Engineering Math

L/R 502. (ENM 402) Numerical Methods and Modeling. (B) Sinno. Prerequisite(s): Knowledge of a computer language, Math 240 and 241; ENM 510 is highly recommended; or their equivalents.

Numerical modeling using effective algorithms with applications to problems in engineering, science, and mathematics, and is intended for graduate and advanced undergraduate students in these areas.  Interpolation and curve fitting, numerical integration, solution of ordinary and partial differential equations by finite difference, and finite element methods.  Includes use of representative numerical software packages such as MATLAB PDE Toolbox.

503. Introduction to Probability and Statistics. (A) Prerequisite(s): MATH 240 or equivalent.

Introduction to probability.  Expectation.  Variance.  Covariance.  Joint probability.  Moment generating functions.  Stochastic models and applications.  Markov chains.  Renewal processes.  Queuing models. Statistical inference.  Linear regression.  Computational probability. Discrete-event simulation.

504. Logic and Computation in Algebra. (B) Prerequisite(s): Discrete mathematics, algebra and set theory (CSE 260, CSE 261), CIS 511 and CIS 500 strong recommended as corequisites.

An introduction to universal algebra, equational reasoning, lambda calculus and computation by term rewriting.  Provides a strong foundation for further studies in computational logic, programming languages, and computational linguistics.  Universal algebra, trees and algebraic terms, unification, equational logic, rewrite systems, applications to automated deduction, lambda calculus, combinatory logic, simple types.  Applications to programming languages.  Connections with computability theory.

508. Engineering Math. (A) Staff.

510. Foundations of Engineering Mathematics - I. (A) Prerequisite(s): MATH 240, MATH 241 or equivalent.

This is the first course of a two semester sequence, but each course is self contained.  Over the two semesters topics are drawn from various branches of applied mathematics that are relevant to engineering and applied science. These include: Linear Algebra and Vector Spaces, Hilbert spaces, Higher-Dimensional Calculus, Vector Analysis, Differential Geometry, Tensor Analysis, Optimization and Variational Calculus, Ordinary and Partial Differential Equations, Initial-Value and Boundary-Value Problems, Green's Functions, Special Functions, Fourier Analysis, Integral Transforms and Numerical Analysis.  The fall course emphasizes the study of Hilbert spaces, ordinary and partial differential equations, the initial-value, boundary-value problem, and related topics.

511. Foundations of Engineering Mathematics - II. (B) Prerequisite(s): ENM 510 or equivalent.

Vector Analysis: space curves, Frenet - Serret formulae, vector theorems, reciprocal systems, co and contra variant components, orthogonal curvilinear systems.  Matrix theory: Gauss-Jordan elimination, eigen values and eigen vectors, quadratic and canonical forms, vector spaces, linear independence, Triangle and Schwarz inequalities, n-tuple space.Variational calculus: Euler-Lagrange equation, Finite elements, Weak formulation, Galerkin technique, FEMLAB.  Tensors: Einstein summation, tensors of arbitrary order, dyads and polyads, outer and inner products, quotient law, metric tensor, Euclidean and Riemannian spaces, physical components, covariant differentiation, detailed evaluation of Christoffel symbols, Ricci's theorem, intrinsic differentiation, generalized acceleration, Geodesics.

Department of Bioengineering
School of Engineering and Applied Science
University of Pennsylvania
210 S. 33rd Street
Room 240 Skirkanich Hall
Philadelphia, PA 19104
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