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Sathyabama Institute of Science and Technology B.E.  Civil Engineering Part Time SM SATHYABAMA INSTITUTE OF SCIENCE AND TECHNOLOGY SMTA1109 ENGINEERING MATHEMATICS  II (Common to all Branches) UNIT 1 PARTIAL DIFFERENTIAL EQUATIONS 9 Hrs. Formation of equations by elimination of arbitrary constants and arbitrary functions – Solutions of PDE general, particular and complete integrals – Solutions of First order Linear PDE (Lagrange’s linear equation) – Solution of Linear Homogeneous PDE of higher order with constant coefficients. UNIT 2 APPLICATIONS OF PARTIAL DIFFERENTIAL EQUATIONS 9 Hrs. One dimensional wave equation – Transverse vibrating of finite elastic string with fixed ends Boundary and initial value problems – Fourier solution – one dimensional heat equation – steady state problems with zero boundary conditions Two dimensional heat equation – steady state heat flow in two dimensions Laplace equation in Cartesian form( No derivations required). UNIT 3 ALGEBRAIC AND TRANSCENDENTAL EQUATIONS 9 Hrs. Solution of Algebraic equation by Regula Falsi Method , Newton Raphson Method – Solution of simultaneous linear algebraic equations – Gauss Elimination Method , Gauss Jacobi & Gauss Seidel Method. UNIT 4 INTERPOLATION, NUMERICAL DIFFERENTATION & INTEGRATION 9 Hrs. Interpolation Newton forward and backward interpolation formula Lagranges formula for unequal intervalsNumerical differentiation Newton’s forward and backward differences to compute first and second derivativesNumerical integration – Trapezoidal rule – Simpson’s one third rule and three eighth rule . UNIT 5 NUMERICAL SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS AND PARTIAL DIFFERENTIAL EQUATIONS 9 Hrs. Ordinary differential equations – Taylor series method – Runge Kutta method for fourth order Partial differential equations – Finite differences – Laplace equation and its solutions by Liebmann’s process Solution of Poisson equation – Solutions of parabolic equations by Bender Schmidt Method – Solution of hyperbolic equations. Max. 45 Hrs. COURSE OUTCOMES On completion of the course, student will be able to CO1  Classify partial differential equation and Categorize and implement the various numerical methods for Interpolation CO2  Form partial differential equation Illustrate the solution of first order exact equations CO3  Apply the concept of the numerical solutions to algebraic and transcendental equations CO4  Appraise the solution of ordinary and partial differential equations by choosing the most suitable numerical method CO5  Produce the solution of ordinary and linear partial differential equations TEXT / REFERENCE BOOKS 1. Kreyszig, E., "Advanced Engineering Mathematics", 8th Edition, John Wiley and Sons (Asia) Pvt. Ltd., Singapore, 2001. 2. Grewal B.S., "Higher Engineering Mathematics", Tata McGraw Hill Publishing Co., New Delhi, 1999. 3. Kandasamy P., Thilagavathy K. and Gunavathy K., "Engineering Mathematics", 4th Edition, S.Chand & Co., New Delhi, 2001. 4. Kandaswamy P. & Co., "Numerical Methods", S.Chand Publications, Chennai 2009. END SEMESTER EXAMINATION QUESTION PAPER PATTERN Max. Marks: 100 Exam Duration: 3 Hrs. PART A: 10 Questions of 2 marks each  No choice 20 Marks PART B: 2 Questions from each unit of internal choice; each carrying 16 marks 80 Marks 
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