Problem 1: Engineering Mathematics
The student needs to answer any one of the following problems. The topics and recommended reading lists for the six problems are:
Topic No. |
Problems on Engineering Mathematics |
Reading list |
---|---|---|
1 |
Fourier analysis of continuous-time signals: Fourier series and Fourier transform representations of continuous time signals, properties (Amengonu) |
Signals and Systems, by Oppenheim, Willsky, and Nawab, 2^{nd} edition, sections 3.0 – 3.5, AND 4.0 – 4.5. |
2 |
The z-transform – region of convergence, properties, frequency response, poles and zeros. (Weldon) |
Discrete Time Signal Processing, by Oppenheim, Schafer, and Buck, 2^{nd} edition, chapter 3, and section 5.3. |
3 |
Probability theory and random variables: concepts of probability and random variables, functions of one and two random variables, joint statistics. (Cox) |
Probability, Random Variables, and Random Signal Principles, 4^{th} edition, by Peyton Z. Peebles, Jr., chapters 1 – 4, and sections 5.0 – 5.3 |
4 |
Laplace transforms: pole-zero plots, properties, transfer function, steady state response characteristics due to standard inputs like step, ramp, exponential, sinusoidal, and their composite inputs. Bode plots. (Cox) |
Signals and Systems, by Oppenheim, Willsky, and Nawab, 2^{nd} edition, sections 9.1 – 9.7 |
5 |
Counting techniques, Recurrence Relations, Graphs. Boolean Algebra. Order analysis (Big-Oh notation). (Sass) |
Discrete Mathematics and Its Applications, 7th Ed. by Kenneth H. Rosen. Chapters 3, 5, 8, 9, 10. |
6 |
Linear algebra: Matrix inversion, solutions to fully determined systems of linear equations, method of elimination, determinants and Cramer’s rule. (Manjrekar) |
Linear Algebra and Its Applications, 3^{rd} Edition, by David C. Lay. Sections 1.1-1.9, 2.1-2.3, 3.1-3.3 and Elementary Differential Equations and Boundary Value Problems, by Edwards and Penney, 3rd edition, sections 4.1-4.2, 5.1 |
7 |
Differential equations: Solutions to first and second order linear ODEs with constant coefficients, solutions to linear systems of differential equations (Zhang) |
Elementary Differential Equations and Boundary Value Problems, by Edwards and Penney, 3rd edition, sections 1.1-1.5, 3.1-3.3, 4.1-4.2, 5.1-5.2, 7.1-7.6 |