Ph.D. Courses

 

 

 

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 Selected Topics in Advanced Mathematics (Advanced Mathematics 2)                                                                         grade: 90

           by Mojtaba Mahzoon Ph.D. in Mechanical Engineering from University of California, Berkeley

                                                                                                                                                                                                          

 

Contents:

1- some applications of complex analysis: complex inversion integral, complex Fourier integral and its inverse, principle of argument, Rouche's theorem, Nyquist criterion, fundamental principle of algebra, analytic continuation, potential theory, Dirichlet and Neumann problems, conformal mapping, Dirichlet and Neumann problems for circle and half plane, Green's function, Schwartz – Christoffel transformation, Joukowsky's transformation, application of complex analusis in two-dimensional flow of ideal fluids, two-dimensional problems in linear elasticity.

 

2- partial differential equations: Quasi - linear first order equations, development of shock, traffic problem, Cauchy – Kovalevsky's theorem, second order equations, reduction of hyperbolic, parabolic and elliptic equations to canonical forms, separation of variables in various coordinate systems, review of second order ordinary differential equations and series solutions, Papperitz equation and hyper geometric differential equation.

 

3- special functions: Gamma function, digamma function, Bessel function of complex order and its integral representation, Bessel function of second kind, recursive relations, modified Bessel functions, Strum – Liouvoille problem and orthogonality of Bessel functions, Legendre function.

 

References:

Advanced Engineering Mathematics by C.R. Wylie

Advanced Calculus for Applications by F.B. Hildebrand

Advanced Mathematics for Engineers by W. Kaplan

Applied Complex Variables by J.W. Dettman

Complex Variables and Applications by R.V. Churchill

Conformal Mapping by Z. Nehari

Introduction to Partial Differential Equations by E.C. Zachmanogolou and D.W. Thoe

Special Functions With Applications by N.N. Lebedev 

 

 

 

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Tensor Analysis                                                                                                                                                                  grade: 92.5

           by Mojtaba Mahzoon Ph.D. in Mechanical Engineering from University of California, Berkeley

                                                                                                                                                            

 

Contents:

History and introduction, transformation of coordinate systems, summation convention, contravariant vectors and tensors, covariant vectors and tensors, mixed tensors, tensor algebra, quotient rule, relative tensors, metric tensor and line element, Riemannian space, review of basic concepts in calculus of variations, geodesic lines and Christoffel symbols, derivative of tensors, curvature of space, special coordinate systems, geodesic deviation, Riemannian curvature, parallel propagation, flat space, Cartesian tensors, physical components of tensors, geometric interpretation of covariant and contravariant tensors, the meaning of covariant derivative, geometry of space curves, Frenet's relations, geometry of surfaces in space, geodesic curvature, normal to surface, tensor derivatives, first and second fundamental forms of surfaces, Weingarten relations and third fundamental form, Gauss and Codazzi equations, curves on surface, some applications of tensor formalism, principle of least action and geometrization of dynamics, equations of fluid flow in Euclidean space, material coordinate systems and convective derivative.

References:

         

        Tensor Calculus, J. L. Synge and A. Schield

        Tensor Analysis; Theory and Applications to Geometry and Mechanics of Continua, I. S. Sokolnikoff 

 

 

 

 

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 Dynamical Systems                                                                                                                                                            grade: 92.5

           by Mojtaba Mahzoon Ph.D. in Mechanical Engineering from University of California, Berkeley

 

Contents:

Analysis of Dynamical System's behavior around fixed points, Lyapunov Stability, Limit Sets, Some Practical Examples of Dynamical Systems modeling (Mechanical, Electrical, Biological, …), Bifurcation, Small Perturbation Method, Analysis of Multi – Dimensional Dynamical Systems, Quasi – Periodic behavior.

 

Text:

Dynamical Systems; differential equations, maps and chaotic behavior by D. K. Arrowsmith and C. M. Place

Fundamentals of Vibrations by L. Meirovitch      

 

 

 

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 Nonlinear Control                                                                                                                                                            grade: 91.5

           by Ali Reza Khayatian Ph.D. in Control Engineering from Georgia Tech

 

Contents:

Lyapunov Stability, Analysis of Feedback Systems, Feedback Control, Exact Feedback Linearization

 

Text:

Nonlinear Systems by M.S. Khalil

 

 

 

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 Optimal Control                                                                                                                                                                grade: 93

           by Ali Reza Khayatian Ph.D. in Control Engineering from Georgia Tech

 

Contents:

Discrete – and Continuous – time Optimal Control, Variational Methods, Linear Quadratic Regulation, Tracking, Optimal Control under Constraints like Minimum – time  Problem, Dynamic Programming

 

Text:

Optimal Control by F. L. Lewis and V. L. Syrmous

 

 

 

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 Robotics                                                                                                                                                                          grade: 93.75

           by Mohammad Eghtesad Ph.D. in Mechanical Engineering from University of Ottawa

 

Contents:

Transformation and Rotation Matrix Representation using Euler Angles, Robot Construction (Matrix Representation), Inverse and Forward Kinematics, Inverse and Forward Dynamics (Newton - Euler Method, Lagrange's Method, Kane's Method), Introduction to Robot Control

 

References:

Theory of Robot Control by C. C. de Wit, B. Siciliano and G. Bastin

Fundamentals of Robotics by R. J. Schilling

Robotics: Control, Sensing, Vision and Intelligence by K. S. Fu, R. C. Gonzalez

 

 

 

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 Finite Elements Method                                                                                                                                                 grade: 90

           by Mehrdad Farid Ph.D. in Mechanical Engineering from University of Calgary

 

Contents:

Finite Difference Method, Weighted Residual Method, Variational Method, Fundamentals of Finite Element Method, FEM for One – Dimensional Problems, Eigenvalue and Time Dependent Problems, Two – Dimensional Problems, Thin Plates (Transverse Loading) and Nonlinear Problems    

 

Text:

An Introduction to The Finite Element Method by J. N. Reddy

Finite Element, Volume 1, E. B. Becker, G. F. Carey and J. T. Oden

 

 

 

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 Advanced Vibration                                                                                                                                                       grade: 90

           by Mehrdad Farid Ph.D. in Mechanical Engineering from University of Calgary

  

Contents:

Review of introductory vibrations, Analytical Dynamics, Multi – Degree of Freedom Systems, Computational Methods, Distributed – Parameter Systems, FEM, Introduction to Nonlinear and Random Vibrations

 

References:

Theory of Vibration with Applications by W. T. Thomson and M. D. Dahleh

Fundamentals of Vibrations by L. Meirovitch

Analytical Methods in Vibrations by L. Meirovitch

Vibration with Measurement, Control and Stability by D. J. Inman

Mechanical and Structural Vibrations; Theory and Applications by J. H. Ginsberg

Vibration; Fundamentals and Practice by C. W. de Silva

 

 

 

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 Modern Control                                                                                                                                                            grade: 95

           by Mohammad Eghtesad Ph.D. in Mechanical Engineering from University of Ottawa

 

Contents:

Analysis and Design of Control Systems in State Space, Selected Topics in Nonlinear, Adaptive and Robust Control

 

References:

Modern Control Engineering by K. Ogata

 

 

 

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