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
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
An introduction to the use of an advanced programming language for use in engineering applications, using C++ as the basic programming language and Microsoft Visual C++ as the program development environment. Topics covered include basic syntax (data types and structures, input/output instructions, arithmetic instructions, loop constructs, functions, subroutines, etc.) needed to solve basic engineering problems as well as an introduction to advanced topics (use of files, principles of objects and classes, libraries, etc.). Algorithmic thinking for development of computational programs and control programs from mathematical and other representations of the problems will be developed. Basic concepts of computer architectures impacting the understanding of a high-level programming language will be covered. Basic concepts of a microcontroller architecture impacting the use of a high-level programming language for development of microcontroller software will be covered, drawing specifically on the microcontroller used in E121 (Engineering Design I).
Engineering graphics: principles of orthographic and auxiliary projections, pictorial presentation of engineering designs, dimensioning and tolerance, sectional and detail views, assembly drawings. Descriptive geometry. Engineering figures and graphs. Solid modeling introduction to computer-aided design and manufacturing (CAD/CAM) using numerically-controlled (NC) machines.
This course introduces students to the process of design and seeks to engage their enthusiasm for engineering from the beginning of the program. The engineering method is used in the design and manufacture of a product. Product dissection is exploited to evaluate how others have solved design problems. Development is started on competencies in professional practice topics, primarily: effective group participation, project management, cost estimation, communication skills and ethics. Corequisites: E 115
Introduction to Programming for Engineers (1-2-3)
(Lecture-Lab-Study Hours)
An introduction to the use of an advanced programming language for use in engineering applications, using C++ as the basic programming language and Microsoft Visual C++ as the program development environment. Topics covered include basic syntax (data types and structures, input/output instructions, arithmetic instructions, loop constructs, functions, subroutines, etc.) needed to solve basic engineering problems as well as an introduction to advanced topics (use of files, principles of objects and classes, libraries, etc.). Algorithmic thinking for development of computational programs and control programs from mathematical and other representations of the problems will be developed. Basic concepts of computer architectures impacting the understanding of a high-level programming language will be covered. Basic concepts of a microcontroller architecture impacting the use of a high-level programming language for development of microcontroller software will be covered, drawing specifically on the microcontroller used in E121 (Engineering Design I). Close
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.
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
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
This course continues the freshman year experience in design. The engineering method introduced in Engineering Design I is reinforced. Further introduction of professional practice topics are linked to their application and testing in case studies and project work.
This course introduces students to the process of design and seeks to engage their enthusiasm for engineering from the beginning of the program. The engineering method is used in the design and manufacture of a product. Product dissection is exploited to evaluate how others have solved design problems. Development is started on competencies in professional practice topics, primarily: effective group participation, project management, cost estimation, communication skills and ethics. 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
Ideal circuit elements; Kirchoff laws and nodal analysis; source transformations; Thevenin/Norton theorems; operational amplifiers; response of RL, RC and RLC circuits; sinusoidal sources and steady state analysis; analysis in frequenct domain; average and RMS power; linear and ideal transformers; linear models for transistors and diodes; analysis in the s-domain; Laplace transforms; transfer functions. 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
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
Vect
ors, 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
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
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 equations 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
Concepts of heat and work, First and Second Laws for closed and open systems including steady processes and cycles, thermodynamic properties of substances and interrelationships, phase change and phase equilibrium, chemical reactions and chemical equilibrium, representative applications.
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
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
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
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
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 l
aw of gravity, simple harmonic motion, wave motion and sound. 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.
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
Descriptive statistics, pictorial and tabular methods, measures of location and of variability, sample space and events, probability and independence, Bayes' formula, discrete random variables, densities and moments, normal, gamma, exp
onential and Weibull distributions, dist
ribution 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, applications for prediction in a regression model. A statistical computer package is used throughout the course for teaching and for project assignments.
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
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.
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
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 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. 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 variables 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
