Sathyabama Institute of Science and Technology B.E. - Civil Engineering SMTA1401 Engineering Mathematics - IV Syllabus

[KunwarR]

Sathyabama Institute of Science and Technology B.E. - Civil Engineering SMTA1401 Engineering Mathematics - IV Syllabus

SATHYABAMA INSTITUTE OF SCIENCE AND TECHNOLOGY SCHOOL OF BUILDING AND ENVIRONMENT

SMTA1401
ENGINEERING MATHEMATICS - IV
(COMMON TO ALL BRANCHES EXCEPT BIO GROUPS, CSE & IT)
L T P Credits Total Marks
3 0 0 3 100

UNIT 1 FOURIER SERIES 9 Hrs.
Fourier series – Euler’s formula – Dirichlet’s conditions – Fourier series for a periodic function – Parseval’s identity (without
proof) – Half range cosine series and sine series – simple problems – Harmonic Analysis.

UNIT 2 APPLICATIONS OF PARTIAL DIFFERENTIAL EQUATION 9 Hrs.
One dimensional wave equation – Transverse vibrating of finite elastic string with fixed ends – Boundary and initial value
problems – 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 NUMERICAL METHODS FOR SOLVING EQUATIONS 9 Hrs.
Solution of algebraic equation and transcendental equation: Regula Falsi Method, Newton Raphson Method (including
solving algebraic equations in two variables f(x,y)=0 and g(x,y)=0) – Solution of simultaneous linear algebraic equations:
Gauss Elimination Method, Gauss Jacobi & Gauss Seidel Method.

UNIT 4 INTERPOLATION, NUMERICAL DIFFERENTATION AND INTEGRATION 9 Hrs.
Interpolation: Newton forward and backward interpolation formula, Lagrange’s formula for unequal intervals – Numerical
differentiation: Newton’s forward and backward differences to compute first and second derivatives – Numerical integration:
Trapezoidal rule, Simpson’s 1/3rd rule and Simpson’s 3/8th 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 - List the formulae in Fourier series, algebraic and transcendental equations. Recall the condition for convergence
of simultaneous linear algebraic equations
CO2 - Understand various numerical methods for Interpolation, differentiation and integration
CO3 - Apply the concepts of ordinary and partial differential equations by choosing the most suitable numerical method
CO4 - Categorize and implement the numerical solutions of algebraic, transcendental, simultaneous linear equations.
CO5 - Appraise the solution of one dimensional wave, one dimensional heat and two dimensional heat equations
CO6 - Develop Fourier series for different types of functions. Evaluate solution for Interpolation, numerical differentiation
and integration.

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", 41st Edition, Khanna Publications, New Delhi, 2011.
3. Kandasamy P., Thilagavathy K. & Gunavathy K., "Engineering Mathematics", 4th Revised Edition, S.Chand & Co.,
New Delhi, 2001.
4. Veerarajan T., "Engineering Mathematics", Tata McGraw Hill Publishing Co., New Delhi, 2005.
5. Steven C. Chapra, Raymond P. Canale, "Numerical Methods for Engineers", Tata McGraw Hill Publishing Co., New
Delhi, 2003.
6. Kandasamy P., Thilagavathy K. and Gunavathy, K., "Applied Numerical Methods", S.Chand & Co., New Delhi, 2003.

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