Lower Division Courses numbered 1–99 are designed primarily for freshmen and sophomores but are open to all students for lower division credit. (Graduate students requesting to enroll in lower-division undergraduate courses will not receive unit credit nor will the course fulfill degree requirements.)
Upper Division Courses courses numbered 100–199 are open to all students who have met the necessary prerequisites as indicated in the catalog course description. Preparation should generally include completion of one lower division course in the given subject or completion of two years of college work.
GRADUATE COURSES
Courses numbered 200–299 are open to graduate students. (Undergraduate students must obtain the signature of the instructor, School Dean, and the Dean of Graduate Studies. Graduate level units will count towards the required 120 units for graduation; however students are urged to meet with their academic advisor in order to determine if graduate course units may be used to fulfill a graduation requirement.)
CROSS-LISTED/CONJOINED COURSES Cross-listed Courses are the same course offered under different course subjects at the same level (either undergraduate or graduate) that share the same meeting time, requirements, units, etc.
Conjoined Courses are the same course but one is undergraduate and one is graduate.
COREQUISITE COURSE
A corequisite course is a course that must be taken at the same time as another course.
PREREQUISITES
Prerequisites for courses should be followed carefully; the responsibility for meeting these requirements rests on the student. If you can demonstrate that your preparation is equivalent to that specified by the prerequisites, the instructor may waive these requirements for you. The instructor also may request that a student who has not completed the prerequisites be dropped from the course. Note: For all courses a “C-” or better grade is required for a course to be used as a prerequisite for another course. If a course was taken for a “P/NP” grade then a “P” grade is required. If the prerequisite for a course is not satisfied, students must obtain the approval of the instructor (or school designee) of the course they wish to take.
This half-semester minicourse introduces students to the writing, implementing, and testing of MATLAB algorithms to solve mathematical problems. Topics include programming syntax, data visualization, debugging, and coding aesthetics.
Introduction to a variety of concepts useful in applied mathematics. Topics covered included floating point arithmetic, methods of proofs, random walks, stereographic projections, transforms, etc. Students are exposed to advanced mathematical topics in preparation for their ongoing studies.
Prerequisite:MATH 023 and MATH 024, both of which may be taken concurrently.Pass/Fail only.
Introduction to rigorous mathematical proofs and concepts pertaining to real
numbers. The class will cover the structure of real numbers, sequences, series and functions of real numbers, and, time permitting, concepts of abstract algebra.
Prerequisite:MATH 023. Normal Letter Grade only.Discussion included.
Introduction to complex variables, analytic functions, contour integration and theory of residues. Mappings of the complex plane. Introduction to mathematical analysis.
Prerequisite:MATH 023 and MATH 024. Normal Letter Grade only.Discussion included.
Introduces advanced solution techniques for ordinary differential
equations (ODE) and elementary solution techniques for partial differential
equations (PDE). Specific topics include higher-order linear ODE, power series
methods, boundary value problems, Fourier series, Sturm-Liouville theory,
Laplace transforms, Fourier transforms, and applications to one-dimensional PDE.
Prerequisite:MATH 023 and MATH 024.Normal Letter Grade only.Discussion included.
Introduces students to the theory of boundary value and initial value problems for partial differential equations with emphasis on linear equations. Topics
covered include Laplace’s equation, heat equation, wave equation, application of
Sturm-Liouville’s theory, Green’s functions, Bessel functions, Laplace transform, method of characteristics.
Prerequisite:MATH 125. Normal Letter Grade only.Discussion included.
Introduction to numerical methods with emphasis on algorithm construction, analysis and implementation. Programming, round-off error, solutions of equations in one variable, interpolation and polynomial approximation, approximation theory, direct solvers for linear systems, numerical differentiation and integration, initial-value problems for ordinary differential equations.
Prerequisite:MATH 024. Normal Letter Grade only.Discussion included.
Initial-value problems for ordinary differential equations, interactive techniques for solving linear systems, numerical solutions of nonlinear systems of equations, boundary-value problems for ordinary differential equations, numerical solutions to partial differential equations.
Prerequisite:(MATH 121 or MATH 125) and MATH 131.Normal Letter Grade only.Discussion included.
Linear programming and a selection of topics from among the following: matrix games, integer programming, semidefinite programming, nonlinear programming, convex analysis and geometry, polyhedral geometry, the calculus of variations and control theory.
Prerequisite:MATH 023. Normal Letter Grade only.Discussion included.
Applied linear analysis of finite dimensional vector spaces. Review of matrix algebra, vector spaces, orthogonality, least-squares approximations, eigenvalue problems, positive definite matrices, singular value decomposition with applications in science and engineering.
Prerequisite:MATH 131, which may be taken concurrently. Normal Letter Grade only.Discussion included.
Applied linear analysis of infinite dimensional vector spaces. Inner product spaces, operators, adjoint operators, Fredholm alternative, spectral theory, Sturm-Liouville operators, distributions and Green’s functions with applications in science and engineering.
Prerequisite:MATH 141. Normal Letter Grade only.Discussion included.
Introduction to the basics of mathematical modeling emphasizing model construction, analysis and application. Using examples from a variety of fields such as physics, biology, chemistry and economics, students will learn how to develop and use mathematical models of real-world systems.
Introduction to the meta-theory of first-order logic. Topics include the consistency,
compactness, completeness and soundness proofs for propositional and first-order logic; model theory; the axiomatization of number theory; Gödel’s incompleteness theorems and related results.
Prerequisite:PHIL 005 or consent of instructor.Discussion included.
Introduction to stochastic processes with emphasis on problem-solving using both
analytical and computational techniques. Markov chains in discrete and continuous
time, martingales, branching processes, renewal processes, and Brownian motion.
Prerequisite:MATH 024 and MATH 032.Normal Letter Grade only.Discussion included.
Students are introduced to ‘scientific teaching’ - an approach to teaching science that uses many of the same skills applied in research. Topics include how people learn, active learning, designing, organizing and facilitating teachable units, classroom management, diversity in the classroom and assessment design.
Partial differential equations (PDEs) of applied mathematics. Topics include modeling physical phenomena, linear and nonlinear first-order PDEs, D’Alembert’s solution, second-order linear PDEs, characteristics, initial and boundary value problems, separation of variables, Sturm-Liouville problem, Fourier series, Duhamel’s Principle, linear and nonlinear stability.
Prerequisite:MATH 122 or consent of instructor.Normal Letter Grade only.Discussion included.
Continuation of MATH 221. Topics include integral transforms, asymptotic methods for integrals, integral equations, weak solutions, point sources and fundamental solutions, conservation laws, Green’s functions, generalized functions, variational properties of eigenvalues and eigenvectors, Euler-Lagrange equations, Maximum principles.
Prerequisite:MATH 221 or consent of instructor. Normal Letter Grade only.Discussion included.
Asymptotic evaluation of integrals, matched asymptotic expansions, multiple scales, WKB, and homogenization. Applications are made to ODEs, PDEs, difference equations, and integral equations to study boundary and shock layers, nonlinear wave propagation, bifurcation and stability, and resonance.
Prerequisite:MATH 221 or consent of instructor.Normal Letter Grade only.Discussion included.
MATH 231: Numerical Solution of Differential Equations I
[4 units]
Examines fundamental methods typically required in the numerical solution of differential equations. Topics include direct and indirect methods for linear systems, nonlinear systems, interpolation and approximation, eigenvalue problems, ordinary-differential equations (IVPs and BVPs), and finite differences for elliptic partial-differential equations. A significant amount of programming is required.
Prerequisite:MATH 132 or consent of instructor. Normal Letter Grade only.Discussion included.
MATH 232: Numerical Solution of Differential Equations II
[4 units]
Fundamental methods presented in Math 231 are used as a base for discussing modern methods for solving partial-differential equations. Numerical methods include variational, finite element, collocation, spectral, and FFT. Error estimates and implementation issues are discussed. A significant amount of programming is required.
Prerequisite:MATH 231 or consent of instructor. Normal Letter Grade only.Discussion included.
Theoretical and practical introduction to parallel scientific computing. Survey of hardware and software environments, and selected algorithms and applications. Topics include linear systems, N-body problems, FFTs, and methods for solving PDEs. Practical implementation and performance analysis are emphasized in the context of demonstrative applications in science and engineering.
Prerequisite:MATH 232 or consent of instructor. Normal Letter Grade only.Discussion included.
Designed to increase the writing proficiency of graduate students, with a focus on strategies for reading critically, organizing and developing thoughts, choosing appropriate vocabulary, and generating and revising writing in a given scientific field. Topics address scientific disciplines. Projects may include writing abstracts, research reports, literature reviews, posters, and grant proposals.
Treatment of a special topic or theme in applied mathematics at the graduate level. May be repeated for credit in a different subject area.
Permission of instructor required.Students may choose Satisfactory/Unsatisfactory grading option with consent of instructor.Course may be repeated for credit.
Centered on a student’s classroom experiences as a Teaching Assistant in an undergraduate Applied Mathematics course. Provides a faculty-directed opportunity to implement teaching practices presented in the course Teaching and Learning in the Sciences. Involves video-taping of teaching, peer review, and weekly meetings with faculty.
Permission of instructor required.Satisfactory/Unsatisfactory only.Course may be repeated 1 time for credit.Discussion, Laboratory included.
Introduction to Fortran and Matlab. Concepts of formatted input/output, data types, variables, arrays, strings, variable scopes, logic statements, loops and repetition, functions and subroutines, and data graphing. Computing examples are drawn from mechanical engineering topics including linear algebraic equations, root search, two and three-dimensional graphics. Laboratory included.
Prerequisite: Freshman Standing. Computer Science and Engineering, Environmental Engineering, Materials Science and Engineering, Mechanical Engineering majors only. Normal Letter Grade only.Laboratory included.
Introduce the basic fundamentals of the finite element methods. Beginning with simple one-dimensional problem, continuing to two- and three-dimensional
elements, and ending with some applications in heat transfer, solid mechanics and fluid mechanics. Covers modeling, mathematical formulation, computer
implementation and engineering software.
Prerequisite:MATH 023 and MATH 024. Normal Letter Grade only.Laboratory included.
Introduction to the use of modern computational tools used for design and analysis. Primary focus will be on product design with solid modeling and finite-element analysis. Software used is representative of that found in industry. Topics such as 2-D and 3-D drawing, tolerance specification, and FEA validation are also covered.
Prerequisite: Junior standing. Normal Letter Grade only.Offered fall only.Laboratory included.
Dynamics of particles and rigid bodies. Vibration of discrete systems with finite
degrees of freedom and continuous structures including beams and plates. Resonance, anti-resonance, damping, and modal coupling. Modal analysis. Proportional, derivative and integral feedback controls of vibrations. Stability concept. Control design by root locus and frequency domain method.
Prerequisite:MATH 024 and ENGR 057.Normal Letter Grade only.Offered spring only.Laboratory included.
Dynamics of Linear Systems, Concepts of Stability, Feedback Control, Root Locus Design, Frequency-Domain Analysis and Compensator Design, State-Space Representation, Controllability and Observability, Linear Observers, Matrix Methods for Control Design, Linear Quadratic Regulator (LQR) Optimal Control.
Prerequisite:MATH 024 and ME 140. Normal Letter Grade only.
Introduction to electro-mechanical systems controlled by microcontroller technology. The course covers theory, design and construction of smart systems; closely coupled and fully integrated products and systems; the synergistic integration of sensors, interfaces, actuators, microcontrollers, control and information technology.
Prerequisite:ENGR 057 and ENGR 065.Normal Letter Grade only.Laboratory included.
Design project must be selected and approved; project feasibility study and outline of the design project is completed; design methodology, optimization, product reliability and liability, economics, use of ASME codes. A final presentation is given at the end of the semester.
Prerequisite: Senior standing and ME 120 and ENGR 135 and ME 137. Normal Letter Grade only.Laboratory included.
Introduction to machine shop technology. Study of basic measuring tools, vernier calipers, steel rules, and micrometers, layout tools, hand tools. Emphasis in the theory and practice in the use of vertical milling machine, lathes and drilling
machines.
Pass/Fail only.Course may be repeated 2 times for credit. Laboratory included.
Lectures on special topics are announced at the beginning of the semester in which the course is offered. Topics may include special mechanisms, non-Newtonian fluid mechanics, non-equlibrium thermodynamics, design methods for special applications, among other possibilities.
Prerequisite:Junior standing.Permission of instructor required.Normal Letter Grade only.Course may be repeated 2 times for credit.
Rigid body dynamics, including topics such as: dynamical systems, motion representation and constraints, Newtonian, Lagrangian and Hamiltonian mechanics, stability analysis and introduction to multibody dynamics.
Prerequisite:MATH 024 and ENGR 057. Normal Letter Grade only.Course may be repeated 1 time for credit. Offered in fall only.
Systematic analysis of fluid flow, heat transfer and mass transfer phenomena, with emphasis on the analogies and specific techniques used in treating such boundary value problems.
Prerequisite:ENGR 135. Normal Letter Grade only. Offered spring only.
Dynamics of Linear Systems, Concepts of Stability, Feedback Control, Root Locus Design, Frequency-Domain Analysis and Compensator Design, State-Space Representation, Controllability and Observability, Linear Observers, Matrix Methods for Control Design, Linear Quadratic Regulator (LQR) Optimal Control. Knowledge in linear algebra and differential equations and Vibration and Controls is strongly suggested.
Phase plane and singularities. Methods for nonlinear analysis. Lyapunov stability theory. Passivity. Lyapunov control design. Topics of nonlinear controls including feedback linearization, sliding control and back stepping design. Adaption algorithms and system identification. Discussion of current research topics in nonlinear controls.
Permission of instructor required.Normal Letter Grade only.
Review of mathematical theory and computations of matrix. LU decomposition. Singular value decomposition. QR decomposition. Schur decomposition. Eigen-decomposition. Cholesky decomposition. Expansion theorem. Pseudoinverse and solution of linear algebraic equations. Matrix representation of dynamical systems, the fundamental solution, and control formulation. Optimal sliding surface. Other engineering applications. Knowledge of the topics covered in ME 140 Vibration
and Control are necessary for the successful completion of this course.
Permission of instructor required.Normal Letter Grade only.
Cartesian tensors in mechanics, coordinate transformations, analysis of stress and strain, principal values, invariants, equilibrium and compatibility equations, constitutive relations, field equations; problems in elasticity; computational methods.
Prerequisite:ENGR 120. Normal Letter Grade only.Offered in fall only.
Basic concepts (forces, displacements, stress, tensor, strain, etc.), linear and nonlinear elastic solids, linear viscous fluids, linear viscoelastic fluids and solids, and selected topics in nonlinear viscoelastic behavior.
Tribology is the study of components moving in relative motion. As such, this course will cover the areas of friction, wear and lubrication. Specific topics include surface properties, wear of materials, frictional contact and energy dissipation, fluid lubricated bearings, lubrication of highly loaded contacts, and nanoscale tribological phenomena.
Heat conduction fundamentals; one-and mutli-deminsional steady state; transient conduction; hyperbolic conduction. Solution methods (separation of variables, integral transforms, integral method, numerical methods). Graduate standing is required. Knowledge in the undergraduate physics sequence; undergraduate thermodynamics; undergraduate heat transfer desirable but not essential.
Fluid transport properties and relevant conservation equations. Momentum, heat and mass transfer in laminar and turbulent internal and external flows. Buoyancy driven flows (free convection). Heat transfer in high-speed flow. Convective mass transfer. Special topics in heat and mass transfer; e.g., ablation, combustion, forced convection boiling and condensation (2-phase flow). Knowledge of undergraduate thermodynamics, heat transfer and graduate fluid mechanics is strongly advised.
Steady and unsteady mass diffusion; mass convection, simultaneous heat and mass transfer; Fick’s law in a moving medium; similarity and integral methods in mass transfer; high mass transfer theory; research project in mass transport.
Normal Letter Grade only.Course may be repeated 1 time for credit.
Thermal radiation fundamentals; radiative properties of opaque’s surfaces; radiative exchange between opaque surfaces; radiative transfer equation; radiative properties of gases and particles; radiative exchange in participating media.
Prerequisite: Undergraduate physics sequence and thermodynamics; undergraduate heat transfer desirable but not essential. Normal Letter Grade only.
Addresses the effects of compressibility in viscous and inviscid flows; steady and unsteady inviscid subsonic and supersonic flows; method of characteristics; small disturbance theories (linearized and hypersonic); shock dynamics; and hypersonic flows. Students are expected to be conversant in materials that are covered in ENGR 120 or the equivalent course.
Study of the Navier-Stokes equations; Stokes’ problems; creeping flows; internal and external flows; similarity and integral methods in boundary layer flows; stability and transition to turbulence. Knowledge of the topics in ENGR 135 or ES 235 Heat Transfer are necessary for the successful completion of this course.
Normal Letter Grade only. Course may be repeated 1 time for credit.Offered fall only.
Provides fundamentals of computational theory and computational methods. The first part covers material fundamentals to the understanding and application of numerical methods. The second part illustrates the use of such methods in solving different types of complex problems encountered in fluid mechanics and convective heat transfer.
Provides the fundamentals and methodologies of non-imaging optics to design energy systems. The first part covers material fundamental to the understanding of imaging optics. This will lead into the non-imaging optical systems and the physics that made it possible to design solar energy concentrators. The second half of the course covers material dedicated to the designs of non-imaging optical systems applied to the solar energy field and optimization and analysis of these systems.
Permission of instructor required.Normal Letter Grade only.Discussion included.
Intended to provide students an overview on energy storage schemes/devices with major focus on electrochemical storages including ionic batteries, fuel cells and super-capacitors. The course will cover operating principles, physics behind them, characterization methods and advantages/issues of each scheme. Exposure to thermodynamics is recommended but not mandatory.
Normal Letter Grade only. Course may be repeated 1 time for credit.
Prepares students with fractional calculus (differentiation or integration of non-integer order) and fractional dynamic modeling of complex mechanical systems such as porous medias, particulate systems, soft matters etc. that have inherent nature of memory, heredity, or long-range dependence (LRD), or long range interactions at or across various scales.
Permission of instructor required.Normal Letter Grade only.Laboratory included.
NSED 023: Introduction to Teaching Science in Elementary School
[1 units]
Introduction to teaching science in elementary school. Emphasis on inquiry-based learning practices and effective research-based teaching strategies. Activities include seminars, discussions, and experimentation using inquiry-based learning modules.
Normal Letter Grade only.Discussion, Laboratory included.
NSED 024: Fieldwork: Introduction to Teaching Science in Elementary School
[1 units]
Fieldwork component for the NSED 023 course. Classroom observations and teaching practicum at an elementary school under the guidance of a mentor teacher. Emphasis on inquiry-based learning practices and effective research-based teaching strategies.
NSED 033: Introduction to Teaching Mathematics in Elementary School
[1 units]
Introduction to teaching mathematics in elementary school. Emphasis on inquiry-based learning practices and effective research-based teaching strategies. Activities include seminars, discussions, and experimentation using inquiry-based learning modules.
Normal Letter Grade only. Discussion, Laboratory included.
NSED 034: Fieldwork - Introduction to Teaching Mathematics in Elementary School
[1 units]
Fieldwork component for the NSED 033 course. Classroom observations and teaching practicum at an elementary school under the guidance of a mentor teacher. Emphasis on inquiry-based learning practices and effective research-based teaching strategies.
NSED 043: Introduction to Teaching Science in Middle School
[1 units]
Introduction to teaching science in middle school. Emphasis on inquiry-based learning practices and effective research-based teaching strategies. Activities include seminars, discussions, and experimentation using inquiry-based learning modules.
NSED 044: Fieldwork - Introduction to Teaching Science in Middle School
[1 units]
Fieldwork component for the NSED 043 course. Classroom observations and teaching practicum at a middle school under the guidance of a mentor teacher. Emphasis on inquiry-based learning practices and effective research-based teaching strategies.
NSED 053: Introduction to Teaching Mathematics in Middle School
[1 units]
Introduction to teaching mathematics in middle school. Emphasis on inquiry-based learning practices and effective research-based teaching strategies. Activities include seminars, discussions, and experimentation using inquiry-based learning modules.
NSED 054: Fieldwork - Introduction to Teaching Mathematics in Middle School
[1 units]
Fieldwork component for the NSED 053 course. Classroom observations and teaching practicum at a middle school under the guidance of a mentor teacher. Emphasis on inquiry-based learning practices and effective research-based teaching strategies.
NSED 063: Introduction to Teaching Science in High School
[1 units]
Introduction to teaching science in high school. Emphasis on inquiry-based learning practices and effective research-based teaching strategies. Activities include seminars, discussions, and experimentation using inquiry-based learning modules.
Normal Letter Grade only.Discussion, Laboratory included.
NSED 064: Fieldwork - Introduction to Teaching Science in High School
[1 units]
Fieldwork component for the NSED 063 course. Classroom observations and teaching practicum at a high school under the guidance of a mentor teacher. Emphasis on inquiry-based learning practices and effective research-based teaching strategies.
NSED 073: Introduction to Teaching Mathematics in High School
[1 units]
Introduction to teaching mathematics in High school. Emphasis on inquiry-based learning practices and effective research-based teaching strategies. Activities include seminars, discussions, and experimentation using inquiry-based learning modules.
Normal Letter Grade only.Discussion, Laboratory included.
NSED 074: Fieldwork - Introduction to Teaching Mathematics in High School
[1 units]
Fieldwork component for the NSED 073 course. Classroom observations and teaching practicum at a high school under the guidance of a mentor teacher. Emphasis on inquiry-based learning practices and effective research-based teaching strategies.
Prerequisite: Applied Mathematical Sciences, Biological Sciences, Chemical Sciences, Earth Systems Science, Physics majors only. Permission of instructor required.Course may be repeated for credit.Discussion included.
NSED 100: Introduction to Instruction, Assessment, and Management for Beginning Teachers
[4 units]
Prepares students for careers in K-12 education. Students gain knowledge of classroom management strategies and learn how to organize a classroom, to plan units and to develop lesson plans. A special focus will be the techniques necessary to effectively teach in multicultural and multilingual schools.
Normal Letter Grade only.Discussion, Laboratory included.
Focusing on American education, we examine historical and current issues of diversity, noting controversial initiatives such as mainstreaming, bilingual education, multiculturalism, and gender-neutral or gender-segregated instruction. Students also consider cultural and linguistic challenges of teaching English language learners, including those who are generation 1.5 students.
NSED 174: Contemporary Issues in Teaching with Fieldwork
[1 units]
Combines study and observation of a K-12 classroom setting and reflection the aspects of teaching which have current importance in the field of education. The course includes fieldwork component where students will be working in classrooms of the local K-12 schools.
Prerequisite: Any lower division NSED course. Normal Letter Grade only. Course may be repeated 3 times for credit.
An introduction to the main areas of philosophy using classic and contemporary sources. Consideration of central and enduring problems in philosophy, such as skepticism about the external world, the mind-body problem and the nature of morality.
Introduction to formal and informal logic. Topics include argumentation analysis, fallacies, soundness vs. validity, inductive vs. deductive reasoning, truth tables, proof techniques in statement and predicate logic, and the probability calculus.
Consideration of central themes in phenomenology and existentialism and their philosophical origins in nineteenth century philosophy. Readings from such figures as Nietzsche, Husserl, Sartre, Freud, Merleau-Ponty, and Heidegger.
Provides oversight and structure for a student’s internship in a field related to philosophy in community organizations, professional research projects, etc. connected to the study of philosophy. Students are required to write an original research paper or relevant product that demonstrates how the internship advanced their knowledge of philosophy.
Permission of instructor required.Pass/Fail only. Course may be repeated 2 times for credit.
Inquiry into the fundamental nature of reality: the categories of being; the differences between abstract entities, concrete entities, substances, properties, and processes; what constitutes identity of objects through time; necessity and possibility; free will and determinism; space, time, and causation.
Prerequisite:PHIL 001 and PHIL 005 or consent of instructor. Normal Letter Grade only.