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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:
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Topic No.
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Problems on Engineering Mathematics
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Reading list
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1
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Fourier analysis of continuous-time signals: Fourier series and Fourier transform representations of continuous time signals, properties
(Sample Problem)
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Signals and Systems, by Oppenheim, Willsky, and Nawab, 2nd edition, sections 3.0 – 3.5, AND 4.0 – 4.5. |
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2
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The z-transform – region of convergence, properties, frequency response, poles and zeros.
(Sample Problem)
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Discrete Time Signal Processing, by Oppenheim, Schafer, and Buck, 2nd edition, chapter 3, and section 5.3.
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3
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Probability theory and random variables: concepts of probability and random variables, functions of one and two random variables, joint statistics.
(Sample Problem)
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Probability, Random Variables, and Random Signal Principles, 4th edition, by Peyton Z. Peebles, Jr., chapters 1 – 4, and sections 5.0 – 5.3 |
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4
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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.
(Sample Problem)
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Signals and Systems, by Oppenheim, Willsky, and Nawab, 2nd edition, sections 9.1 – 9.7
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5
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Counting techniques, Recurrence Relations, Graphs. Boolean Algebra. Order analysis (Big-Oh notation).
(Sample Problem)
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Discrete Mathematics and Its Applications, 3rd Ed. by Kenneth H. Rosen (ISBN 0-07-053965-0). Chapters 5, 6, 7, and 9.
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6
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Linear algebra: Matrix inversion, solutions to fully determined systems of linear equations, method of elimination, determinants and Cramer’s rule.
(Sample Problem)
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Linear Algebra and Its Applications, 3rd 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 |
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7
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Differential equations: Solutions to first and second order linear ODEs with constant coefficients, solutions to linear systems of differential equations
(Sample Problem)
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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 |
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