Transform Techniques and Optimization Theory (1BMATEC301)

Transform Techniques and Optimization Theory

Course Code 1BMATEC301 
Scheme 2025
Type of Course ASC 
Semester III
Teaching Hours/Week (L:T:P) 3:2:0 
CIE Marks 50
Total Hours of Pedagogy (L :T:P:SL&TW) 42:28:0:50 
SEE Marks 50
Credits 4 
Total Marks 100
Examination type (SEE) Theory 
Exam Hours 3

Module-1

Fourier series: Periodic functions, Euler’s Formula, Conditions for Fourier expansion (Dirichlet’s condition), Fourier series of functions i) having points of discontinuity, ii) with period 2𝜋, iii) with change of interval (arbitrary period) and iv) Even and odd functions. Half rang Fourier series. Practical harmonic analysis.

Module-2

Fourier Transforms: Infinite Fourier transform, Infinite Fourier sine and cosine transforms, Properties-Linear property, Change of scale, shifting property, Modulation theorem. Inverse transforms, Convolution theorem and its significance, Fourier transform of derivatives and integrals, Solution of PDE’s using Fourier transforms. Discrete Fourier transform (DFT), Inverse DFT, Fast Fourier transform (FFT)

Module-3

Discrete Transforms - Z transforms: Z-transform of Standard functions, Linearity property, Damping rule, Shifting property, Initial and final value theorems, Inverse Z-transform- Power series method, Partial fraction method, inverse integral method. Convolution theorem, Application of Z-transforms to solve difference equations.

Module-4

Linear programming problems: Introduction to optimization techniques, nature and characteristics of operation research; Introduction to Linear programming, graphical solution, solution by simplex and Big M method.

Module-5

Transportation problems: Formulation of transportation problem, Initial Basic feasible solution by North-West Corner method, Least cost method, Vogel’s approximation method. Optimal solutions-Problems. Formulation of assignment problems, Hungarian method-Problems

Suggested Learning Resources: 

Text books:

1. B.S. Grewal, Higher Engineering Mathematics, 45th Edition, Khanna Publishers.

2. Erwin Kreyszig, Advanced Engineering Mathematics, 10th Edition, Wiley India.

3. H.K. Dass and Er. Rajnish Verma, Higher Engineering Mathematics, S. Chand Publications.

Reference books / Manuals:

1. Ruel V. Churchill and James Ward Brown, Fourier Series and Boundary Value Problems, McGraw-Hill Education.

2. Hamdy A. Taha, Operations Research: An Introduction, Pearson Education.

3. Schaum's Outline of Fourier Analysis and Applications, McGraw-Hill.

4. Murray R. Spiegel, John Schiller and R. Alu Srinivasan, Schaum's Outline of Probability and Statistics, McGraw-Hill.

5. S. D. Sharma, Operations Research, Kedar Nath Ram Nath Publications.