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 realworld 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.
Administration:
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 12pm in CSE E309.
Grading:
curved
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 preapproved 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
(112), 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
(114), 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
(112), 15,21,27,3032,39,52,55
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
(17,12,14,15), 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
(3,4,711, 14), 15, (18), 24,29, 4345
 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
(114), 15,27,28,31 (3335), 36, (38), 42, 62 (6870)
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
(112), (1720), 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
(110), 14, 24 (2529), 4951
 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
(15,10), 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)
EqConstr Quadratic Problem
(video; not required)
Catalog description and prereqes
COT 4501 Numerical AnalysisA 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 ABETrelated 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 oncampus for students having personal problems or
lacking clear career and academic goals. The resources include

UF Counseling and Wellness Center, 3190 Radio Rd, 3921575, psychological and psychiatric services

Career Resource Center, Reitz Union, 3921601, career and job search services.

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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
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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.