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

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, “Advanced Engineering Mathematics”, Jones and Bartlett
  • B. Noble, J. W. Daniel, “Applied Linear Algebra”, Prentice Hall

Recommended Classes @ DU

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

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

Recommended Classes @ DU

  • ENEE 2022 – Circuits II (Spring Quarter)

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., “Microelectronics Circuits”, any of the book editions above 7th (Part I Devices and Basic Circuits)

Recommended Classes @ DU

  • ENEE 2211 – Electronics (Fall Quarter)

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

  • Donald D. Givone, “Digital Principles and Design”, McGraw-Hill
  • M. Moris Mano and Michael D. Ciletti, “Digital Design”, 4th Edition, Pearson Prentice Hall

Recommended Classes @ DU

  • ENCE 3100 – Advance Digital Design (Fall Quarter)

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, “Computer Organization and Design: The Hardware / Software Interface”, Elsevier

Recommended Classes @ DU

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

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, “Verilog HDL”, Prentice Hall

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)

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, “Programmable Microcontrollers – Applications on the MSP432 Launchpad”, McGraw-Hill
  • Joseph Yiu, “The definitive Guide to ARM Cortex-M0 and Cortex-M0+ Processors”, Elsevier

Recommended Classes @ DU

  • ENCE 3231 – Embedded Systems Design (Spring Quarter)

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 ,“Introduction to Algorithms”, 3rd Edition

Recommended Classes @ DU

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

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

Recommended Classes @ DU

  • ENGR 3721 – Controls (Winter Quarter)

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

Recommended Classes @ DU

  • ENEE 3111 – Signals and Systems (Fall Quarter)

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, “Fundamentals of Applied Electromagnetics”, Pearson

Recommended Classes @ DU

  • ENEE 2611 – Engineering Electromagnetics (Fall Quarter)

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

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