Functions of one variable, limits, continuity, derivatives, chain rule, maxima and minima, exponential functions and logarithms, inverse functions, antiderivatives, elementary differential equations, Riemann sums, the Fundamental Theorem of Calculus, vectors and determinants.
Atomic structure and periodic properties, stoichiometry, properties of gases, thermochemistry, chemical bond types, intermolecular forces, liquids and solids, chemical kinetics and introduction to organic chemistry and biochemistry. Corequisites: CH 117
General Chemistry Laboratory I (0-3-1)
(Lecture-Lab-Study Hours)
Laboratory work to accompany CH 115: experiments of atomic spectra, stoichiometric analysis, qualitative analysis, and organic and inorganic syntheses, and kinetics. Close
Laboratory work to accompany CH 115: experiments of atomic spectra, stoichiometric analysis, qualitative analysis, and organic and inorganic syntheses, and kinetics. Corequisites: CH 115
General Chemistry I (3-0-6)
(Lecture-Lab-Study Hours)
Atomic structure and periodic properties, stoichiometry, properties of gases, thermochemistry, chemical bond types, intermolecular forces, liquids and solids, chemical kinetics and introduction to organic chemistry and biochemistry. Close
This is a first course in computer programming for students with no prior experience. Students will learn the core process of programming: given a problem statement, how does one design an algorithm to solve that particular problem and then implement the algorithm in a computer program? The course will also introduce elementary programming concepts like basic control concepts (such as conditional statements and loops) and a few essential data types (e.g., integers and doubles). Exposure to programming will be through a self-contained user-friendly programming environment, widely used by the scientific and engineering communities, such as Matlab. The course will cover problems from all fields of science, engineering, and business.
Vectors, kinetics, Newton’s laws, dynamics or particles, work and energy, friction, conserverative forces, linear momentum, center-of-mass and relative motion, collisions, angular momentum, static equilibrium, rigid body rotation, Newton’s law of gravity, simple harmonic motion, wave motion and sound. Corequisites: MA 115
Calculus I (3-0-0)
(Lecture-Lab-Study Hours)
Functions of one variable, limits, continuity, derivatives, chain rule, maxima and minima, exponential functions and logarithms, inverse functions, antiderivatives, elementary differential equations, Riemann sums, the Fundamental Theorem of Calculus, vectors and determinants. Close
Techniques of integration, infinite series and Taylor seri
es, polar c
oordinates, double integrals, improper integrals, parametric curves, arc length, functions of several variables, partial derivatives, gradients and directional derivatives.
Functions of one variable, limits, continuity, derivatives, chain rule, maxima and minima, exponential functions and logarithms, inverse functions, antiderivatives, elementary differential equations, Riemann sums, the Fundamental Theorem of Calculus, vectors and determinants. Close
Phase equilibria, properties of solutions, chemical equilibrium, strong and weak acids and bases, buffer solutions and titrations, solubility, thermodynamics, electrochemistry, properties of the elements and nuclear chemistry.
Atomic structure and periodic properties, stoichiometry, properties of gases, thermochemistry, chemical bond types, intermolecular forces, liquids and solids, chemical kinetics and introduction to organic chemistry and biochemistry. Close
Laboratory work to accompany CH 116: analytical techniques properties of solutions, chemical and phase equilibria, acid-base titrations, thermodynamic properties, electrochemical cells, and properties of chemical elements. Corequisites: CH 116
General Chemistry II (3-0-6)
(Lecture-Lab-Study Hours)
Phase equilibria, properties of solutions, chemical equilibrium, strong and weak acids and bases, buffer solutions and titrations, solubility, thermodynamics, electrochemistry, properties of the elements and nuclear chemistry. Close
Laboratory work to accompany CH 115: experiments of atomic spectra, stoichiometric analysis, qualitative analysis, and organic and inorganic syntheses, and kinetics. Close
Biological principles and their physical and chemical aspects are explored at the cellular and molecular level. Major emphasis is placed on cell structure, the processes of energy conversion by plant and animal cells, genetics and evolution, and applications to biotechnology.
Coulomb’s law, concepts of electric field and potential, Gauss’ law, capacitance, current and resistance, DC and R-C transient circuits, magnetic fields, Ampere’s law, Faraday’s law of induction, inductance, A/C circuits, electromagnetic oscillations, Maxwell’s equations and electromagnetic waves.
Functions of one variable, limits, continuity, derivatives, chain rule, maxima and minima, exponential functions and logarithms, inverse functions, antiderivatives, elementary differential equations, Riemann sums, the Fundamental Theorem of Calculus, vectors and determinants. Close
Vectors, kinetics, Newton’s laws, dynamics or particles, work and energy, friction, conserverative forces, linear momentum, center-of-mass and relative motion, collisions, angular momentum, static equilibrium, rigid body rotation, Newton’s law of gravity, simple harmonic motion, wave motion and sound. Close
Ordinary differential equations of first and second order, homogeneous and non-homogeneous equations; improper integrals, Laplace transforms; review of infinite series, series solutions of ordinary differential equations near an ordinary point; boundary-value problems; orthogonal functions; Fourier series; separation of variables for partial differential equations.
Techniques of integration, infinite series and Taylor series, polar coordinates, double integrals, improper integrals, parametric curves, arc length, functions of several variables, partial derivatives, gradients and directional derivatives. Close
Concepts of geometrical optics for reflecting and refracting surfaces, thin and thick lens formulations, optical instruments in modern practice, interference, polarization and diffraction effects, resolving power of lenses and instruments, X-ray diffraction, introduction to lasers and coherent optics, principles of holography, concepts of optical fibers, optical signal processing. Fall semester.
Coulomb’s law, concepts of electric field and potential, Gauss’ law, capacitance, current and resistance, DC and R-C transient circuits, magnetic fields, Ampere’s law, Faraday’s law of induction, inductance, A/C circuits, electromagnetic oscillations, Maxwell’s equations and electromagnetic waves. Close
An introduction to experimental measurements and data analysis. Students will learn how to use a variety of measurement techniques, including computer-interfaced experimentation, virtual instrumentation, and computational analysis and presentation. First semester experiments include basic mechanical and electrical measurements, motion and friction, RC circuits, the physical pendulum, and electric field mapping. Second semester experiments include the second order electrical system, geometrical and physical optics and traveling and standing waves.
Coulomb’s law, concepts of electric field and potential, Gauss’ law, capacitance, current and resistance, DC and R-C transient circuits, magnetic fields, Ampere’s law, Faraday’s law of induction, inductance, A/C circuits, electromagnetic oscillations, Maxwell’s equations and electromagnetic waves. Close
Vectors, kinetics, Newton’s laws, dynamics or particles, work and energy, friction, conserverative forces, linear momentum, center-of-mass and relative motion, collisions, angular momentum, static equilibrium, rigid body rotation, Newton’s law of gravity, simple harmonic motion, wave motion and sound. Close
SKIL (Science Knowledge Integration Ladder) is a six-semester sequence of project-centered courses. This course introduces students to the concept of working on projects that foster independent learning, innovative problem solving, collaboration and teamwork, and knowledge of integration under the guidance of a faculty advisor. SKIL I familiarizes the student with the ideas and realization of project-based learning using simple concepts and basic scientific knowledge. Specific emphasis is put on the development of “Guesstimates” skills, application and recognition of scaling laws as well as fundamental measurement techniques.
Coulomb’s law, concepts of electric field and potential, Gauss’ law, capacitance, current and resistance, DC and R-C transient circuits, magnetic fields, Ampere’s law, Faraday’s law of induction, inductance, A/C circuits, electromagnetic oscillations, Maxwell’s equat
ions and
electromagnetic waves. Close
Review of matrix operations, Cramer’s rule, row reduction of matrices; inverse of a matrix, eigenvalues and eigenvectors; systems of linear algebraic equations; matrix methods for linear systems of differential equations, normal form, homogeneous constant coefficient systems, complex eigenvalues, nonhomogeneous systems, the matrix exponential; double and triple integrals; polar, cylindrical and spherical coordinates; surface and line integrals; integral theorems of Green, Gauss and Stokes. Engineering curriculum requirement. Corequisites: MA 221
Differential Equations (4-0-8)
(Lecture-Lab-Study Hours)
Ordinary differential equations of first and second order, homogeneous and non-homogeneous equations; improper integrals, Laplace transforms; review of infinite series, series solutions of ordinary differential equations near an ordinary point; boundary-value problems; orthogonal functions; Fourier series; separation of variables for partial differential equations. Close
An introduction to experimental measurements and data analysis. Students will learn how to use a variety of measurement techniques, including computer-interfaced experimentatio
n, virtual instrumentation, and computational analysis and presentation. First semester experiments include basic mechanical and electrical measurements, motion and friction, RC circuits, the physical pendulum, and electric field mapping. Second semester experiments include the second order electrical system, geometrical and physical optics and traveling and standing waves.
An introduction to experimental measurements and data analysis. Students will learn how to use a variety of measurement techniques, including computer-interfaced experimentation, virtual instrumentation, and computational analysis and presentation. First semester experiments include basic mechanical and electrical measurements, motion and friction, RC circuits, the physical pendulum, and electric field mapping. Second semester experiments include the second order electrical system, geometrical and physical optics and traveling and standing waves.
Simple harmonic motion, oscillations and pendulums; Fourier analysis; wave properties; wave-particle dualism; the Schrödinger equation and its interpretation; wave functions; the Heisenberg uncertainty principle; quantum mechanical tunneling and application; quantum mechanics of a particle in a "box," the hydrogen atom; electronic spin; properties of many electron atoms; atomic spectra; principles of lasers and applications; electrons in solids; conductors and semiconductors; the n-p junction and the transistor; properties of atomic nuclei; radioactivity; fusion and fission. Spring Semester.
Coulomb’s law, concepts of electric field and potential, Gauss’ law, capacitance, current and resistance, DC and R-C transient circuits, magnetic fields, Ampere’s law, Faraday’s law of induction, inductance, A/C circuits, electromagnetic oscillations, Maxwell’s equations and electromagnetic waves. Close
Continuation and extension of SKIL I to complex projects. In the lecture part, the concept of software simulations for experiment development and parameter evaluation as well as advanced data analysis will be discussed. In parallel the conceptualization, design and realization of a first self-chosen experiment in groups of four to six students constitute the main focus of the laboratory part.
SKIL (Science Knowledge Integration Ladder) is a six-semester sequence of project-centered courses. This course introduces students to the concept of working on projects that foster independent learning, innovative problem solving, collaboration and teamwork, and knowledge of integration under the guidance of a faculty advisor. SKIL I familiarizes the student with the ideas and realization of project-based learning using simple concepts and basic scientific knowledge. Specific emphasis is put on the development of “Guesstimates” skills, application and recognition of scaling laws as well as fundamental measurement techniques. Close
This course introduces basic concepts of linear algebra from a geometric point of view. Topics include the method of Gaussian elimination to solve systems of linear equations; linear spaces and dimension; independent and dependent vectors; norms, inner product, and bases in vector spaces; determinants, eigenvalues and eigenvectors of matrices; symmetric, unitary, and normal matrices; matrix representations of linear transformations and orthogonal projections; the fundamental theorems of linear algebra; and the least-squares method and LU-decomposition.
Vector and tensor fields and transformation properties under rotation of axes, vector identities, gradient, divergence, curl, tensor contraction, geometric interpretation of symmetric and antisymmetric tensors, divergence-Gauss' theorem for tensor fields and Stokes' theorem, Helmholtz' theorem, and scalar and vector potentials. Applications to inertia tensor, particle mechanics, transport, electromagnetism (Maxwell's equations), and viscous fluid dynamics (the Navier-Stokes equation, Euler equati
on, and the Bernoulli equat
ion). Introduction to the Dirac delta-function and Green’s function technique for solving linear inhomogeneous equations. Orthogonal curvilinear coordinates (general, also spherical, and cylindrical). N-dimensional complex space and unitarity, matrix notation, inverse of matrix, Pauli spin matrices, relativity, and Lorentz transformation. Tensors and pseudotensors in n-dimensions. Similarity transformations and diagonalization of Hermitian and unitary matrices, eigenvectors, and eigenvalues of Hermitian and unitary matrices, and Schmidt orthogonalization. Applications to coupled oscillators, rigid body dynamics, etc. Linear independence and completeness. Functions of a complex variable, analyticity, Cauchy’s theorem, Residue theorem, Taylor and Laurent expansions, classification of singularities, analytic continuation, Liouville’s theorem, multiple-valued functions, contour integration, Jordan’s lemma, applications, and asymptotics. Fall Semester.
Particle motion in one dimension. Simple harmonic oscillators. Motion in two and three dimensions, kinematics, work and energy, conservative forces, central forces, and scattering. Systems of particles, linear and angular momentum theorems, collisions, linear spring systems, and normal modes. Lagrange’s equations and applications to simple systems. Introduction to moment of inertia tensor and to Hamilton’s equations.
Ordinary differential equations of first and second order, homogeneous and non-homogeneous equations; improper integrals, Laplace transforms; review of infinite series, series solutions of ordinary differential equations near an ordinary point; boundary-value problems; orthogonal functions; Fourier series; separation of variables for partial differential equations. Close
Higher advanced measurement concepts including averaging, modulation, Lock-In detection, boxcar averaging, spectrum analyzer, RF and HF modulation as well as handling and understanding of the corresponding electronics measurement devices. Continuation and extension of individual or team SKIL II projects to more complex projects. Projects may include research participation in well-defined research projects.
Continuation and extension of SKIL I to complex projects. In the lecture part, the concept of software simulations for experiment development and parameter evaluation as well as advanced data analysis will be discussed. In parallel the conceptualization, design and realization of a first self
-chosen experiment in groups of four to six students constitute the main focus of the laboratory part. Close
Ordinary differential equations of first and second order, homogeneous and non-homogeneous equations; improper integrals, Laplace transforms; review of infinite series, series solutions of ordinary differential equations near an ordinary point; boundary-value problems; orthogonal functions; Fourier series; separation of variables for partial differential equations. Close
The general study of field phenomena; scalar and vector fields and waves; dispersion phase and group velocity; interference, diffraction and polarization; coherence and correlation; geometric and physical optics. Typical text: Hecht and Zajac, Optics. Spring semester.
Introduces the essentials of probability theory and elementary statistics. Lectures and assignments greatly stress the manifold applications of probability and statistics to computer science, production management, quality control, and reliability. A statistical computer package is used throughout the course for teaching and for assignments. Contents include: descriptive statistics, pictorial and tabular methods, and measures of location and of variability; sample space and events, probability axioms, and counting techniques; conditional probability and independence, and Bayes' formula; discrete random variables, distribution functions and moments, and binomial and Poisson distributions; continuous random variables, densities and moments, normal, gamma, and exponential and Weibull distributions unions; distribution of the sum and average of random samples; the Central Limit Theorem; confidence intervals for the mean and the variance; hypothesis testing and p-values, and applications for the mean; simple linear regression, and estimation of and inference about the parameters; and correlation and prediction in a regression model.
Techniques of integration, infinite series and Taylor series, polar coordinates, double integrals, improper integrals, parametric curves, arc length, functions of several variables, partial derivatives, gradients and directional derivatives. Close
In the lecture part, the students are trained in classification of different sensors as well as their use.An overview of the most common sensors, their parameters as well as their functionality will be provided in group work and assembled into a complete survey. In parallel to this activity a continuation and extension of individual or team SKIL III projects will be undertaken.
Higher advanced measurement concepts including av
eraging, modulation, Lo
ck-In detection, boxcar averaging, spectrum analyzer, RF and HF modulation as well as handling and understanding of the corresponding electronics measurement devices. Continuation and extension of individual or team SKIL II projects to more complex projects. Projects may include research participation in well-defined research projects. Close
This course is an introduction to quantum mechanics for students in physics and engineering. Techniques discussed include solutions of the Schrodinger equation in one and three dimensions, and operator and matrix methods. Applications include infinite and finite quantum wells, barrier penetration and scattering in one dimension, the harmonic oscillator, angular momentum, central force problems, including the hydrogen atom, and spin. Fall semester. Typical text: Quantum Physics by Gasiorowicz
Ordinary differential equations of first and second order, homogeneous and non-homogeneous equations; improper integrals, Laplace transforms; review of infinite series, series solutions of ordinary differential equations near an ordinary point; boundary-value problems; orthogonal functions; Fourier series; separation of variable
s for partial differential equations. Close
Simple harmonic motion, oscillations and pendulums; Fourier analysis; wave properties; wave-particle dualism; the Schrödinger equation and its interpretation; wave functions; the Heisenberg uncertainty principle; quantum mechanical tunneling and application; quantum mechanics of a particle in a "box," the hydrogen atom; electronic spin; properties of many electron atoms; atomic spectra; principles of lasers and applications; electrons in solids; conductors and semiconductors; the n-p junction and the transistor; properties of atomic nuclei; radioactivity; fusion and fission. Spring Semester. Close
In the lecture part, the students are trained in classification of different sensors as well as their use.An overview of the most common sensors, their parameters as well as their functionality will be provided in group work and assembled into a complete survey. In parallel to this activity a continuation and extension of individual or team SKIL III projects will be undertaken. Close
This course is meant as the first in a two-course sequence on non-relativistic quantum mechanics for physics graduate students, with an emphasis on applications to atomic, molecular, and solid state physics. Undergraduate students may take this course as a Technical Elective. Topics covered include: review of Schrödinger wave mechanics; operator algebra, theory of representation, and matrix mechanics; symmetries in quantum mechanics; spin and formal theory of angular momentum, including addition of angular momentum; and approximation methods for stationary problems, including time independent perturbation theory, WKB approximation, and variational methods. Typical text: Quantum Mechanics by E. Merzbacher.
Particle motion in one dimension. Simple harmonic oscillators. Motion in two and three dimensions, kinematics, work and energy, conservative forces, central forces, and scattering. Systems of particles, linear and angular momentum theorems, collisions, linear spring systems, and normal modes. Lagrange’s equations and applications to simple systems. Introduction to moment of inertia tensor and to Hamilton’s equations. Close
This course is an introduction to quantum mechanics for students in physics and engineering. Techniques discussed include solutions of the Schrodinger equation in one and three dimensions, and operator and matrix methods. Applications include infinite and finite quantum wells, barrier penetration and scattering in one dimension, the harmonic oscillator, angular momentum, central force problems, including the hydrogen atom, and spin. Fall semester. Typical text: Quantum Physics by Gasiorowicz Close
