7/14/2023 0 Comments Sou edu math 361 syllabus textbook![]() Many important problems in a wide range of disciplines within computer science and throughout science are solved using techniques from linear algebra. This course will introduce students to some of the most widely used algorithms and illustrate how they are actually used. Some specific topics: the solution of systems of linear equations by Gaussian elimination, dimension of a linear space, inner product, cross product, change of basis, affine and rigid motions, eigenvalues and eigenvectors, diagonalization of both symmetric and non-symmetric matrices, quadratic polynomials, and least squares optimazation. ![]() The ideas and tools provided by this course will be useful to students who intend to tackle higher level courses in digital signal processing, computer vision, robotics, and computer graphics.Īpplications will include the use of matrix computations to computer graphics, use of the discrete Fourier transform and related techniques in digital signal processing, the analysis of systems of linear differential equations, and singular value deompositions with application to a principal component analysis. Mathematics 4800 will open with a review of the basics of real analysis (brief or extended background requires). * mastery of necessary tools of matrix algebra * basic theory of vector-valued solutions * solving homogeneous linear system with constant coefficients, includingĥ.The review will include: introduction of the real numbers through Dedekind cuts, continuity of real-valued functions on the real line Cantor nested-interval principle, basic results for continuous functions, Maximum and Intermediate Value theorems, Heine-Borel Theorem, Uniform Continuity on closed intervals metric spaces, convergence of sequences, Cauchy sequences, completeness, more general uniform continuity and intermediate value theorems general topology, separation, compactness, product spaces, Tychonoff's Theorem. 4.) Demonstrate skill with the theory for solving systems of first-order linear differentialĮquations. * homogeneous equations with constant coefficients * non-homogenous equations * methods of undetermined coefficients and variation of parameters * series solutions * using the theory Laplace transforms to solve differential equations. ISBN-13: 978-8-2, 153.50 at campus Textbook Annex (138.99 on-line from publisher) Stewart, Calculus: Early Transcendentals, 7th Edition, Enhanced WebAssign Homework and eBook LOE Printed Access Card for Multi Term Math and Science, ISBN-13: 978-7-1, 107.75 at campus Textbook Annex (95.00 on-line from publisher). * linear equations * separable and exact nonlinear equations.ģ.) Demonstrate skill with solution methods of second- and higher order ordinary differentialĮquations. Learning Outcomes for AMS 361, Applied Calculus IV: Differential Equationsġ.) Build differential equations models of phenomena in: * physical sciences * biological sciences * engineering.Ģ.) Demonstrate skill with solution methods for first-order ordinary differentialĮquations. Partial differential equations and separation of variables – 4 classes. Solutions with power series and special functions - 4 classes 7. Solutions with Laplace transforms –- 6 classes. Systems of linear differential equations and matrices - 6 classes 5. The textbook is the same as for Math 103-104-114, namely Thomas’ Calculus Early Tran-scendentals (Custom Edition for U. Nonhomogeneous linear differential equations –- 6 classes. Methods of approximate solution of differential equations –- 6 classes 3. Exact methods and homogeneous linear differential equations - 6 classes 2. ![]() Recommended Only Textbook: "Elementary Differential Equations and Boundary Value Problems" by C. World Scientific, Second Edition OctoISBN: 97-13-5 (paperback) Prerequisite: AMS 161 or MAT 127 or 132 or 142 or MPE level 9 4 creditsĪMS 361 Instructor webpage Required Textbook: "Lectures, Problems and Solutions for Ordinary Differential Equations" by Yuefan Deng, May not be taken for credit in addition to the equivalent It includes 24 to 25 lectures with 5 or 4 hours left for leeway and exams. This syllabus assumes 29 lecture hours in the semester. AMS 361, Applied Calculus IV: Differential EquationsĬatalog Description: Homogeneous and inhomogeneous linear differential equations systems of linear differentialĮquations solution with power series and Laplace transforms partial differentialĮquations and Fourier series. Calculus I Lecture Syllabus Textbook: Stewart, Calculus: Early Transcendentals, 8th edition, with Enhanced Webassign, Thomson Brooks/Cole.
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