- Academics

# Applied Physics, B.S.

Applied Physics is devoted to the study and understanding of nature. Considered the most fundamental science, it deals with the constituents, properties, and evolution of the entire universe, from the smallest subatomic particles to the largest galaxies.

At the School of Engineering, our BS in Applied Physics students study physics while working directly alongside engineers. That relationship provides lasting value, as graduates learn to adapt their careers to existing opportunities. You’re encouraged to explore your interests in such fields as entrepreneurship, biophysics, or biomedical instrumentation. Integrated circuit electronics, scanning probe metrology, and computational science are also options. Best of all, your explorations can propel you toward a dual degree, particularly in subjects such as electrical engineering, mechanical engineering, and chemistry.

With a strong foundation in physics, many of our students go on to pursue advanced studies at the master’s level. Many of our graduates seek positions within and beyond the sciences, in fields that include law, writing, and business. Others find a career in disciplines that rely on a solid foundation in physics, be it in industry, government, or education.

## Curriculum

OverviewYou must complete 128 credits, as defined below, to graduate from the School of Engineering with a Bachelor of Science in Applied Physics. Please note that the curriculum that follows applies to students who began classes in the fall of 2014 or later. If you entered the School of Engineering prior to that date, please consult the curriculum and typical course schedule for students entering prior to fall 2014.

The Department of Applied Physics also offers a Minor in Applied Physics and a Concentration and Minor in Nuclear Science and Engineering. A full list of the department's undergraduate offerings is available here.

Core Physics Requirements (37 Credits)

- 2 Credits Physics: the Genesis of Technology PH-UY1002
- This course introduces contemporary topics in physics, along with readings and discussions of topics with technological implications.

Prerequisite: Only first-year students are permitted to enroll in this introductory level course. - 3 Credits Mechanics PH-UY1013
- This course is the first of a three-semester lecture sequence in general physics for science and engineering students. Motion of particles and systems of particles. One-dimensional motion. Vectors and two-dimensional motions. Forces and acceleration. Conservation of energy and momentum. Rotations. The free and driven harmonic oscillator. Gravitation. (This class meets four hours per week for lectures and recitation.)

Prerequisites: MA-UY 1024 or an approved equivalent. Corequisites: MA-UY 1124 or approved equivalent, and EX-UY 1 - 3 Credits Electricity, Magnetism, & Fluids PH-UY2023
- This is the second course of a three-semester lecture sequence in general physics for science and engineering students. Fluids at rest and in motion. An introduction to electric and magnetic forces and fields. Electric charge density. Electric fields from simple charge distributions. Electric potential. Capacitance. Magnetic forces. Magnetic field from a current loop. Inductance. Magnetism in matter. Current and resistance. (This class meets four hours per week for lectures and recitation.)

Prerequisites: PH-UY 1013 and MA-UY 1124 or an approved equivalent. Co-requisite: PH-UY 2121 General Physics Laboratory I, and EX-UY 1 - 3 Credits Waves, Optics, & Thermodynamics PH-UY2033
- This is the third course of a three-semester lecture sequence in general physics for science and engineering students. Water, sound and electromagnetic waves. Reflection, scattering and absorption. Standing waves and spectra. Superposition, diffraction and beats. Geometrical optics. Introduction to thermodynamics; temperature, heat, and entropy. (This class meets four hours per week for lectures and recitation.)

Prerequisites: PH-UY 2121 and PH-UY 2023. Co-requisites: PH-UY 2131, and EX-UY 1. - 4 Credits Analytical Mechanics PH-UY2104
- 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 - 1 Credits General Physics Laboratory I PH-UY2121
- PH-UY 2121 General Physics Laboratory I (0.5:1:0:1). An introductory level experimental course. Fundamental laboratory experiments in classical mechanics and electrostatics. Stresses basic experimental techniques, error analysis, and written presentation of experiment results. Experiments require progressively more detailed and sophisticated analysis. This laboratory class meets for three hours on alternate weeks.

Prerequisites: PH-UY 1013 and MA-UY 1124 or equivalent. Co-requisite: PH-UY 2023. - 1 Credits General Physics Laboratory II PH-UY2131
- PH 2131 General Physics Laboratory II (0.5:1:0:1). The second part of the introductory physics laboratory program. Fundamental laboratory experiments in E&M, waves, optics, and thermodynamics. Stresses experimental models and design, error and data analysis. This laboratory class meets for three hours on alternate weeks.

Prerequisites: PH-UY 2121 and PH-UY 2023. Corequisite: PH-UY 2033 - 4 Credits Introduction to Modern and Solid State Physics PH-UY2344
- 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; Co-requisite: PH-UY 2033 and MA-UY 2034. - 2 Credits Junior Physics Laboratory PH-UY3002
- An intermediate level laboratory course providing in depth exposure to a selection of classic physics experiments. Students' experimental skill set is expanded and data analysis and communication skills developed.

Prerequisites: PH-UY 2131 and PH-UY 2033; Co-requisites: PH-UY 2344 and MA-UY 2224. - 4 Credits Electricity and Magnetism PH-UY3234
- 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-UY4124
- 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-UY4364
- 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-UY4912
- 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 (40 Credits)

- 4 Credits Calculus I for Engineers MA-UY1024
- 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 rules, the chain rule, applications of the chain rule, maxima and minima, optimization. The definite integral, the Fundamental Theorem of Calculus and interpretations, theorems about definite integrals, anti-derivatives. MA-UY 1324 is for students who wish to take MA-UY 1024 but need more review of precalculus. MA-UY 1324 covers the same material as MA-UY 1024 but with more contact hours per week, incorporating a full discussion of the required precalculus topics.

Prerequisite: Placement Exam or MA-UY 912 or MA-UY 914 (with a grade of B or better). Corequisite: EX-UY 1 - 4 Credits Calculus II for Engineers MA-UY1124
- This course covers 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, functions of two variables, graphs of functions of two variables, contour diagrams, linear functions, functions of three variables. MA-UY 1424 is for students who wish to take MA-UY 1124 but need more review of precalculus. MA-UY 1424 covers the same material as MA-UY 1124 but with more contact hours per week, incorporating a full discussion of the required precalculus topics.

Prerequisites: MA-UY 1022 (with a grade of B or better) or MA-UY 1024 or MA-UY 1324 (with a grade of B or better).

Corequisite: EX-UY 1. - 4 Credits Linear Algebra and Differential Equations MA-UY2034
- MA-UY 2034 is an introduction to ordinary differential equations and linear algebra. The course develops the techniques for the analytic and numeric solutions of ordinary differential equations (and systems) that are widely used in modern engineering and science. Linear algebra is used as a tool for solving systems of linear equations as well as for understanding the structure of solutions to linear (systems) of differential equations. Topics covered include the fundamental concepts of linear algebra such as Gaussian elimination, matrix theory, linear transformations, vector spaces, subspaces, basis, eigenvectors, eigenvalues and the diagonalization of matrices, as well as the techniques for the analytic and numeric solutions of ordinary differential equations (and systems) that commonly appear in modern engineering and science.

Prerequisite: MA-UY 1124, MA-UY 1424 or MA-UY 1132. Note: Not open to students who have taken MA-UY 3044 or MA-UY 3054 or MA-UY 3083 or MA-UY 4204. - 4 Credits Calculus Iii: Multi-dimensional Calculus MA-UY2114
- Vectors in the plane and space. Partial derivatives with applications, especially Lagrange multipliers. Double and triple integrals. Spherical and cylindrical coordinates. Surface and line integrals. Divergence, gradient, and curl. Theorems of Gauss and Stokes.

Prerequisite: MA-UY 1124 or MA-UY 1424 or MA-UY 1132. Anti-requisite: MA-UY 2514 - 4 Credits Data Analysis MA-UY2224
- An introductory course to probability and statistics. It affords the student some acquaintance with both probability and statistics in a single term. Topics in Probability include mathematical treatment of chance; combinatorics; binomial, Poisson, and Gaussian distributions; the Central Limit Theorem and the normal approximation. Topics in Statistics include sampling distributions of sample mean and sample variance; normal, t-, and Chi-square distributions; confidence intervals; testing of hypotheses; least squares regression model. Applications to scientific, industrial, and financial data are integrated into the course.NOTE: Not open to students who have taken MA-UY 2233 or MA-UY 3012 or MA-UY 3022.

Prerequisite: MA-UY 1124, MA-UY1424, or MA-UY 1132 - 3 Credits Engineering Problem Solving and Programming CS-UY1133
- This introductory course in engineering problem solving and computer programming is for all undergraduate engineering students without prior programming experience in any language. The course covers the fundamentals of computer programming and its underlying principles using the MATLAB programming language. Concepts and methods are illustrated by examples from various engineering disciplines. Useful numerical techniques and their applications to real-world problems in science and engineering are also discussed. ABET competencies: a, e, k.

Corequisite: EX-UY 1. - 4 Credits Writing the Essay: EXPOS-UA1
- This foundational writing course is required for CAS, Stern, Nursing, Social Work, Steinhardt and Tandon incoming undergraduates. "Writing the Essay" provides instruction and practice in critical reading, creative and logical thinking, and clear, persuasive writing. Students learn to analyze and interpret written texts, to use texts as evidence, to develop ideas, and to write exploratory and argumentative essays. Exploration, inquiry, reflection, analysis, revision, and collaborative learning are emphasized. In FALL 2020, sections 001, 002, 004, 005, 006, and 007 are reserved for CAS first-year students with a strong interest in science and/or prehealth who were placed in these sections as part of the virtual advising process (in spring, sections 1,2,4,6). They are not open to other students and there are no exceptions. Sections 008, 010, 011, 013 are reserved for students who have been selected for the “Goddard Residential Stream.” In Fall, the following sections are available to incoming undergraduates on the WSQ campus: 009, 014-019, 023-024, 026-028, 031-076, 078-124. In Fall, the following sections are available to incoming Tandon undergraduates on the Brooklyn campus 126-148, 150-169. In Fall, the following sections have been designated for “Go Local” students at Shanghai, and meet at China Standard Time as designated in Albert: sections 020, 021, 022, 025, 029, 077 (Tandon only). These sections are department controlled. Please check the notes to each section to understand the teaching mode: “Online” at the meeting pattern designated; “Blended” with all students meeting in person on campus one day and the other day, online, according to the designated meeting pattern; and “In Person”, all students meeting in a physical classroom twice weekly at the designated meeting pattern. Students who are not able to attend the session at the location or time specified must register for an on-line section that works with their time zone. For questions and access, please email "ewp@nyu.edu"
- 4 Credits The Advanced College Essay EXPOS-UA2
- The course follows Writing the Essay (EW 1013) and provides advanced instruction in analyzing and interpreting written texts from a variety of academic disciplines, using written texts as evidence, developing ideas, and writing argumentative essays. It stresses analysis, argument, reflection, revision, and collaborative learning.

Prerequisite(s): EW 1013 - 1 Credits Engineering and Technology Forum EG-UY1001
- In this course the notion of invention, innovation and entrepreneurship (i2e) is introduced to the students’ educational experience. Students will be exposed to elements of a research-intensive institution and diverse research performed by leading engineers, scientists, inventors and entrepreneurs.

Two interchangeable courses

- 4 Credits General Chemistry I CM-UY1014
- This course covers chemical equations, chemical conservation laws, stoichiometry, thermochemistry, properties of gases, atomic structure, periodic table, chemical bonding and molecular structure. The course is required for students in the Biomolecular Science Program.

Corequisite: EX-UY 1. - 4 Credits General Chemistry II CM-UY1024
- This course covers states of matter, chemical thermodynamics and equilibria, kinetics, acid-base chemistry, electrochemistry, introduction to organic chemistry, natural and synthetic polymers. The course is required for students in the Biomolecular Science Program.

Prerequisite: CM-UY 1004 or CM-UY 1014. Corequisite: EX-UY 1.

Or

- 4 Credits General Chemistry for Engineers CM-UY1004
- 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 - BMS-UY1004 Please refer to the bulletin for more information

Physics and Math Electives (23 Credits)

You should select 5 applied physics elective courses totaling at least 16 Credits, and 2 math elective courses totaling at least 7 Credits. The program adviser may approve substitution of electives from other disciplines as appropriate.

Electives in the Humanities and Social Sciences (16 Credits)

You must take 16 elective credits in the humanities and social sciences, requiring EXPOS-UA1 and EXPOS-UA2 as prerequisites. To gain some breadth and depth of knowledge, it is required that you take courses in at least two disciplines and at least one course at an advanced level.

Free Electives, Independent Study and Projects (12 Credits)

You should take 12 credits of applied physics independent study and free electives. It is recommended that you use 6 of these credits toward a senior project or thesis topic.

## Sample Course Schedule

OverviewBelow is a semester-by-semester presentation of what your schedule might look like as you work to fulfill the 128 credits required for a Bachelor of Science in Applied Physics degree at the School of Engineering.

First Year

#### Fall Semester

Choose one*:

- 4 Credits General Chemistry for Engineers CM-UY1004
- 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 General Chemistry I CM-UY1014
- This course covers chemical equations, chemical conservation laws, stoichiometry, thermochemistry, properties of gases, atomic structure, periodic table, chemical bonding and molecular structure. The course is required for students in the Biomolecular Science Program.

Corequisite: EX-UY 1.

Take all:

- 2 Credits Physics: the Genesis of Technology PH-UY1002
- This course introduces contemporary topics in physics, along with readings and discussions of topics with technological implications.

Prerequisite: Only first-year students are permitted to enroll in this introductory level course. - 4 Credits Calculus I for Engineers MA-UY1024
- 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 rules, the chain rule, applications of the chain rule, maxima and minima, optimization. The definite integral, the Fundamental Theorem of Calculus and interpretations, theorems about definite integrals, anti-derivatives. MA-UY 1324 is for students who wish to take MA-UY 1024 but need more review of precalculus. MA-UY 1324 covers the same material as MA-UY 1024 but with more contact hours per week, incorporating a full discussion of the required precalculus topics.

Prerequisite: Placement Exam or MA-UY 912 or MA-UY 914 (with a grade of B or better). Corequisite: EX-UY 1 - 4 Credits Writing the Essay: EXPOS-UA1
- This foundational writing course is required for CAS, Stern, Nursing, Social Work, Steinhardt and Tandon incoming undergraduates. "Writing the Essay" provides instruction and practice in critical reading, creative and logical thinking, and clear, persuasive writing. Students learn to analyze and interpret written texts, to use texts as evidence, to develop ideas, and to write exploratory and argumentative essays. Exploration, inquiry, reflection, analysis, revision, and collaborative learning are emphasized. In FALL 2020, sections 001, 002, 004, 005, 006, and 007 are reserved for CAS first-year students with a strong interest in science and/or prehealth who were placed in these sections as part of the virtual advising process (in spring, sections 1,2,4,6). They are not open to other students and there are no exceptions. Sections 008, 010, 011, 013 are reserved for students who have been selected for the “Goddard Residential Stream.” In Fall, the following sections are available to incoming undergraduates on the WSQ campus: 009, 014-019, 023-024, 026-028, 031-076, 078-124. In Fall, the following sections are available to incoming Tandon undergraduates on the Brooklyn campus 126-148, 150-169. In Fall, the following sections have been designated for “Go Local” students at Shanghai, and meet at China Standard Time as designated in Albert: sections 020, 021, 022, 025, 029, 077 (Tandon only). These sections are department controlled. Please check the notes to each section to understand the teaching mode: “Online” at the meeting pattern designated; “Blended” with all students meeting in person on campus one day and the other day, online, according to the designated meeting pattern; and “In Person”, all students meeting in a physical classroom twice weekly at the designated meeting pattern. Students who are not able to attend the session at the location or time specified must register for an on-line section that works with their time zone. For questions and access, please email "ewp@nyu.edu"
- 1 Credits Engineering and Technology Forum EG-UY1001
- In this course the notion of invention, innovation and entrepreneurship (i2e) is introduced to the students’ educational experience. Students will be exposed to elements of a research-intensive institution and diverse research performed by leading engineers, scientists, inventors and entrepreneurs.

#### Spring Semester

Choose one*****:

- 4 Credits General Chemistry II CM-UY1024
- This course covers states of matter, chemical thermodynamics and equilibria, kinetics, acid-base chemistry, electrochemistry, introduction to organic chemistry, natural and synthetic polymers. The course is required for students in the Biomolecular Science Program.

Prerequisite: CM-UY 1004 or CM-UY 1014. Corequisite: EX-UY 1. - BMS-UY1004 Please refer to the bulletin for more information

Take all:

- 3 Credits Mechanics PH-UY1013
- This course is the first of a three-semester lecture sequence in general physics for science and engineering students. Motion of particles and systems of particles. One-dimensional motion. Vectors and two-dimensional motions. Forces and acceleration. Conservation of energy and momentum. Rotations. The free and driven harmonic oscillator. Gravitation. (This class meets four hours per week for lectures and recitation.)

Prerequisites: MA-UY 1024 or an approved equivalent. Corequisites: MA-UY 1124 or approved equivalent, and EX-UY 1 - 4 Credits Calculus II for Engineers MA-UY1124
- This course covers 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, functions of two variables, graphs of functions of two variables, contour diagrams, linear functions, functions of three variables. MA-UY 1424 is for students who wish to take MA-UY 1124 but need more review of precalculus. MA-UY 1424 covers the same material as MA-UY 1124 but with more contact hours per week, incorporating a full discussion of the required precalculus topics.

Prerequisites: MA-UY 1022 (with a grade of B or better) or MA-UY 1024 or MA-UY 1324 (with a grade of B or better).

Corequisite: EX-UY 1. - 4 Credits The Advanced College Essay EXPOS-UA2
- The course follows Writing the Essay (EW 1013) and provides advanced instruction in analyzing and interpreting written texts from a variety of academic disciplines, using written texts as evidence, developing ideas, and writing argumentative essays. It stresses analysis, argument, reflection, revision, and collaborative learning.

Prerequisite(s): EW 1013

**Choose a 2-semester sequence in chemistry, or a combination of a single semester of chemistry and a semester of biology*

Second Year

#### Fall Semester

- 3 Credits Electricity, Magnetism, & Fluids PH-UY2023
- This is the second course of a three-semester lecture sequence in general physics for science and engineering students. Fluids at rest and in motion. An introduction to electric and magnetic forces and fields. Electric charge density. Electric fields from simple charge distributions. Electric potential. Capacitance. Magnetic forces. Magnetic field from a current loop. Inductance. Magnetism in matter. Current and resistance. (This class meets four hours per week for lectures and recitation.)

Prerequisites: PH-UY 1013 and MA-UY 1124 or an approved equivalent. Co-requisite: PH-UY 2121 General Physics Laboratory I, and EX-UY 1 - 1 Credits General Physics Laboratory I PH-UY2121
- PH-UY 2121 General Physics Laboratory I (0.5:1:0:1). An introductory level experimental course. Fundamental laboratory experiments in classical mechanics and electrostatics. Stresses basic experimental techniques, error analysis, and written presentation of experiment results. Experiments require progressively more detailed and sophisticated analysis. This laboratory class meets for three hours on alternate weeks.

Prerequisites: PH-UY 1013 and MA-UY 1124 or equivalent. Co-requisite: PH-UY 2023. - 4 Credits Linear Algebra and Differential Equations MA-UY2034
- MA-UY 2034 is an introduction to ordinary differential equations and linear algebra. The course develops the techniques for the analytic and numeric solutions of ordinary differential equations (and systems) that are widely used in modern engineering and science. Linear algebra is used as a tool for solving systems of linear equations as well as for understanding the structure of solutions to linear (systems) of differential equations. Topics covered include the fundamental concepts of linear algebra such as Gaussian elimination, matrix theory, linear transformations, vector spaces, subspaces, basis, eigenvectors, eigenvalues and the diagonalization of matrices, as well as the techniques for the analytic and numeric solutions of ordinary differential equations (and systems) that commonly appear in modern engineering and science.

Prerequisite: MA-UY 1124, MA-UY 1424 or MA-UY 1132. Note: Not open to students who have taken MA-UY 3044 or MA-UY 3054 or MA-UY 3083 or MA-UY 4204. - 3 Credits Engineering Problem Solving and Programming CS-UY1133
- This introductory course in engineering problem solving and computer programming is for all undergraduate engineering students without prior programming experience in any language. The course covers the fundamentals of computer programming and its underlying principles using the MATLAB programming language. Concepts and methods are illustrated by examples from various engineering disciplines. Useful numerical techniques and their applications to real-world problems in science and engineering are also discussed. ABET competencies: a, e, k.

Corequisite: EX-UY 1.

**Humanities and Social Sciences Elective 1** * 4 Credits*

#### Spring Semester

- 3 Credits Waves, Optics, & Thermodynamics PH-UY2033
- This is the third course of a three-semester lecture sequence in general physics for science and engineering students. Water, sound and electromagnetic waves. Reflection, scattering and absorption. Standing waves and spectra. Superposition, diffraction and beats. Geometrical optics. Introduction to thermodynamics; temperature, heat, and entropy. (This class meets four hours per week for lectures and recitation.)

Prerequisites: PH-UY 2121 and PH-UY 2023. Co-requisites: PH-UY 2131, and EX-UY 1. - 4 Credits Analytical Mechanics PH-UY2104
- 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 - 1 Credits General Physics Laboratory II PH-UY2131
- PH 2131 General Physics Laboratory II (0.5:1:0:1). The second part of the introductory physics laboratory program. Fundamental laboratory experiments in E&M, waves, optics, and thermodynamics. Stresses experimental models and design, error and data analysis. This laboratory class meets for three hours on alternate weeks.

Prerequisites: PH-UY 2121 and PH-UY 2023. Corequisite: PH-UY 2033 - 4 Credits Introduction to Modern and Solid State Physics PH-UY2344
- 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; Co-requisite: PH-UY 2033 and MA-UY 2034. - 4 Credits Calculus Iii: Multi-dimensional Calculus MA-UY2114
- Vectors in the plane and space. Partial derivatives with applications, especially Lagrange multipliers. Double and triple integrals. Spherical and cylindrical coordinates. Surface and line integrals. Divergence, gradient, and curl. Theorems of Gauss and Stokes.

Prerequisite: MA-UY 1124 or MA-UY 1424 or MA-UY 1132. Anti-requisite: MA-UY 2514

**To gain some breadth and depth of knowledge, take courses in at least two disciplines and at least one course at an advanced level.*

Third Year

#### Fall Semester

- 2 Credits Junior Physics Laboratory PH-UY3002
- An intermediate level laboratory course providing in depth exposure to a selection of classic physics experiments. Students' experimental skill set is expanded and data analysis and communication skills developed.

Prerequisites: PH-UY 2131 and PH-UY 2033; Co-requisites: PH-UY 2344 and MA-UY 2224. - 4 Credits Electricity and Magnetism PH-UY3234
- 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 Data Analysis MA-UY2224
- An introductory course to probability and statistics. It affords the student some acquaintance with both probability and statistics in a single term. Topics in Probability include mathematical treatment of chance; combinatorics; binomial, Poisson, and Gaussian distributions; the Central Limit Theorem and the normal approximation. Topics in Statistics include sampling distributions of sample mean and sample variance; normal, t-, and Chi-square distributions; confidence intervals; testing of hypotheses; least squares regression model. Applications to scientific, industrial, and financial data are integrated into the course.NOTE: Not open to students who have taken MA-UY 2233 or MA-UY 3012 or MA-UY 3022.

Prerequisite: MA-UY 1124, MA-UY1424, or MA-UY 1132

**Physics Elective** *3 Credits*

**Humanities and Social Sciences Elective 2** *4 Credits**

#### Spring Semester

- 4 Credits Introduction to the Quantum Theory PH-UY4364
- 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. - Chemical Laboratory Safety CM-GY5040
- This course discusses problems of health and safety in chemical laboratories, including how to work safely with dangerous chemicals. This course must be completed by graduate and undergraduate chemistry students before they begin laboratory research.

**Physics Elective** *4 Credits*

**Math Elective** *4 Credits*

**Humanities and Social Sciences Elective 3** *4 Credits**

**To gain some breadth and depth of knowledge, take courses in at least two disciplines and at least one course at an advanced level.*

Fourth Year

#### Fall Semester

- 4 Credits Thermodynamics and Statistical Physics PH-UY4124
- 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. - 2 Credits Introduction to Senior Project in Physics PH-UY4902
- A qualified senior physics student or group of students work with a faculty member (and possibly graduate students) on an advanced problem in physics. In this introductory phase the student(s) and adviser select a suitable theoretical or experimental problem in the subject area and use various resources to solve it.
- 2 Credits Senior Seminar in Physics PH-UY4912
- 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.

**Physics Elective** *3 Credits*

**Math Elective** *3 Credits*

**Free Elective** *3 Credits*

#### Spring Semester

- 4 Credits Senior Project in Physics PH-UY4904
- In the project’s concluding phase, senior physics students or group of students work with a faculty member (and possibly graduate students) to solve an advanced problem in interdisciplinary physics. The conclusion of the project is a written report and an oral presentation made to the supervising faculty.

**Physics Electives** *3 Credits*

**Physics Electives** *3 Credits*

** Humanities and Social Sciences Elective 4** *4 Credits**

**Free Elective** *3 Credits*

**To gain some breadth and depth of knowledge, take courses in at least two disciplines and at least one course at an advanced level.*