Degree Requirements

Requirements for the Ph.D. Degree in Mechanical Engineering

A. Course Requirements
1. A minimum of 18 approved graduate ‘course’ credits beyond the Mechanical Engineering M.S. degree requirement (or equivalent). Any students who do not previously hold an M.S. degree must consult with the Graduate Program Director to satisfy this requirement.

Any credits from MEC 596, 597, 599, 696, 698 and/or 699 are not counted toward this requirement. Of 18 credits, a minimum of 9 credits must be taken in the Department of Mechanical Engineering.

2. All courses taken outside the Department for application to the Ph.D. degree requirements are subject to approval of the student’s advisor and the Graduate Program Director. The advisor may impose additional course requirements.

3. MEC 507 - The Graduate Program Director may waive this requirement if the student has taken sufficient applied mathematics courses elsewhere.

4. All full-time graduate students are required to register for MEC 691 each semester and obtain a satisfactory grade.

B. Transfer Credits
A maximum of 6 graduate credits from other programs, including those of other institutions, may be transferred toward the Ph.D. degree. Credits used to obtain any prior degrees are not eligible for transfer. Requests for transfer of credits must be approved by the Graduate Program Director.

C. Written Qualifying Examination
The written qualifying examination is offered once every year, usually in January. Students who enter the graduate program with an M.S. degree from another institution may take the examination after they finish one semester of academic residency. Students who enter the graduate program without an M.S. degree are encouraged to take the examination after they finish three semesters of academic residency. Both categories of students who do not take this opportunity must take the examination the next time it is offered during their residency. Part-time students should follow a rule based on graduate course credit hours (determined by the equivalence of 9 credits with one semester in residence). Each student can take the written qualifying examination two times before being dismissed from the Ph.D. program.

The written qualifying examination consists of two parts. Part I covers Applied Mathematics. Topics that are covered in this exams are:

1. Linear Algebra: Basic concepts,

• Matrices, vectors, determinants.
• Solution of linear systems. Eigenvalues and eigenvectors. Eigenbases and diagonalization.

1. Multiple Integrals

• Integrations over curves, areas and volumes
• Gauss and Stokes theorems. Green’s theorem.

1. Variational Calculus

• Differential calculus of multivariable functions.
• Divergence, gradient, Curl, Laplacian. Maximization/minimization and Lagrange multipliers.
• Euler-Langrange equations.

1. Ordinary Differential Equations (ODEs)

• Application to engineering problems.
• Homogeneous and non-homogeneous equations.
• System of equations as in dynamical system.
• Power series solutions. Solution via special functions. Laplace Transform. 

1. Partial Differential Equations (PDE’s)

• Elliptic, parabolic and hyperbolic equations.
• Fourier Series/Transforms. Sturm-Liouville problem.
• Separation of variables. Diffusion and Wave equations. D’Alembert’s solution.

1. Functions of Complex Variables:

• Polar form.
• Complex integral calculus. Cauchy integral formula. Laurent series

1. Others

• Taylor series
• Newton’s method

Part II corresponds to the student’s core area of concentration, selected from one of the following:

• Design and Manufacturing
• Solid Mechanics
• Thermal Sciences and Fluid Mechanics

More precise information on the exam is available in the departmental office, as are samples of previous examination questions.

Each student taking the examination is required to submit a written statement to the graduate program director with a declaration of both areas chosen at least one month before the announced exam date.

Recommended courses related to each subject area are as follows:

Design and Manufacturing

MEC 532: Vibration and Control
MEC 568: Advanced Dynamics

Expected knowledge from undergraduate courses
MEC 310: Introduction to Machine Design
MEC 410: Design of Machine Elements
MEC 411: Control System Design and Analysis

Solid Mechanics
MEC 530(455): Applied Stress Analysis
MEC 536:  Mechanics of Solids
MEC 541: Elasticity

Expected knowledge from undergraduate courses
MEC 363: Mechanics of Solids

Thermal Sciences and Fluid Mechanics
MEC 501: Convective Heat Transfer and Heat Exchange
MEC 502: Conductive Heat Transfer and Thermal Radiation
MEC 512: Mechanics of Viscous Fluid Flow
MEC 521: Thermodynamics

Expected knowledge from undergraduate courses
MEC 305: Heat Transfer
MEC 364: Fluid Mechanics
MEC 301: Thermodynamics

D. Minor Area of Concentration
In addition to the major area of concentration, each student must select a minor area from the following list: Thermodynamics and Heat Transfer, Fluid Mechanics, Solid Mechanics, Design and Manufacturing, Electrical Engineering, Material Science and Engineering, Computer Science, Applied Mathematics (not in general area), and Biomedical Engineering. More information is available in PhD minor requirements.

A student will be required to take a coherent sequence of three graduate level courses in the minor area and obtain a grade of B or better in each of the courses. However, students must submit a list of five courses from the proposed minor field no later than the time he or she applies to take the qualifying exam. The courses in the minor field must be approved by the Graduate Program Director, with the recommendation of the student’s advisor. Upon submission of the list of five courses, students must provide an explanation for the list, how the courses are related, and the rationale for the courses. Note that students are not required to have taken the courses in the minor field before taking the qualifying exam. However, the minor requirement must be satisfied before the student can be admitted to candidacy.

E. Advancement to Candidacy
A student will be advanced to candidacy (G5 status) for the Ph.D. degree when all formal coursework has been completed and all the requirements listed in items A through D have been satisfied. These requirements must be completed within one calendar year after passing the written qualifying examination. Advancement to candidacy must be one year before the beginning of the semester in which a student plans to defend his/her dissertation.

F. Teaching
Ph.D. students are required to take 3 credits of MEC 698 Practicum in Teaching II. MEC 698 is taken under the supervision of a faculty advisor who is responsible for proving feedback and providing a formal evaluation of the student's work. The format of this practicum may include making class presentations, teaching in recitation classes, and preparation and supervision of laboratory classes. All Teaching Assistants are required to take MEC 697 Practicum in Teaching I, which does not meet this requirement.

G. Dissertation
The student chooses a dissertation topic in consultation with his/her doctoral dissertation advisor as soon as possible after passing the written qualifying examination. Dissertation research is an apprenticeship for the candidate, who, under the supervision of the dissertation advisor, independently carries out original work of significance. Within one year after passing the written qualifying examination, a dissertation examining committee is established. The committee must include at least three members from the Department of Mechanical Engineering, including the dissertation advisor, and at least one member from another program or from outside the University. The committee must be approved by the graduate program director upon recommendation by the dissertation advisor. The official recommendation for the appointment of the dissertation examining committee is made to the Dean of the Graduate School.

The dissertation examining committee provides a means of exposing the candidate’s ideas to a variety of views, and helps to guide and oversee the candidate’s research progress, which is reviewed by the committee each year. The chairperson of the committee must submit a written report to the graduate program director on the student’s progress after each review.

Dissertation Proposal: In addition, the student is required to submit a written dissertation proposal and present it in an oral examination conducted by the dissertation examining committee. The written dissertation proposal must be distributed to the committee members at least two weeks before the oral examination. The oral examination probes the doctoral student’s ability and examines the progress, direction and methodology of the dissertation research. The student will be examined on the dissertation topic and its objective, the problem formulation, research approach, and knowledge in related areas. The majority of the dissertation examining committee must approve the student’s performance. The dissertation proposal must be submitted/presented at least 1 year before the dissertation defense.

Dissertation Defense: At the completion of the dissertation, approval of the dissertation involves a formal oral defense. The formal defense is open to all interested members of the University community. The final approval of the dissertation must be by a majority vote of the dissertation examining committee.

• The proposed  dissertation defense must be scheduled at least two weeks before the thesis submission deadline set by the Graduate School (generally the semester end date).
• Committee Appointment Request Form must be submitted by the Graduate Program Coordinator at least five weeks before the schedule defense date.
• Doctoral Defense Announcement Form which includes the thesis title, abstract, date, location must be submitted to the Graduate Program Coordinator at least four weeks before the schedule date.
• Copies of proposed dissertation  must be given to the committee members as well as to the Department office for examination by the faculty  at least two weeksweeks before the schedule date.
• The approved dissertation (with Adobe Sign Signature Page) must be submitted before the thesis submission deadline set by the Graduate School for each semester.
• Dissertation format must adhere to the guideline set by the Graduate School. It must be also electronically  submitted (ProQuest). Please see here for more information.
• One copy of approved dissertation including the signed signature page must be submitted to the Department.