# PhD Qualifying Exams

### Official Website

For more information about the qualifying exams go to the following link:

2021-2022 Graduate Bulletin – Program of Study

### PhD Common Exam Topics

**Engineering Mathematics ****(Calculus, Engineering Analysis, Linear Algebra)**

**Topics Covered**

- Fundamentals of Calculus
- First-Order Differential Equations
- Higher-Order Differential Equations
- Laplace-Transform
- Fourier-Transform
- Orthogonal Functions
- Z-Transform
- Series Solutions of Linear Differential Equations
- Vectors
- Matrices
- Vector Calculus
- Systems of Linear Differential Equations
- Boundary-Value Problems
- Complex Variables
- Functions of Complex Variables
- Series and Residues Eigenvalues and Eigenvectors

**Suggested References**

- Dennis G. Zill,
, Jones and Bartlett*“Advanced Engineering Mathematics”* - B. Noble, J. W. Daniel,
, Prentice Hall*“Applied Linear Algebra”*

**Recommended Classes @ DU**

- ENEE 3611 – Engineering Mathematics (Fall Quarter)
- ENGR 3735 – Linear Systems (Fall Quarter)

**Circuits and Electronics **

**Circuits**

**Topics Covered**

- Kirchhoff’s law
- Node voltage and mesh current analysis technique
- Circuit reduction (i.e. parallel circuits, series circuits)
- Thévenin and Norton Equivalent circuits
- Interface power transfer and maximum power transfer
- Analysis using dependent sources
- Basic Op Amps
- Basic transistors (quiescent point calculations)
- Basic signals (step, impulse, ramp, sinusoidal functions)
- RC/RL circuits, RLC circuits
- Frequency response
- Laplace
- Fourier Transforms

**Suggested References**

- Thomas and Rosa,
, any of the book editions from 3 to 8 (Chapters 1 to 13)*“The Analysis and Design of Linear Circuits”* - Irwin and Nelms,
, any book edition from 7 to 9 (Chapters 1 to 9)*“Basic Engineering Circuits Analysis”*

**Recommended Classes @ DU**

- ENEE 2022 – Circuits II (Spring Quarter)

**Electronics**

**Topics Covered**

- Signals and Amplifiers
- Operational Amplifiers
- Semiconductors
- Diodes
- MOS Filed-Effect Transistors (MOSFETs)
- Bipolar Junction Transistors (BJTs)
- Transistor Amplifiers
- Power Amplifiers

**Suggested References**

- Adel S. Sedra and Kenneth C.,
, any of the book editions above 7th (Part I Devices and Basic Circuits)*“Microelectronics Circuits”*

**Recommended Classes @ DU**

- ENEE 2211 – Electronics (Fall Quarter)

**Digital Design, Computer Org, and HDL**

**Digital Design**

**Topics Covered**

- Binary number system
- Boolean algebra, combinational logic, and logic gates
- Simplifications of Boolean expressions
- Flip Flops, counters, and registers Logic Design with MSI, PLDs, etc. components
- Advanced techniques for simplifications of Boolean Expressions (High order K-maps, Quine McCluskey, …)
- Circuit Timing and Timing Hazards
- Synchronous Sequential Networks
- Asynchronous Sequential Networks
- Algorithmic State Machines

**Suggested References**

- Stephen Brown, and Zvonko Vranesic
, McGraw-Hill*“Fundamentals of Digital Logic with Verilog Design”*

**Recommended Classes @ DU**

- ENCE 3100 – Advance Digital Design (Fall Quarter)

**Computer Org**

**Topics Covered**

- Converting between binary representations
- Binary arithmetic with finite and infinite precision
- IEEE 754 floating point format and rounding
- Casting implications in C
- Compiling C code into assembly
- Writing procedure calls in assembly that make appropriate use of the stack
- Given an ISA, convert between machine language (byte codes) and assembly language
- Design a simple sequential processor given an Instruction Set Architecture (ISA)
- Compute the data characteristics of a disk drive given physical parameters of a disk drive
- Design a cache memory (direct-mapped, set associative) of a given configuration
- Given a cache, trace a series of memory accesses and note cache misses and hits

**Suggested References**

- D. A. Patterson and J. L. Hennessy,
, Elsevier*“Computer Organization and Design: The Hardware / Software Interface”*

**Recommended Classes @ DU**

- ENCE 3241 – Computer Organization and Architecture (Winter Quarter)

**HDL**

**Topics Covered**

- Digital design flow
- Verilog language concepts
- Combinational circuit description
- Sequential circuit description
- Component test and verification
- Switch level modeling

**Suggested References**

- Samir Palnitkar,
, Prentice Hall*“Verilog HDL”*

**Recommended Classes @ DU**

- ENCE 3100 – Advanced Digital Design (Fall Quarter)

### PhD Specific Area Exam Topics

- Circuits and Electronics
**(only if NOT taken for the common component)** - Digital Design, Computer Organization, and HDL
**(only if NOT taken for the common component)**

**Microprocessors**

**Topics Covered**

- Architectures & Instruction Set
- Instruction Set Usage Examples
- Programming with C and Assembly
- Memory System
- Digital Input and Output
- Exceptions and Interrupts
- Power management and Timing Operations
- Mixed Signals (Comparator, ADC, DAC)
- Digital Communications (UART, I2C, SPI)
- Wireless Communication
- Flash Memory and RAM Operations Real-Time Operating Systems (RTOS)

**Suggested References**

- Cem Unsalan and H. Deniz Gurhan and M. Erkin Yucel,
, McGraw-Hill*“Programmable Microcontrollers – Applications on the MSP432 Launchpad”* - Joseph Yiu,
, Elsevier*“The definitive Guide to ARM Cortex-M0 and Cortex-M0+ Processors”*

**Recommended Classes @ DU**

- ENCE 3231 – Embedded Systems Design (Spring Quarter)

**Data Structures, Algorithms and Operating Systems**

**Topics Covered**

- greedy algorithms
- dynamic programming
- divide-and-conquer
- randomized algorithms
- network flow
- NP-completeness
- computability theory
- approximation algorithms
- randomized algorithms

**Suggested References**

- Thomas H. Cormen and Charles E. Leiserson
**,**, 3rd Edition*“Introduction to Algorithms”*

**Recommended Classes @ DU**

- COMP 2370 – Introduction to Algorithms and Data Structures (Spring Quarter)

**Controls, Signals and Systems**

**Controls**

**Topics Covered**

- Elementary Continuous- and Discrete- Time Signals and Systems
- Linear Time-Invariant Systems (LTI)
- Differential and Difference LTI Systems
- Laplace-, Fourier- and z- Transform
- Filtering
- Mathematical Modeling of Dynamic Systems
- Impulse and Step Responses
- Convolution
- 1st, 2nd, 3rd Order Systems
- State Models of LTI Systems
- Open-Loop, Closed-Loop Systems
- Application of Transform Techniques to LTI Feedback Control Systems
- Transient-Response Analysis
- Root-Locus Analysis
- Control Systems Design by the Root-Locus Method
- Frequency-Response Analysis
- Control Systems Design by Frequency Response
- Classical PID Control
- PID Controller Design
- State Space Analysis of Control Systems
- Design of Control Systems in State Space
- Stability

**Suggested References**

- B. C. Kuo
**,**, Prentice Hall*“Automatic Control Systems”* - G. C. Goodwin and S. F. Graebe, and M. E. Salgado
**,**, Pearson Education*“Control System Design”* - Note: any book on the subject may serve as reference for the above topics

**Recommended Classes @ DU**

- ENGR 3721 – Controls (Winter Quarter)

**Signals and Systems**

**Topics Covered**

- Discrete time and continuous time signal synthesis and analysis
- Linear system analysis
- Fourier transform theory and application to signal and system analysis
- Laplace transform for system analysis
- Discrete time signal and system analysis using z-transform techniques
- Discrete Fourier transform
- Fast Fourier transform

**Suggested References**

- Gopalan
**,**, Cengage Learning*“Introduction to Signals and Systems Analysis”* - Oppenheim, Willsky, and Nawab
**,**, Prentice-Hall*“Signals and Systems”* - McClellan, Schafer, and Yoder
**,**, Prentice-Hall*“Signal Processing First”* - Roberts
**,**, McGraw Hill*“Fundamentals of Signals and Systems”* - Note: any basic signals and systems textbook

**Recommended Classes @ DU**

- ENEE 3111 – Signals and Systems (Fall Quarter)

**Electromagnetics**

**Topics Covered**

- Waves and Phasors
- Transmission Lines
- Vector Analysis
- Electrostatics
- Magnetostatics
- Maxwell’s Equations for Time-Varying Signals
- Plane-Wave Propagation
- Wave Reflection and Transmission
- Radiation and Antennas
- Satellite Communication Systems and Radar Sensors

**Suggested References**

- Fawwaz T. Ulaby and Umberto Ravaioli,
, Pearson*“Fundamentals of Applied Electromagnetics”*

**Recommended Classes @ DU**

- ENEE 2611 – Engineering Electromagnetics (Fall Quarter)

**Power & Energy Systems**

**Topics Covered**

- The physical basis of electromagnetics and electro-mechanics
- Three phase power
- Transformers
- AC machinery fundamentals
- The synchronous machine
- Induction motors
- Power system modeling for power flow studies
- Power flows

**Suggested References**

- Stephen Chapman,
, Chapters 1 to 5, 7, 9, 10, and 11*“Electric Machinery and Power System Fundamentals”* - J. Duncan Glover, Mulukutla S. Sarma, and Thomas Jeffrey Overbye,
, 5th Edition, Chapters 1 to 6*“Power System Analysis and Design”*

**Recommended Classes @ DU**

- ENGR 3530 – Intro to Power and Energy Systems (Fall Quarter)

(It will be updated soon)

- Optoelectronics and Optical Fiber Communication
- Communication & DSP
- Robotics
- Image Processing & Computer Vision
- Pattern Recognition