An introduction to differential and integral calculus for functions of one variable. The differential calculus includes limits, continuity, the definition of the derivative, rules for differentiation, and applications to curve sketching, optimization, and elementary initial value problems. The integral calculus includes the definition of the definite integral, the Fundamental Theorem of Calculus, techniques for finding antiderivatives, and applications of the definite integral. Transcendental and inverse functions are included throughout.
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.
Laboratory work to accompany CH 115: experiments of atomic spectra, stoichiometric analysis, qualitative analysis, and organic and inorganic syntheses, and kinetics.
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.
Continues from MA 115 with improper integrals, infinite series, Taylor series, and Taylor polynomials. Vectors operations in 3-space, mathematical descriptions of lines and planes, and single-variable calculus for parametric curves. Introduction to calculus for functions of two or more variables including graphical representations, partial derivatives, the gradient vector, directional derivatives, applications to optimization, and double integrals in rectangular and polar coordinates.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Particle motion in one dimension. Simple harmonic oscillators. Motion in two and three dimensions, kinematics, work and energy, conservative forces, central forces, scattering. Systems of particles, linear and angular momentum theorems, collisions, linear spring systems, normal modes. Lagrange's equations, applications to simple systems. Introduction to moment of inertia tensor and to Hamilton's equations
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 equation, and the Bernoulli equation). 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.
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.
This course is designed to make students comfortable with the handling and use of various optical components, instruments, techniques,and applications. Included will be the characterization of lens, wavefront division and multiple beam interferometry, partial coherence, spectrophotometry,coherent propogation, and properties of optical fibers.
This course is meant to serve as an introduction to formal quantum mechanics as well as to apply the basic formalism to several generic and important applications.
Basic concepts of quantum mechanics, states, operators; time development of Schrödinger and Heisenberg pictures; representation theory; symmetries; perturbation theory; systems of identical particles, L-S and j-j coupling; fine and hyperfine structure; scattering theory; molecular structure.
