Course Descriptions

CREDIT HOURS: 3

This course is offered to graduate students enrolled in Applied Mathematics who wish to gain knowledge in a specific area for which no appropriate graduate level courses are offered. Each student taking this course will be assigned a suitable course advisor familiar with the specific area of interest. The student will be required to present the work of one term (not less than 90 hours in the form of directed research, and individual study) in an organized publication format.

CREDIT HOURS: 3

This course explains wavelets and filter banks using both the language of filters and the language of linear algebra. The course concentrates on the underpinnings of this relatively young (1980's) subject which has now stabilized. Applications to the areas of image and video compression, speech, audio and ECG compression and denoising are presented.

CREDIT HOURS: 3

This course is concerned with the theory of functions of complex variables and its applications in various branches of science and engineering. Topics included are: analytic functions, Cauchy-Riemann conditions, elementary functions, simple mappings, complex integrations, Taylor's and Laurent's expansions; the calculus of residues and its applications in computing integrals; the use of Bromwich contour and Nyquist stability criterion; the application of conformal mappings i.e. Schwartz-Christoffel transformation to the solution of fluid-flow, heat transfer and electrical potential problems; and the integral form of Poisson's equation.

CREDIT HOURS: 3

Classical boundary-value problems of mathematical physics. Classical analytical solutions of boundary-value problems. Special functions. Numerical aspects of the classical analytical solutions. Integral transforms and their application to classical problems of mathematical physics.

FORMAT: Lecture

CREDIT HOURS: 3

Linear partial differential equations. Derivation of classical equations, classification and boundary condition, separation of variable technique, integral transform method of solving partial differential equations.

PREREQUISITES: ENGM 6612

CREDIT HOURS: 3

Vibrations and transient response of linear lumped-parameter physical systems. Analogies between electric circuits, mechanical systems and acoustics. Systems with one degree of freedom. Systems with non-linear and variable spring characteristics. Method of successive approximations and Ritz method of non-linear vibrations.

Vibratory systems with several degrees of freedom. Approximate methods of calculating frequencies of natural vibrations. Solution of eigenvalue problems by matrix iteration. Vibration of elastic bodies. Wave equation. Applications of rods, plates and shells. Plane waves and spherical waves in unbounded homogeneous elastic media.

Elements of harmonic wave phenomenon; reflection, resonance, relaxation and reverberation. Wave propagation through fluid and solid layers.

CREDIT HOURS: 3

This class introduces Numerical Methods used to solve mathematical problems encountered by engineers and scientists. It covers methods for solving algebraic systems, data fitting, numerical calculus, ordinary and partial differential equations. Students will learn about the accuracy and efficiency of different approaches, and they will conduct an independent research project.

FORMAT: Lecture

LECTURE HOURS PER WEEK: 3

PREREQUISITES: Single-variable calculus, linear algebra, differential equations, or permission of instructor

EXCLUSIONS: ENGM 3052, ENGM 3356, CHEE 3602

CREDIT HOURS: 3

The topics covered in this course include: matrix and vector norms, condition number, singular value decomposition, LU decomposition, QR decomposition, Cholesky decomposition, error analysis and complexity of matrix algorithms, Toeplitz matrix algorithms, orthogonalization and least squares methods, the symmetric and unsymmertric eigenvalue problems, and iterative methods. The student is expected to code most of the algorithms on the computer.

PREREQUISITES: Ability to programme in C or Fortran.

CREDIT HOURS: 3

This course begin with a study of solution techniques or ordinary differential equations. Then a review of the basic partial differential equations of engineering mathematics is undertaken. The finite difference method is used to discretize these equations and concepts of stability, consistency, and convergence in the solutions are introduced. The student is expected to write several computer programs.

PREREQUISITES: Ability to programme in C or Fortran.

CREDIT HOURS: 3

This course covers aspects of the solution of linear static and dynamic partial differential equations through the use of finite element models derived from the Galerkin approximation. Emphasis is placed on the derivation of the approximate matrix equations from the strong form of the boundary value problem and on issues concerning the accuracy of the solution, on integration techniques, completeness, and element tests. Students are expected to code and validate an element appropriate to their specific research interests.

PREREQUISITES: Familiarity with partial differential equations and numerical linear algebra.

CREDIT HOURS: 3

This course covers aspects of the solution of non-linear partial differential equations through the use of finite element models. Emphasis is placed on the modeling of engineering materials. The course addresses such topics as common plasticity relationships, numerical implementation of various yield models, finite deformations, consistent linearization schemes, and theorems dealing with existence, uniqueness and stability. Students are expected to implement a non-linear finite element algorithm on the computer.

PREREQUISITES: ENGM 6659.03 is recommended

CREDIT HOURS: 3

This course will emphasize practical rather than theoretical considerations and will make extensive use of computer packages. The topics to be covered include: simple linear regression, analysis of residuals and remedial measures, transformation of data, multiple, polynomial and weighted regression, model selection techniques, joint confidence regions, use of indicator variables, analysis of covariance and an introduction to non-linear regression.

CREDIT HOURS: 3

This course introduces risk assessment and system reliability methodologies, from classical event trees to simulation. Examples of risk-based decision making analyses will be covered, ranging from oil exploration to environmental site remediation. The student will carry out a risk assessment involving design decisions on a project of their own choosing.

CREDIT HOURS: 3

The class introduces Machine Learning (ML) for engineers. After a review of linear algebra, calculus, probability, and classic machine learning, the class will focus on deep learning starting with simple multilayer perceptronâ€™s and ending with modern convolutional neural networks (CNNs). Datasets for engineering problems will be utilized in this course.

FORMAT: Lecture

LECTURE HOURS PER WEEK: 3

CREDIT HOURS: 3

Students develop and apply mathematical models of marine and freshwater ecosystems to study biological production, biogeochemical cycling etc. Lectures provide theoretical background for coupling nutrient and plankton dynamics, including parameterizing biological processes and physical effects. Computer sessions provide hands-on modelling experience. Students also critique literature and conduct an independent research project.

FORMAT:

FORMAT COMMENTS: Computer Programming

CROSS-LISTING: OCEA 5680.03, ENGM 4680.03

CREDIT HOURS: 3

This course is offered to graduate students enrolled in Applied Mathematics who wish to gain knowledge in a specific area for which no appropriate graduate level courses are offered. Each student taking this course will be assigned a suitable course advisor familiar with the specific area of interest. The student will be required to present the work of one term (not less than 90 hours in the form of directed research, and individual study) in an organized publication format.

CREDIT HOURS: 0

CREDIT HOURS: 0

**ENGM 6000 Directed Studies in Applied Mathematics**CREDIT HOURS: 3

This course is offered to graduate students enrolled in Applied Mathematics who wish to gain knowledge in a specific area for which no appropriate graduate level courses are offered. Each student taking this course will be assigned a suitable course advisor familiar with the specific area of interest. The student will be required to present the work of one term (not less than 90 hours in the form of directed research, and individual study) in an organized publication format.

**ENGM 6610 Wavelets and Filter Banks**CREDIT HOURS: 3

This course explains wavelets and filter banks using both the language of filters and the language of linear algebra. The course concentrates on the underpinnings of this relatively young (1980's) subject which has now stabilized. Applications to the areas of image and video compression, speech, audio and ECG compression and denoising are presented.

**ENGM 6611 Functions of Complex Variables**CREDIT HOURS: 3

This course is concerned with the theory of functions of complex variables and its applications in various branches of science and engineering. Topics included are: analytic functions, Cauchy-Riemann conditions, elementary functions, simple mappings, complex integrations, Taylor's and Laurent's expansions; the calculus of residues and its applications in computing integrals; the use of Bromwich contour and Nyquist stability criterion; the application of conformal mappings i.e. Schwartz-Christoffel transformation to the solution of fluid-flow, heat transfer and electrical potential problems; and the integral form of Poisson's equation.

**ENGM 6612 Methods of Applied Mathematics I**CREDIT HOURS: 3

Classical boundary-value problems of mathematical physics. Classical analytical solutions of boundary-value problems. Special functions. Numerical aspects of the classical analytical solutions. Integral transforms and their application to classical problems of mathematical physics.

FORMAT: Lecture

**ENGM 6613 Methods of Applied Mathematics II**CREDIT HOURS: 3

Linear partial differential equations. Derivation of classical equations, classification and boundary condition, separation of variable technique, integral transform method of solving partial differential equations.

PREREQUISITES: ENGM 6612

**ENGM 6621 Vibrations and Waves**CREDIT HOURS: 3

Vibrations and transient response of linear lumped-parameter physical systems. Analogies between electric circuits, mechanical systems and acoustics. Systems with one degree of freedom. Systems with non-linear and variable spring characteristics. Method of successive approximations and Ritz method of non-linear vibrations.

Vibratory systems with several degrees of freedom. Approximate methods of calculating frequencies of natural vibrations. Solution of eigenvalue problems by matrix iteration. Vibration of elastic bodies. Wave equation. Applications of rods, plates and shells. Plane waves and spherical waves in unbounded homogeneous elastic media.

Elements of harmonic wave phenomenon; reflection, resonance, relaxation and reverberation. Wave propagation through fluid and solid layers.

**ENGM 6650 Numerical Methods for Engineers and Scientists**CREDIT HOURS: 3

This class introduces Numerical Methods used to solve mathematical problems encountered by engineers and scientists. It covers methods for solving algebraic systems, data fitting, numerical calculus, ordinary and partial differential equations. Students will learn about the accuracy and efficiency of different approaches, and they will conduct an independent research project.

FORMAT: Lecture

LECTURE HOURS PER WEEK: 3

PREREQUISITES: Single-variable calculus, linear algebra, differential equations, or permission of instructor

EXCLUSIONS: ENGM 3052, ENGM 3356, CHEE 3602

**ENGM 6657 Numerical Linear Algebra**CREDIT HOURS: 3

The topics covered in this course include: matrix and vector norms, condition number, singular value decomposition, LU decomposition, QR decomposition, Cholesky decomposition, error analysis and complexity of matrix algorithms, Toeplitz matrix algorithms, orthogonalization and least squares methods, the symmetric and unsymmertric eigenvalue problems, and iterative methods. The student is expected to code most of the algorithms on the computer.

PREREQUISITES: Ability to programme in C or Fortran.

**ENGM 6658 Numerical Solution of Differential Equations**CREDIT HOURS: 3

This course begin with a study of solution techniques or ordinary differential equations. Then a review of the basic partial differential equations of engineering mathematics is undertaken. The finite difference method is used to discretize these equations and concepts of stability, consistency, and convergence in the solutions are introduced. The student is expected to write several computer programs.

PREREQUISITES: Ability to programme in C or Fortran.

**ENGM 6659 Finite Element Solution of Linear Partial Differential Equations**CREDIT HOURS: 3

This course covers aspects of the solution of linear static and dynamic partial differential equations through the use of finite element models derived from the Galerkin approximation. Emphasis is placed on the derivation of the approximate matrix equations from the strong form of the boundary value problem and on issues concerning the accuracy of the solution, on integration techniques, completeness, and element tests. Students are expected to code and validate an element appropriate to their specific research interests.

PREREQUISITES: Familiarity with partial differential equations and numerical linear algebra.

**ENGM 6660 Finite Element Solution of Non-Linear Partial Differential Equations**CREDIT HOURS: 3

This course covers aspects of the solution of non-linear partial differential equations through the use of finite element models. Emphasis is placed on the modeling of engineering materials. The course addresses such topics as common plasticity relationships, numerical implementation of various yield models, finite deformations, consistent linearization schemes, and theorems dealing with existence, uniqueness and stability. Students are expected to implement a non-linear finite element algorithm on the computer.

PREREQUISITES: ENGM 6659.03 is recommended

**ENGM 6671 Applied Regression Analysis**CREDIT HOURS: 3

This course will emphasize practical rather than theoretical considerations and will make extensive use of computer packages. The topics to be covered include: simple linear regression, analysis of residuals and remedial measures, transformation of data, multiple, polynomial and weighted regression, model selection techniques, joint confidence regions, use of indicator variables, analysis of covariance and an introduction to non-linear regression.

**ENGM 6675 Risk Assessment and Management**CREDIT HOURS: 3

This course introduces risk assessment and system reliability methodologies, from classical event trees to simulation. Examples of risk-based decision making analyses will be covered, ranging from oil exploration to environmental site remediation. The student will carry out a risk assessment involving design decisions on a project of their own choosing.

**ENGM 6676 Machine Learning For Engineers**CREDIT HOURS: 3

The class introduces Machine Learning (ML) for engineers. After a review of linear algebra, calculus, probability, and classic machine learning, the class will focus on deep learning starting with simple multilayer perceptronâ€™s and ending with modern convolutional neural networks (CNNs). Datasets for engineering problems will be utilized in this course.

FORMAT: Lecture

LECTURE HOURS PER WEEK: 3

**ENGM 6680 Ecosystems Modeling of Marine and Freshwater Environments**CREDIT HOURS: 3

Students develop and apply mathematical models of marine and freshwater ecosystems to study biological production, biogeochemical cycling etc. Lectures provide theoretical background for coupling nutrient and plankton dynamics, including parameterizing biological processes and physical effects. Computer sessions provide hands-on modelling experience. Students also critique literature and conduct an independent research project.

FORMAT:

- Lecture
- Discussion

FORMAT COMMENTS: Computer Programming

CROSS-LISTING: OCEA 5680.03, ENGM 4680.03

**ENGM 7000 Directed Studies Engineering Math II**CREDIT HOURS: 3

This course is offered to graduate students enrolled in Applied Mathematics who wish to gain knowledge in a specific area for which no appropriate graduate level courses are offered. Each student taking this course will be assigned a suitable course advisor familiar with the specific area of interest. The student will be required to present the work of one term (not less than 90 hours in the form of directed research, and individual study) in an organized publication format.

**ENGM 9000 Masterâ€™s Thesis**CREDIT HOURS: 0

**ENGM 9530 PhD Thesis**CREDIT HOURS: 0