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Syllabus B Tech Computer Science Fourth Semester Mathematics III BT401

- by Team_Engineers
Computer-Science-Engineering-4

Syllabus B Tech Computer Science Fourth Semester Mathematics III BT401

The concepts developed in this course will aid in quantification of several concepts in Computer Science Engineering that have been introduced at the Engineering courses. Technology is being increasingly based on the latest Syllabus B Tech Computer Science Fourth Semester Mathematics III BT401 is given here.

The objective of this course “Syllabus B Tech Computer Science Fourth Semester Mathematics III BT401“ is to develop ability and gain insight into the process of problem-solving, with emphasis on thermodynamics. Specially in following manner: Apply conservation principles (mass and energy) to evaluate the performance of simple engineering systems and cycles. Evaluate thermodynamic properties of simple homogeneous substances. Analyze processes and cycles using the second law of thermodynamics to determine maximum efficiency and performance. Discuss the physical relevance of the numerical values for the solutions to specific engineering problems and the physical relevance of the problems in general and Critically evaluate the validity of the numerical solutions for specific engineering problems. More precisely, the objectives are:

  • To enable young technocrats to acquire mathematical knowledge to understand Laplace transformation, Inverse Laplace transformation and Fourier Transform which are used in various branches of engineering.
  • To introduce effective mathematical tools for the Numerical Solutions algebraic and transcendental equations.
  • To acquaint the student with mathematical tools available in Statistics needed in various field of science and engineering.

BT 401 – Mathematics III

Unit 1
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.
Unit 2
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.
Unit 3
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.
Unit 4
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.
Unit 5
Module 5: Concept of Probability: (8 hours): Probability Mass function, Probability Density Function, Discrete Distribution: Binomial, Poisson’s, Continuous Distribution: Normal Distribution, Exponential Distribution.

Books Recommended

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.

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