Biomedical and Chemical Engineering Ph.D. - Curriculum

This course will expose student to the basic properties of data collected from biological systems and issues involved in the statistical analysis of such data. Specifically, this course will review the motivations and rationale behind conventional regression models, issues that arise in applying these methods to biological data, and specific extensions of these methods required to obtain meaningful results. Specific examples of these approaches and their application will be given at different levels of biology. The analysis of such problems will require the use of advanced regression techniques directed at resolving the partial confounding that is typical of living (closed loop regulated) systems, applied under statistical software packages (e.g., spreadsheets, graphing, Matlab, SPSS, Simca). (This class is restricted to degree-seeking graduate students or those with permission from instructor.) Lab 3 (Biannual).

The course begins with a pertinent review of linear and nonlinear ordinary differential equations and Laplace transforms and their applications to solving engineering problems. It then continues with an in-depth study of vector calculus, complex analysis/integration, and partial differential equations; and their applications in analyzing and solving a variety of engineering problems. Topics include: ordinary and partial differential equations, Laplace transforms, vector calculus, complex functions/analysis, complex integration. Chemical engineering applications will be discussed throughout the course. (Prerequisites: Graduate standing in Chemical Engineering.) Lecture 3 (Fall).

The course trains students to utilize mathematical techniques from an engineering perspective, and provides essential background for success in graduate level studies. The course begins with a pertinent review of matrices, transformations, partitions, determinants and various techniques to solve linear equations. It then transitions to linear vector spaces, basis definitions, normed and inner vector spaces, orthogonality, eigenvalues/eigenvectors, diagonalization, state space solutions and optimization. Applications of linear algebra to engineering problems are examined throughout the course. Topics include: Matrix algebra and elementary matrix operations, special matrices, determinants, matrix inversion, null and column spaces, linear vector spaces and subspaces, span, basis/change of basis, normed and inner vector spaces, projections, Gram-Schmidt/QR factorizations, eigenvalues and eigenvectors, matrix diagonalization, Jordan canonical forms, singular value decomposition, functions of matrices, matrix polynomials and Cayley-Hamilton theorem, state-space modeling, optimization techniques, least squares technique, total least squares, and numerical techniques. Electrical engineering applications will be discussed throughout the course. (Prerequisites: This course is restricted to graduate students in the EEEE-MS, EEEE-BS/MS program.) Lecture 3 (Fall, Spring).

The course begins with a pertinent review of linear and nonlinear ordinary differential equations and Laplace transforms and their applications to solving engineering problems. It then continues with an in-depth study of vector calculus, complex analysis/integration, and partial differential equations; and their applications in analyzing and solving a variety of engineering problems especially in the areas of control, circuit analysis, communication, and signal/image processing. Topics include: ordinary and partial differential equations, Laplace transforms, vector calculus, complex functions/analysis, complex integration, and numerical techniques. Electrical engineering applications will be discussed throughout the course. (This class is restricted to degree-seeking graduate students or those with permission from instructor.) Lecture 3 (Fall, Spring, Summer).

This course presents an in-depth study of the primary concepts of experimental design. Its applied approach uses theoretical tools acquired in other mathematics and statistics courses. Emphasis is placed on the role of replication and randomization in experimentation. Numerous designs and design strategies are reviewed and implications on data analysis are discussed. Topics include: consideration of type 1 and type 2 errors in experimentation, sample size determination, completely randomized designs, randomized complete block designs, blocking and confounding in experiments, Latin square and Graeco Latin square designs, general factorial designs, the 2k factorial design system, the 3k factorial design system, fractional factorial designs, Taguchi experimentation. (Prerequisites: ISEE-325 or STAT-257 or MATH-252 or equivalent course or students in ISEE-MS, SUSTAIN-MS, ENGMGT-ME, or MIE-PHD programs.) Lecture 3 (Spring).

This course is an introduction to the probabilistic models and statistical techniques used in the analysis of biological and medical data. Topics include univariate and multivariate summary techniques, one and two sample parametric and nonparametric inference, censoring, one and two way analysis of variance, and multiple and logistic regression analysis. (This class is restricted to graduate students in COS, KGCOE, GCCIS, CHST or CLA.) Lecture 3 (Spring).