## COT 4501: Numerical Analysis, a Computational Approach

• ### Course Objectives

To master the theory and practice of numerical techniques so that they can be used to solve real-world problems. Techniques include: linear and nonlinear systems of equations, integration, nonlinear equations, differential equations, and interpolation.

• Machine Learning, AI, movie making, etc. all rely on Numerical Computing.
• Computational Science has become the third branch of science, along with theory and experimentation to simulate complex scenarios that are costly to validate by experiments and currently beyond the reach of theory.
• Numerical techniques are integral part of Computer Engineering / Computer Science.

Place and Time: CSE E121, MWF 10:40 am
Instructor: Jorg Peters CSE E328
email: jorg.peters at gmail.com
Office hours: Mon Fri after class + by appointment
Teaching Assistant: Ruiliang Gao (contact via canvas)
office hours: W 1-2pm in CSE E309.
3 Tests at 15%, Final 30%
Test Dates : Feb 07, Mar 14, Apr 18 (Wed, in class)
Final : 1D = Tuesday May 01 at 3pm in class room
(makeup: needs to be pre-approved or proof of sick on day)
25% Homeworks (matlab) submission via canvas
Textbook and other resources: Scientific Computing: An Introductory Survey by Michael Heath (required).
MATLAB is available as an app     Cleve Moler's books

### Course outline:

All sections of the book are shown below. Sections/chapters that we will skip are struck out in light grey, like this.
• Chapter 1: Scientific Computing (1-12), 18, (22,23) 24, 28
• 1.1 Introduction
• 1.2 Approximations in Scientific Computation (skipped, revisit later)
• 1.3 Computer Arithmetic Cleve's Corner: Floating points   Jan10
• 1.4 Mathematical Software (skipped)
• 1.5 Historical Notes and Further Reading (skipped)
Homework 1
• Chapter 2: Systems of Linear Equations (1-14), 16,20,21,26,27,30,32,35,36 (38,39) 42, 53,54,55,68   Jan19
• 2.1 Linear Systems
• 2.2 Existence and Uniqueness
• 2.3 Sensitivity and Conditioning   Jan24
• 2.4 Solving Linear Systems   Jan29   Jan31
• 2.5 Special Types of Linear Systems
• 2.6 Iterative Methods for Linear Systems
• 2.7 Software for Linear Systems
• 2.8 Historical Notes and Further Reading
Homework 2 (1-12), 15,21,27,30-32,39,52,55   discussion
Test 1: some questions from the review section of Heath
sample test
office hour review of LU factorization QA
• Chapter 3: Linear Least Squares
• 3.1 Linear Least Squares Problems   Feb12
• 3.2 Existence and Uniqueness
• 3.3 Sensitivity and Conditioning
• 3.4 Problem Transformations
• 3.5 Orthogonalization Methods   Feb16
• 3.6 Singular Value Decomposition   Feb21
• 3.7 Comparison of Methods
• 3.8 Software for Linear Least Squares
• 3.9 Historical Notes and Further Reading
• Chapter 4: Eigenvalue Problems (1-7,12,14,15), 26,32,37,41,43, 51
• 4.1 Eigenvalues and Eigenvectors
• 4.2 Existence and Uniqueness (covered lightly)
• 4.3 Sensitivity and Conditioning
• 4.5 Computing Eigenvalues and Eigenvectors (covered lightly)   Feb26
• 4.6 Generalized Eigenvalue Problems (skip)
• 4.7 Computing the Singular Value Decomposition (skip)
• 4.8 Software for Eigenvalue Problems (skip)
• 4.9 Historical Notes and Further Reading
Homework 3
• Chapter 5: Nonlinear Equations (3,4,7-11, 14), 15, (18), 24,29, 43-45
• 5.1 Nonlinear Equations
• 5.2 Existence and Uniqueness
• 5.3 Sensitivity and Conditioning
• 5.4 Convergence Rates and Stopping Criteria
• 5.5 Nonlinear Equations in One Dimension
• 5.6 Systems of Nonlinear Equations   Mar 12   Mar 13
• 5.7 Software for Nonlinear Equations (skip)
• 5.8 Historical Notes and Further Reading   Quasi Newton
Test 2: sample test     sol u tions
• Chapter 6: Optimization (1-14), 15,27,28,31 (33-35), 36, (38), 42, 62 (68-70)   overview
• 6.1 Optimization Problems
• 6.2 Existence and Uniqueness
• 6.3 Sensitivity and Conditioning (skip)
• 6.4 Optimization in One Dimension
• 6.5 Multidimensional Unconstrained Optimization   Mar 26
• 6.6 Nonlinear Least Squares (skip)
• 6.7 Constrained Optimization (skip)
• 6.8 Software for Optimization (skip)
• 6.9 Historical Notes and Further Reading
suggestions
• Chapter 7: Interpolation   (1-12), (17-20), 21 (24), 26, 27, 30, 32 (37,38), 52   Mar 29
• 7.1 Interpolation
• 7.2 Existence, Uniqueness, and Conditioning
• 7.3 Polynomial Interpolation
• 7.4 Piecewise Polynomial Interpolation   Apr 04   Apr 06   Apr 09   Lagrange Interpolation
• 7.5 Software for Interpolation (skip)
• 7.6 Historical Notes and Further Reading
Homework 4
• Chapter 8: Numerical Integration and Differentiation   (1-10), 14, 24 (25-29), 49-51
• 8.1 Integration   Apr 13
• 8.2 Existence, Uniqueness, and Conditioning
• 8.3 Numerical Quadrature (partial coverage)
• 8.4 Other Integration Problems (skip)
• 8.5 Integral Equations
• 8.6 Numerical Differentiation
• 8.7 Richardson Extrapolation (skip)
• 8.8 Software for Numerical Integration and Differentiation (skip)
• 8.9 Historical Notes and Further Reading
Test 3: sample test     solution (worked problems)     questions
• Chapter 9: Initial Value Problems for Ordinary Differential Equations (1-5,10), 22,43, 51, (61,65)   Apr 25
• 9.1 Ordinary Differential Equations
• 9.2 Existence, Uniqueness, and Conditioning
• 9.3 Numerical Solution of ODEs (lightly covered)
• 9.4 Software for ODE Initial Value Problems (skip)
• 9.5 Historical Notes and Further Reading
• Chapter 10: Boundary Value Problems for Ordinary Differential Equations (skip)
• Chapter 11: Partial Differential Equations (skip)
• Chapter 12: Fast Fourier Transform (skip)
• Chapter 13: Random Numbers and Stochastic Simulation (skip)
Eq-Constr Quadratic Problem (video; not required)
• ### Catalog description and prereqes

COT 4501 Numerical Analysis-A Computational Approach. Credits: 3; Prereq: COP 3504 or COP 3503 and MAS 3114. Numerical integration, nonlinear equations, linear and nonlinear systems of equations, differential equations and interpolation.
• ### Contribution to ABET-related outcomes:

• (a) an ability to apply knowledge of mathematics, statistics, computer science, and electrical engineering as it applies to computer hardware and software.
• (b) an ability to design and conduct experiments, as well as to analyze and interpret data.
• (e) an ability to identify, formulate, and solve hardware and software computer engineering problems, accounting for the interaction between hardware and software.
• ### Other standard policy:

• Honesty Policy: All students admitted to the University of Florida have signed a statement of academic honesty committing themselves to be honest in all academic work and understanding that failure to comply with this commitment will result in disciplinary action. This statement is a reminder to uphold your obligation as a UF student and to be honest in all work submitted and exams taken in this course and all others.
• Accommodation for Students with Disabilities: Students Requesting classroom accommodation must first register with the Dean of Students Office. That office will provide the student with documentation that he/she must provide to the course instructor when requesting accommodation.
• UF Counseling Services: Resources are available on-campus for students having personal problems or lacking clear career and academic goals. The resources include
• UF Counseling and Wellness Center, 3190 Radio Rd, 392-1575, psychological and psychiatric services
• Career Resource Center, Reitz Union, 392-1601, career and job search services.
• Software Use: All faculty, staff and student of the University are required and expected to obey the laws and legal agreements governing software use. Failure to do so can lead to monetary damages and/or criminal penalties for the individual violator. Because such violations are also against University policies and rules, disciplinary action will be taken as appropriate. We, the members of the University of Florida community, pledge to uphold ourselves and our peers to the highest standards of honesty and integrity.