Overview: Analytic Geometry: Double and triple integrals: Double integrals over rectangles, double integrals over general regions, double integrals in polar coordinates, center of mass, triple integrals, triple integrals in cylindrical coordinates, triple integrals in spherical coordinates, change of variables. (Research) programs in Mathematics.Ĭredits (Lec:Tut:Lab)= 3:1:0 (3 lectures and 1 tutorial weekly) If time permits – Tensor Products or Quadratic FormsĬore course for B.Sc. Normal operators, orthogonal linear transformations, polar decomposition, otherĦ. Unitary and Normal operators, Positive operators, Spectral theorems for self-adjoint and Spectral Theorem: Self-adjoint operators, matrix of self-adjoint operators, Hermitian, Product spaces, inner products on dual space, orthogonal projections.ĥ. Adjoints: Adjoint of a linear transformation, existence in finite dimensional inner ![]() Inner Product Spaces: Inner products, Cauchy-Schwarz Inequality, Gramian, orthogonalĪnd orthonormal sets, Gram-Schmidt orthogonalisation, complete orthonormal sets, orthogonal complements, perpendicular projections, Complexification.Ĥ. Linear Transformations: Range, null space, rank, nullity, row rank, column rank,ģ. Transpose, matrix of a linear transformation, determinants, characteristic polynomial,Ĭayley-Hamilton theorem, minimal polynomial, characteristic roots, eigenvalues,Ģ. Review: Vector spaces, subspaces, linear span, linear independence, quotient spaces,īasis, dimension, linear transformations, linear functionals, dual spaces, annihilators, If time permits, we shall look atĮither tensor products or quadratic forms.ġ. Theorems for Self-adjoint and Normal operators will be proved. ![]() Situation in finite dimensional linear spaces. Questions (and the answers) asked about these operators, it is essential to understand the Each quiz will have a time limit of 1 hour and 30 minutes (CLO: A, B, C, D, and E FSLOs: SSI 1, SSI 2b, and SSI 3).Overview: Hermitian, Unitary and Normal operators are used widely. The student must include his/her name on the paper. It must be written on paper and solved, and then an image of the solution must be uploaded during the quiz. This multi-part problem will be given at the time of the quiz. In addition, quizzes for Modules 2, 3, 5, 6, and 7: Weeks 2, 3, 5, 6, and 7 will have 1 multi-part problem. Each quiz will be open-book/open-notes and contain 25 multiple-choice and true/false questions and a 5 part matching question. These homework assignments will reinforce the content of the course textbook readings from the assigned module (CLO: A, B, C, D, and E FSLO: SSI and SSI 3).Įach quiz will build on the homework assignments and cover the Learn material for the assigned module. Course AssignmentĪfter reading the Course Syllabus and Student Expectations, the student will complete the related checklist found in the Course Overview.įor each Module: Week, the student will complete various online exercises in Cengage’s Inquiry into Physics system, WebAssign. ![]() PHYS 101 is an introductory course designed for non-science and non-math majors to partially fulfill the general education requirement in the area of natural science. Since science and technology are dominant themes in our culture, every student should be exposed to some area of natural science. For information regarding prerequisites for this course, please refer to the Academic Course Catalog.
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