! ROCHESTER INSTITUTE OF TECHNOLOGY COURSE OUTLINE FORM COLLEGE OF SCIENCE School of Mathematical Sciences New Revised COURSE: COS-MATH-412 Numerical Linear Algebra 1.0 Course Designations and Approvals: Required Course Approvals: Approval Approval Request Date Grant Date Academic Unit Curriculum Committee 4-08-10 4-15-10 College Curriculum Committee 11-01-10 12-17-10 Optional Course Designations: Yes No General Education Writing Intensive Honors Approval Request Date Approval Grant Date 2.0 Course information: Course Title: Numerical Linear Algebra Credit Hours: 3 Prerequisite(s): COS-MATH-221, -231, -341, and some programming knowledge Co-requisite(s): None Course proposed by: School of Mathematical Sciences Effective date: Fall 2013 Contact Hours Maximum Students/section Classroom 3 25 Lab Workshop Other (specify) 2.1 Course Conversion Designation: (Please check which applies to this course) Semester Equivalent (SE) to: 1016-512 Semester Replacement (SR) to: New 2.2 Semester(s) offered: Fall Spring Summer Offered every other year only Other Page 1 of 6
2.3 Student Requirements: Students required to take the course: Students majoring in Computational Mathematics Students who might elect to take the course: Students majoring in Applied Statistics and students doing a minor in mathematics. Students majoring in Applied Mathematics must take either COS-MATH-411 or COS- MATH-412. 3.0 Goals of the course: (including rationale for the course, when appropriate) 3.1 To be able to apply matrix formulations in problem solving. 3.2 To learn canonical decompositions used in developing matrix-based algorithms. 3.3 To be able to use existing software packages in solving matrix-based problems. 4.0 Course description: (as it will appear in the RIT Catalog, including pre- and co-requisites, semesters offered) COS-MATH-412 Numerical Linear Algebra This course covers numerical techniques for the solution of systems of linear equations, eigenvalue problems, singular values and other decompositions, applications to least squares, boundary value problems, and additional topics at the discretion of the instructor. (COS- MATH-221, -231, -341, and some programming knowledge) Class 3, Credit 3 (S) 5.0 Possible resources: (texts, references, computer packages, etc.) 5.1 Lloyd Trefethen and David Bau, Numerical Linear Algebra, SIAM, Philadelphia, PA. 5.2 E. E. Tyrtyshnikov, A Brief Introduction to Numerical Analysis, Birkhauser, Boston, MA. 5.3 David Kincaid and Ward Cheney, Numerical Analysis, Brooks/Cole, Pacific Grove, CA. 5.4 Gilbert Stewart, Afternotes Goes to Graduate School, SIAM, Philadelphia, PA. 5.5 Matlab software 6.0 Topics: (outline) Topics with an asterisk(*) are at the instructor s discretion, as time permits 6.1 Direct Methods for Solving Systems of Linear Equations 6.1.1 Gaussian Elimination, Partial Pivoting and Back-Substitution 6.1.2 LU and Choleski Decomposition 6.2 Error Analysis 6.2.1 Vector and Matrix Norms 6.2.2 Rounding Errors, Forward and Backward Stability 6.2.3 Conditioning, Perturbation Analysis and Residual 6.3 Iterative Methods 6.3.1 Gauss-Jacobi and Gauss-Seidel Page 2 of 6
6.3.2 Successive Overrelaxation Method 6.4 Eigenvalues 6.4.1 Power Method, Inverse Power method and Shifts 6.4.2 Rayleigh Quotient Iteration 6.4.3 Review of Orthogonal Matrices and QR Decomposition 6.4.4 QR Algorithm 6.4.5 Hessenberg Form 6.4.6 Application to Singular Value Decomposition 6.5 Applications 6.5.1 Least Squares, Normal Equations and Pseudo-Inverses 6.5.2 Newton and Quasi-Newton Methods for Systems of Nonlinear Equations 7.0 Intended learning outcomes and associated assessment methods of those outcomes: Assessment methods with an asterisk(*) are at the instructor s discretion Learning Outcomes Homework Assessment Methods Understand and apply direct methods for solving systems of linear equations Understand error analysis Understand and apply iterative methods for solving systems of linear equations Compute eigenvalues of a matrix Understand orthogonal matrices and QR decomposition Compute least squares, normal equations and pseudoinverses Quiz/Exam Final Exam Project Computer Lab Class Presentation 8.0 Program goals supported by this course: 8.1 To develop an understanding of the mathematical framework that supports engineering, science, and mathematics. 8.2 To develop critical and analytical thinking. 8.3 To develop an appropriate level of mathematical literacy and competency. 8.4 To provide an acquaintance with mathematical notation used to express physical and natural laws. Page 3 of 6
9.0 General education learning outcomes and/or goals supported by this course: Page 4 of 6
Assessment Methods General Education Learning Outcomes 9.1 Communication Express themselves effectively in common college-level written forms using standard American English Revise and improve written and visual content Express themselves effectively in presentations, either in spoken standard American English or sign language (American Sign Language or English-based Signing) Comprehend information accessed through reading and discussion 9.2 Intellectual Inquiry Review, assess, and draw conclusions about hypotheses and theories Analyze arguments, in relation to their premises, assumptions, contexts, and conclusions Construct logical and reasonable arguments that include anticipation of counterarguments Use relevant evidence gathered through accepted scholarly methods and properly acknowledge sources of information 9.3 Ethical, Social and Global Awareness Analyze similarities and differences in human experiences and consequent perspectives Examine connections among the world s populations Identify contemporary ethical questions and relevant stakeholder positions 9.4 Scientific, Mathematical and Technological Literacy Explain basic principles and concepts of one of the natural sciences Apply methods of scientific inquiry and problem solving to contemporary issues Comprehend and evaluate mathematical and statistical information Perform college-level mathematical operations on quantitative data Describe the potential and the limitations of technology Use appropriate technology to achieve desired outcomes 9.5 Creativity, Innovation and Artistic Literacy Homework Quiz/Exam/Final Project Computer Work Class Presentation Page 5 of 6
Assessment Methods General Education Learning Outcomes Demonstrate creative/innovative approaches to coursebased assignments or projects Interpret and evaluate artistic expression considering the cultural context in which it was created Homework Quiz/Exam/Final Project Computer Work Class Presentation 10.0 Other relevant information: (such as special classroom, studio, or lab needs, special scheduling, media requirements, etc.) Computer lab Page 6 of 6