Sathyabama Institute of Science and Technology B.E. - Mechanical Engineering Part Time SMTA1109 Engineering Mathematics - II Syllabus

[Arvind Kumar]

Sathyabama Institute of Science and Technology B.E. - Mechanical Engineering Part Time SMTA1109 Engineering Mathematics - II Syllabus

SATHYABAMA INSTITUTE OF SCIENCE AND TECHNOLOGY SCHOOL OF MECHANICAL ENGINEERING

SMTA1109
ENGINEERING MATHEMATICS - II
(COMMON TO ALL BRANCHES)
L T P Credits Total Marks
3 * 0 3 100

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 AND INTEGRATION 9 Hrs.
Interpolation- Newton forward and backward interpolation formula- Lagranges formula for unequal intervals-Numerical
differentiation- Newton’s forward and backward differences to compute first and second derivatives-Numerical 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