

AD-401_Mathematics III_Assignment_Unit-5 

Textbooks/References:

1. P. Kandasamy, K. Thilagavathy, K. Gunavathi, Numerical Methods, S. Chand & Company, 2nd Edition, Reprint 2012.

2. S.S. Sastry, Introductory methods of numerical analysis, PHI, 4th Edition, 2005.

3. Erwin kreyszig, Advanced Engineering Mathematics, 9th Edition, John Wiley & Sons, 2006.

4. B.S. Grewal, Higher Engineering Mathematics, Khanna Publishers, 35th Edition, 2010.

5. N.P. Bali and Manish Goyal, A text book of Engineering Mathematics, Laxmi Publications, Reprint, 2010.

6. Veerarajan T., Engineering Mathematics, Tata McGraw-Hill, New Delhi, 2008.

7. P. G. Hoel, S. C. Port and C. J. Stone, Introduction to Probability Theory, Universal Book Stall, 2003 (Reprint).

8. S. Ross, A First Course in Probability, 6th Ed., Pearson Education India, 2002.

9. W. Feller, An Introduction to Probability Theory and its Applications, Vol. 1, 3rd Ed., Wiley, 1968. Statistics