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Course Criteria
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3.00 Credits
No course description available.
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3.00 Credits
No course description available.
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0.00 Credits
No course description available.
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3.00 Credits
No course description available.
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3.00 Credits
This course is specifically designed to provide students in the space science program, the chemistry and the environmental science program, the physics program, and the computer science program with a survey of the basic tools from abstract and linear algebra that are used by physical scientists. The traditional topics on sets, basic counting principles and formulas, relations, mappings, linear transformations and matrixes as well as applications of these concepts to the sciences will be discussed in detail. Basic matrix algebra, inverses, transposes, adjoints and special matrices (such as unitary and hermitian matrices), along with systems of linear algebraic equations will be presented. Eigenvalues and eigenvectors, diagonalization of matrices and functions of matrices will be studied and applications of matrices to such areas in the physical and computer sciences as quantum mechanics, physical chemistry, advanced inorganic chemistry and networks, and computer graphics will be emphasized. Throughout the course the emphasis will be on the application(s) of abstract mathematical systems to the physical sciences. Use of the mathematical software MAPLE w
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3.00 Credits
This course is designed to provide students in the Mathematical Sciences Program with an introduction to the classical (local) differential geometry of curves and surfaces in R3 using vector methods. The concepts of arc length, curvature, torsion along with the fundamental systems of basic unit vectors and the associated lines and planes will be discussed. The Serret-Frenet formulas and their application and the moving trihedron will be investigated in detail. The representation problem in terms of the natural parameter (arc lengths) and the general theory of smooth space (twisted or gauche) curves will be emphasized, as will the representation problem and elementary theory of smooth surfaces embedded in Euclidean space. The First and Second Fundamental Forms will be presented and the various curves on embedded surfaces (such as lines of curvature, asymptotic lines, and directions) will be discussed, as will Meusnier's theorem, Euler's theorem and the Dupin indicatrix. Elementary principles and methods of the tensor calculus will be introduced as a means of investigating the Fundamental Theorem of Surface Theory, the Gauss-Weingarten equations, and the
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3.00 Credits
This course is designed to provide students in the Space Science Program, the Physics Program, and the Mathematical Sciences Program with a practical introduction to tensors. The course will emphasize those aspects of the theory, and cosmology. Eigenvectors ad eigenvalues as well as bi-linear and quadratic forms will be discussed as will functions of matrices (such as the matrix exponential) and partitioning, Kronecker sums and products will be investigated in detail. Tensor formalism, notation, and algebra will be presented along with the Kronecker delta and its properties. Students will be given detailed instruction on how to express certain well-known principles (such as the Maxwell Equations) in tensor form. Covariant and contravariant tensors and vectors, symmetric tensors, associate tensors, the Ricci tensor and its properties, metric tensors, and other forms will be emphasized. Covariant formulation of electrodynamics, the Christoffel symbols, and the Riemann-Christoffel curvature tensor will be presented.
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3.00 Credits
This course is designed to provide students in the Space Science Program, the Physics Program, and the Mathematical Sciences Program with a survey of classical partial differential equations and boundary-value problems. The traditional classification schemes involving concepts such as linearity/non-linearity, homogeneity/non-homogeneity, and constant/variable coefficients will be investigated. The emphasis will be on applications of partial differential equations to physics and chemistry. The method of separation of variables will be emphasized and Fourier series will be discussed. Orthogonal function and Green's functions will be presented along with the Fourier integral and double Fourier series. Laplace transform methods will also be examined as will the method of characteristics. Graphical and geometric methods will be presented. Although the emphasis throughout the course will be on closed-form solutions and the physical/geometrical interpretations of the equations and their associated boundary conditions, computers will be used for drill and practice work once the main analytical technique has been thoroughly investigated.
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3.00 Credits
This course is designed to introduce students in the Space Science P, the Physics Program, and the Mathematical Sciences Program to the application of the differential geometry of curves and surfaces to the classical theory of relativity. The concepts to be discussed will be presented first from a mathematical point of view and then from a physical point of view using mathematical formalism. The topics to be presented will include the theory of space curves and three-dimensional surfaces and their proprieties. These basic differential geometric concepts will then be used to develop the geometric principles that govern flat space-time or the special of relativity. The mathematical topics to be presented in this course will include a brief review of vector geometry and analysis, the hyperbolic functions, the geometry of curves and their representations, the geometry of surfaces in E3, the first fundamental form, the second fundamental form, mean curvature, Gauss curvature, geodesics, the curvature tensor, the Glorious Theorem Gauss and invariance, and extensions and manifolds. The topics from physic to be presented include an informal historical analysis
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3.00 Credits
This course is designed to allow all students pursuing an interest in the music industry, an understanding of the current operating systems, hardware, and software added to the comprehensive study of music technology from MIDI, sound generation, computer assisted instructions, digital recording, sampling, music scoring and composing. The course is a practical reference source for students using the computer to arrange or compose music to set up a music technology studio. Also, students will be exposed to elements of music theory, which includes circle of fifths, scales, key signatures, melody, harmony and chord progressions.
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