# Academics - Undergraduate Program

## Approved Technical Electives

Also, any 3xx or 4xx CPEG or ELEG courses count for general technical electives.

For courses not listed, contact Associate Chair for Undergraduates, boncelet@udel.edu

### Math

##### MATH 401 Introduction to Real Analysis

*3 credits*

A rigorous treatment of one variable calculus. Topics will include sequences of real numbers, limit theorems, monotone sequences, Cauchy sequences, Bolzano- Weierstrass Theorem, continuity, uniform continuity, differentiability and Riemann integral. A historical perspective on the development of these topics will be provided.

PREREQ: MATH245.

##### MATH 426 Computational Mathematics I

*3 credits*

Floating point numbers; conditioning and stability; LU, Cholesky, and QR factorizations; square and overdetermined linear systems; Newton and quasi-Newton rootfinding methods; piecewise polynomials for interpolation, integration, and finite differences; explicit methods for initial-value problems. Prerequisites: MATH 305, MATH 349, or MATH 351. Students may not receive credit for both MATH 353 and MATH 426.

May be cross-listed with CISC410.

PREREQ**:** MATH305 or MATH351 or MATH349.

RESTRICTIONS: Requires familiarity with computing (e.g., programming language).

##### MATH 428 Computational Mathematics II

*3 credits*

Eigenvalue and singular-value decompositions; power and Krylov subspace iterations; global interpolation and quadrature; methods for boundary-value problems and Poisson's equation; implicit solvers for stiff problems; method of lines for partial differential equations; diffusion and advection problems.

May be cross-listed with CISC411.

PREREQ**:** MATH426 or CISC410 or MATH353.

##### MATH 451 Abstract Algebra

*3 credits*

Basic properties of the integers and the rationals, fields of quotients, polynomial rings, root-finding, introduction to groups, rings and fields. A historical perspective on the development of the notion of number and algebraic structure.

PREREQ: MATH349 and MATH245.

##### MATH 503 Advanced Calculus and Nonlinear Dynamics

*3 credits*

Change of variables, surface integrals, Stokes' Theorem, Divergence Theorem, Calculus of Variations, Euler's Equation, Brachistochrone and isoperimetric problems. Introduction to the qualitative theory of ordinary differential equations, including linear systems, phase space analysis, Lyapanov's Methods, and elements of the analysis of nonlinear systems.

PREREQ: 300 level or above courses in ordinary differential equations and linear algebra.

##### MATH 508 Introduction to Complex Variables and Applications

*3 credits*

Introduction to analytic functions, contour integration, power series, residues and conformal mapping.

PREREQ: MATH243.

##### MATH 530 Optimization and Game Theory

*3 credits*

Convex functions and sets, duality, fixed point theorems, elementary game theory and the theory of Nash and Walrasian equilibria; non-linear programming and the Kuhn-Tucker Theorem; dynamic optimization including dynamic programming and Pontryagin's Maximum Principle. Emphasis on applications and interpretation in terms of economic models.

May be cross-listed with ECON530.

PREREQ: MATH 302, MATH 349, ECON 301 and ECON 303.

##### MATH 535 Introduction to Partial Differential Equations

*3 credits*

Theory and applications of parabolic, elliptic and hyperbolic partial differential equations originating from various mathematical physics problems.

PREREQ: MATH302 or MATH342 or MATH352.

### Physics

##### PHYS 309 Physics of the Twentieth and Twenty First Centuries

*3 credits*

Fundamentals in physics that help form a modern understanding of science and technology. Intended for physical science and engineering majors, the emphasis is on electromagnetic radiation, quantum mechanics, nuclear reactions, Bohr atom, solid state physics and devices, and relativity.

PREREQ: PHYS208.

COREQ: MATH243 suggested.

##### PHYS 310 Introduction to Thermal Physics

*3 credits*

Basic concepts of thermodynamics including properties of substance, first and second law analysis of systems and control volumes, entropy and availability. Power and refrigeration cycles.

PREREQ: PHYS207.

##### PHYS 313 Physical Optics

*4 credits*

A detailed treatment of optics at an intermediate level appropriate for physics, engineering and other students with a physical science background. Emphasis is on physical concepts and analysis of geometric optics, wave optics and applications of optics.

COREQ: MATH243.

##### PHYS 424 Quantum Mechanics

*3 credits*

Introduces quantum mechanical concepts by reviewing experiments which cannot be explained by classical physics. The Schrodinger equation is solved for simple cases such as free-particle motion, the simple harmonic oscillator and the hydrogen atom, with a basic treatment of angular momentum.

May be cross-listed with CHEM424 and/or ELEG424.

PREREQ: PHYS309, MATH302 and MATH349.

##### PHYS 431 Acoustics

*3 credits*

Vibrations of particles, strings and membranes; acoustic waves; radiation of sound; room acoustics; and acoustic measurements.

PREREQ: MATH243 and PHYS207.

##### PHYS 460 Computational Methods of Physics

*3 credits*

Introduction to basic computational techniques in science with application to a number of disciplines of current research interest, such as quantum physics, biophysics, statistical mechanics and chaos.

PREREQ: MATH302 or MATH341, CISC105 or equivalent, PHYS208.

### Materials Science

##### MSEG 302 Materials Science for Engineers

*3 credits*

Crystal binding and structure; energetics and structure of lattice defects; elasticity, plasticity, and fracture; phase equilibria and transformations; relations of structure and treatment to properties; structures of inorganic and organic polymers; and electronic and magnetic properties.

### Computer & Information Science

##### CISC 260 Machine Organization and Assembly Language

*3 credits*

Introduction to the basics of machine organization. Programming tools and techniques at the machine and assembly levels. Assembly language programming and computer arithmetic techniques.

PREREQ: A minimum grade of C- in CISC181.

RESTRICTIONS: CISC220 recommended as a prerequisite.

##### CISC 275 Introduction to Software Engineering

*3 credits*

Object oriented software design and development through use of the Java programming language. Topics include team programming, design patterns, graphical user interfaces, software engineering tools (eg., integrated development environments, version control, build management, bug tracking, automated testing).

PREREQ: CISC220.

##### CISC 320 Introduction to Algorithms

*3 credits*

Design and analysis of algorithms: worst/average case analysis, proofs for correctness and performance of algorithms. Algorithmic strategies (divide and conquer, greedy methods, dynamic programming, etc.). Algorithms for searching, forming and traversal of strings, trees and graphs. Categorization of computational problems: classes P and NP. NP completeness.

PREREQ: MATH210 and a minimum grade of C- in CISC220.

##### CISC 372 Parallel Programming

*3 credits*

Introduction to parallel programming concepts, methodologies, and tools. Programming techniques for programs that contain code segments which will run simultaneously on multiple processors. Topics include: concurrency, program decomposition, data distribution, communication, load balancing, scalability, locality, granularity, debugging, performance evaluation.

PREREQ: CISC220.

##### CISC 401 Elements of the Theory of Computation

*3 credits*

General models of computation, formal languages and automata theory and algorithmic unsolvability.

PREREQ: CISC303.

RESTRICTIONS: Credit cannot be received for both CISC401 and CISC601.

##### CISC 440 Computer Graphics

*3 credits*

Computer graphics technology, two- and three-dimensional systems, graphics software systems, modeling and object hierarchy, and animation.

PREREQ: CISC220 and MATH241.

RESTRICTIONS: CISC320 recommended. Credit cannot be received for both

CISC440 and CISC640.