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Sathyabama Institute of Science and Technology B.E. - Aeronautical Engineering SMTA1301 Engineering Mathematics Syllabus


SATHYABAMA INSTITUTE OF SCIENCE AND TECHNOLOGY SCHOOL OF MECHANICAL ENGINEERING

SMTA1301
ENGINEERING MATHEMATICS - III
(COMMON TO AERO, AUTO, MECH AND MECHATRONICS)
L T P Credits Total Marks
3 * 0 3 100

UNIT 1 COMPLEX VARIABLES 9 Hrs.
Analytic functions – Cauchy - Riemann equations in Cartesian and polar form – Harmonic functions – Properties of
analytic functions – Construction of analytic functions using Milne – Thompson method – Some Standard Transformations
– Translation, Magnification and Rotation, Inversion and Reflection and simple problems based on the above - Bilinear
transformation.

UNIT 2 COMPLEX INTEGRATION 9 Hrs.
Cauchy’s integral theorem – Cauchy’s integral formula – problems – Taylor’s and Laurent’s series – Singularities – Poles
and Residues – Cauchy’s residue theorem and problems – Contour Integration (Integration around the Unit circle)

UNIT 3 Z TRANSFORMATION AND DIFFERENCE EQUATIONS 9 Hrs.
Z –Transform – Elementary properties – Inverse Z – Transform – Partial Fraction method, Convolution method, Residue
method – Formation of difference equations – Solution of difference equations using Z-Transform.

UNIT 4 PARTIAL DIFFERENTIAL EQUATIONS 9 Hrs.
Formation of equations by elimination of arbitrary constants and arbitrary functions – Solutions of First order Linear PDE –
Lagrange’s linear equation – Solution of Linear Homogeneous PDE of higher order with constant coefficients.

UNIT 5 THEORY OF SAMPLING AND TESTING OF HYPOTHESIS 9 Hrs.
Test of Hypothesis – Large samples – Z test – Single proportion – Difference of proportions – Single mean – Difference of
means – Small samples – Student‘s t test – Single mean – Difference of means –Test of variance – Fisher’s test –
Chi square test: Goodness of fit, Independence of attributes.
Max.45 Hrs.

COURSE OUTCOMES
On completion of the course, student will be able to
CO1 - Define analytic functions, theorems on complex integration, Singularities. List Fourier transform of standard
functions and Parseval’s identity. Form partial differential equation.
CO2 - Explain the properties of analytic functions and Fourier transform. Understand the concept of Taylor’s and
Laurent’s series Understanding the concepts of Z- transformation and its applications and solving it.
CO3 - Apply bilinear transformation, Taylor’s and Laurent’s series. Solve problems on Fourier transform.
CO4 - Classify partial differential equation and test of hypothesis.
CO5 - Evaluate problems on complex integration and Appraise sampling theory using different tests.
CO6 - Construct an analytic function, produce the solution of linear partial differential equations.

TEXT / REFERENCE BOOKS
1. Erwin Kreyszig, Advanced Engineering Mathematics, 8th Edition, John Wiley and Sons Asia Pvt. Ltd., Singapore,
2001.
2. Grewal B.S., Higher Engineering Mathematics, 41th Edition, Khanna Publications, 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., NewDelhi, 1999.
5. J.W. Brown and R.V. Churchill, Complex Variables and Applications, 7th Ed., Mc.Graw Hill, 2004.
6 Gupta S.C., Kapoor V.K., Fundamentals of Mathematical Statistics, S. Chand & Company, 2012.
7 Bali N.P and Manish Goyal, A Text book of Engineering Mathematics, Eigth Edition, Laxmi Publications Pvt Ltd.,
2011.

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