# PhD Qualifying Exams

### Official Website

For more information about the qualifying exams follow the link below.

2022-2023 Graduate Bulletin – Program of Study

### PhD Common Exam Topics

This is a common two-hour written exam. Each student, with advice from his/her advisor must choose one of the three subject areas. The Common Exam will be graded as pass/fail. Minimum of 70% is required and serves as passing grade.

**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

This part of the exam will consist of two written subject area texts lasting two hours each. Students must pick two specific subject areas and cannot be the same subject area as the topic chosen for the PhD Common Exam. The Specific Area Exam will be graded as pass/fail; Minimum of 70% is required and serves as passing grade.

- 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