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.

#### Math Requirements (29 credits)

- 4 Credits Calculus I for Engineers 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 for Engineers 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. - 3 Credits Introduction to Mathematical Statistics MA-UY 4113
- This is a standard first course in mathematical statistics, recommended for those who will take advanced courses in statistics. Topics covered: Sampling distributions, tests of hypotheses, significance tests, point and interval estimation, regression and analysis of variance.

Prerequisite: MA-UY 3012. - 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.

#### Physics Requirements (30 credits)

- 4 Credits Introductory Physics I PH-UY 1004
- This course is the first of a two-semester integrated lecture and laboratory sequence in general physics for science and engineering students. One-dimensional motions. Vectors and two-dimensional motions. Newton’s laws of motion. Conservation of energy and momentum. Rotational motions. Gravity. Statics and elasticity. Fluids. Oscillations. Heat and the laws of thermodynamics.

Prerequisite: MA-UY 1024 or an approved equivalent. Co-requisite: MA-UY 1124 or an approved equivalent, and EX-UY 1 - 4 Credits Introductory Physics II PH-UY 2004
- This is the second course of a two-semester, integrated lecture and laboratory sequence in general physics for science and engineering students. Electric forces and fields. Electric potential and capacitance. Electric current. Magnetic forces and fields. Faradays law and inductance. Maxwell’s equations. Mechanical and electromagnetic waves. Geometrical optics. Interference and diffraction.

Prerequisites: PH-UY 1004, MA-UY 1124 or an approved equivalent. Corequisite: EX-UY 1 - 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.

Prerequisites: PH-UY 2023 and MA-UY 2034; Co-requisite: 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.

Prerequisite: PH-UY 2023; Co-requisite: MA-UY 2034 - 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: PH-UY 2033 and MA-UY 2114. - 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: PH-UY 2344, MA-UY 2114, and MA-UY 2224. - 4 Credits Introduction to the Quantum Theory PH-UY 4364
- The course introduces quantitative introduction to the quantum theory, which describes understanding light, electrons, atoms, nuclei and solid matter. Superposition principle, expectation values, momentum operator and wave function, duality, current vector, Hermitian operators, angular momentum, solution of the radial equation, electron in a magnetic field, perturbation theory, WKB approximation, identical particles. Applications include alpha decay, electrons in a periodic lattice, hydrogen spectrum, helium atom, neutron-proton scattering, and quark model of baryons.

Prerequisites: PH-UY 2344, MA-UY 2114, and MA-UY 2224. - 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.

#### Other Required Courses (20 Credits)

- 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 Introduction 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 - 4 Credits Writing & Humanities 1 EN-UY 1014
- 4 Credits Writing & Humanities 2 EN-UY 1204
- 4 Credits Modern World History HI-UY 2104

#### Math Electives (9 credits)

You should select 9 credits from the list of undergraduate math elective courses. Graduate courses may be substituted with advisor’s approval.

#### Physics Electives (12 Credits)

You should select 12 credits from the list of undergraduate applied physics elective courses. Graduate courses may be substituted with advisor’s approval.

#### Electives in the Humanities and Social Sciences (12 Credits)

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.

#### Free Electives, Independent Study and Projects (16 Credits)

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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