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The core of this program is 29 credits of required math courses and 30 credits of required physics courses. In addition, you must take 9 credits of math electives and 12 credits of physics electives. 16 credits are reserved for free electives and independent study courses, of which 6 to 8 credits are recommended for a project. The remaining credits are used to satisfy other Institute and state requirements.

- 4 Credits Calculus I MA-UY 1024
- This course covers library of Functions: functions of one variable. Limits, derivatives of functions defined by graphs, tables and formulas, differentiation rules for power, polynomial, exponential and logarithmic functions, derivatives of trigonometric functions, the product and quotient rule, the chain rule, applications of the chain rule, maxima and minima, optimization. MA 1324 is for students who wish to take MA 1024 but need more review of precalculus. MA1324 covers the same material as MA1024 but with more contact hours a week, incorporating a full discussion of the required precalculus topics.

Prerequisite: Placement Exam or MA-UY 912 or MA-UY 914. Corequisite: EX-UY 1 - 4 Credits Calculus II MA-UY 1124
- This course covers definite integrals, theorems about integrals, anti-derivatives, second fundamental theorem of calculus, techniques of integration, introduction to ordinary differential equations, improper integrals, numerical methods of integration, applications of integration, sequences, series, power series, approximations of functions via Taylor polynomials, Taylor series.

Corequisite: EX-UY 1. - 2 Credits Multivariable Calculus A MA-UY 2112
- This course introduces Multivariable Calculus. Analysis of functions of several variables, vector valued functions, partial derivatives and multiple integrals.

Prerequisite: MA-UY 2012. - 2 Credits Multivariable Calculus B MA-UY 2122
- This course continues Multivariable Calculus. Optimization techniques, parametric equations, line integrals, surface integrals and major theorems concerning their applications.

Prerequisite: MA-UY 2112. - 2 Credits Elements of Linear Algebra I MA-UY 2012
- This course introduces vector concepts. Linear transformations.Matrices and Determinants. Characteristic roots and eigenfunctions.

Prerequisite: MA-UY 1124 or equivalent. - 2 Credits Ordinary Differential Equations MA-UY 2132
- This course covers first order differential equations: modeling and solving. Stability of autonomous equations. Higher order linear ordinary differential equations: Solution bases, Wronskian and initial value problems. Linear system of first-order differential equations with constant coefficients: Elimination and eigenvalue method of solution. Elementary concepts of numerical analysis. Numerical solution of initial value problems for ordinary differential equations.

Prerequisite or Corequisite: MA-UY 2012. - 2 Credits Introduction to Probability I MA-UY 3012
- This course covers probability of events. Random variables. Discrete and continuous distributions. Joint distributions. Expectation. Functions of a random variable. Central limit theorem.

Prerequisite: MA-UY 2112 or MA-UY 2114. - 2 Credits Complex Variables I MA-UY 3112
- This course covers functions of a complex variable. Derivatives and Cauchy-Riemann equations. Integrals and Cauchy integral theorem. Power and Laurent Series. Residue theory.

Prerequisite: MA-UY 2122 or equivalent. - MA-UY 4113 (Please refer to the bulletin)
- 3 Credits Applied Partial Differential Equations MA-UY 4413
- This course looks at the heat equation, homogeneous and non-homogeneous boundary conditions, Green’s function, separation of variables, Fourier series and Fourier transform, Maximum principle, existence and uniqueness, Poisson integral formula, the wave equation. Shock waves, conservation laws.

Prerequisite: MA-UY 2132 and MA-UY 3112. - 3 Credits Introductory Numerical Analysis MA-UY 4423
- This course covers: Polynomial interpolation and approximation of functions. Divided differences. Least-squares data fitting, orthogonal polynomials. Numerical differentiation and integration. Solution of nonlinear equations. Gaussian elimination, pivoting, iterative refinement, conditioning of matrices. Numerical solution of ordinary differential equations.

Prerequisites: MA-UY 2132 and some experience in computer programming.

- PH-UY 1004 (Please refer to the bulletin)
- PH-UY 2004 (Please refer to the bulletin)
- 4 Credits Introduction to Modern and Solid State Physics PH-UY 2344
- Special theory of relativity, Michelson Morley experiment. Planck’s quantum hypothesis, photoelectric effect, Compton effect, Rutherford scattering, Bohr’s atom, DeBroglie wavelength, electron diffraction, wave function, uncertainty principle, Schrodinger equation. Application to: square well potential, one electron atom. Atomic nucleus, fission and fusion. Energy bands in a periodic lattice, Kronig Penney model, valence, conduction bands, impurity states, electron mobility. Semiconductor properties. Introduction to superconductivity; electron pairs, energy gap, Josephson effect.

Prerequisite: PH-UY 2004 or PH-UY 2023; Co-requisites: PH-UY 2033. - 4 Credits Analytical Mechanics PH-UY 2104
- The course covers statics by virtual work and potential energy methods. Stability of equilibrium. Particle dynamics, harmonic oscillator and planetary motion. Rigid body dynamics in two and three dimensions. Lagrangian mechanics. Dynamics of oscillating systems.

Prerequisites: MA-UY 2122, and PH-UY 2004 or PH-UY 2023. - 4 Credits Electricity and Magnetism PH-UY 3234
- The course covers properties of the electrostatic, magnetostatic and electromagnetic field in vacuum and in material media. Maxwell’s equations with applications to elementary problems.

Prerequisites: MA-UY 2122, and PH-UY 2004 or PH-UY 2033. - 4 Credits Thermodynamics and Statistical Physics PH-UY 4124
- The course covers fundamental laws of macroscopic thermodynamics, heat, internal energy and entropy. Topics include an introduction to statistical physics, and applications of Maxwell, Fermi-Dirac and Bose-Einstein distributions.

Prerequisites: MA-UY 2122 and PH-UY 2344. - PH-UY 4364 (Please refer to the bulletin)
- 2 Credits Senior Seminar in Physics PH-UY 4912
- Senior physics students, in consultation with the instructor, study and prepare presentations on several current research topics in the general area of interdisciplinary physics. Students’ performance is based on the mastery of the material chosen and also on the quality of the presentation made to the instructor and the seminar members.

- 4 Credits General Chemistry For Engineers CM-UY 1004
- This is a one-semester introductory course in general chemistry. It covers chemical equations, stoichiometry, thermodynamics, gases, atomic and molecular structure, periodic table, chemical bonding, states of matter, chemical equilibrium, organic, inorganic and polymeric materials and electrochemistry.

Corequisite: EX-UY 1 - 4 Credits Intro to Programming & Problem Solving CS-UY 1114
- This course introduces problem solving and computer programming and is for undergraduate Computer Science and Computer Engineering majors who have limited prior experience in programming in any language. The course covers fundamentals of computer programming and its underlying principles using the Python programming language. Concepts and methods introduced in the
course are illustrated by examples from various disciplines. ABET competencies: a,b,c, e, f, g, k

Corequisite: EX-UY 1 - EN-UY 1014 (Please refer to the bulletin)
- EN-UY 1204 (Please refer to the bulletin)
- HI-UY 2104 (Please refer to the bulletin)

You should select 9 credits from the following list of math elective courses.

- MA-UY 3103 (Please refer to the bulletin)
- MA-UY 3303 (Please refer to the bulletin)
- 3 Credits Analysis I MA-UY 4613
- This course covers the study of basic topics in analysis with emphasis on methods. Sequences, series, functions, uniform convergence, continuity, partial differentiation, extreme value problems with constraints, Riemann integrals, line integrals, improper integrals, integrals with parameters, transformations, Riemann-Stieltjes integral, uniform and absolute convergence of integrals. Beta and Gamma functions.

Prerequisites: MA-UY 2122 and MA-UY 2132. - 3 Credits Analysis II MA-UY 4623
- This course covers the study of basic topics in analysis with emphasis on methods. Sequences, series, functions, uniform convergence, continuity, partial differentiation, extreme value problems with constraints, Riemann integrals, line integrals, improper integrals, integrals with parameters, transformations, Riemann-Stieltjes integral, uniform and absolute convergence of integrals. Beta and Gamma functions.

Prerequisites: MA-UY 4613 - MA-UY 3203 (Please refer to the bulletin)
- MA-UY 4013 (Please refer to the bulletin)
- MA-UY 4023 (Please refer to the bulletin)

You should select 12 credits from the following list of physics elective courses.

- 3 Credits Astronomy and Astrophysics PH-UY 2813
- This course covers historical development of observational astronomy. Traditional and modern observational techniques. Theories of formation and evolution of stars, planets and galaxies. Current developments in astronomy, cosmology and astrophysics.

Prerequisite: PH-UY 2031 and PH-UY 2033 - 4 Credits Introduction to Polymer Physics PH-UY 3054
- This course introduces polymer physics and its applications in engineering. The course includes polymer assemblies, morphology and motion, mechanical and dielectric response, transitions and relaxations, time-temperature equivalence, yield and fracture, conducting polymers, optics of polymers, oriented structures, nanofibers, composites.

Prerequisite: CM-UY 1004 or C-UY 1014; Co-requisites: PH-UY 2004 or PH-UY 2023. - PH-UY 3244 (Please refer to the bulletin)
- PH-UY 3424 (Please refer to the bulletin)
- 4 Credits Introduction to Modern Optics PH-UY 3474
- This course covers the physics of optics using both classical and semi-classical descriptions. The classical and quantum interactions of light with matter. Diffraction of waves and wave packets by obstacles. Fourier transform optics, holography, Fourier transform spectroscopy. Coherence and quantum aspects of light. Geometrical optics. Matrix optics. Crystal optics. Introduction to electro-optics and nonlinear optics.

Prerequisite: PH-UY 2004 or PH-UY 2033. - PH-UY 4244 (Please refer to the bulletin)
- PH-UY 4444 (Please refer to the bulletin)
- PH-UY 4554 (Please refer to the bulletin)

*Graduate courses may be substituted with adviser's approval for the following physics elective courses:*

- PH-GY 5343 (Please refer to the bulletin)
- PH-GY 5443 (Please refer to the bulletin)
- PH-GY 5473 (Please refer to the bulletin)
- PH-GY 5493 (Please refer to the bulletin)
- PH-GY 5553 (Please refer to the bulletin)
- PH-GY 5663 (Please refer to the bulletin)

You are required to take 12 credits in the humanities and social sciences, with EN 1204 and HI 2104 as prerequisites. To gain depth of knowledge, it is recommended that one or more of these electives be taken at advanced level.

Sixteen credits are reserved for free electives and independent study courses, of which 6 to 8 credits are recommended for use on a project or thesis topic.

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