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CS 450: Numerical Analysis, Lecture notes of Differential Equations

Second half of course focuses on analytic problems, including numerical integration and differentiation and initial and boundary value problems for differential.

Typology: Lecture notes

2022/2023

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CS 450: Numerical Analysis
Course Description
Numerical solution of mathematical problems arising in computational modeling and data analysis,
including proper problem formulation, selection of effective solution algorithms, and interpretation of
results. First half of course focuses on algebraic problems, including linear and nonlinear algebraic
equations, eigenvalue problems, and optimization. Second half of course focuses on analytic problems,
including numerical integration and differentiation and initial and boundary value problems for differential
equations. Prerequisites include linear algebra, multivariate calculus, and basic programming ability,
preferably using Python. No prior familiarity with numerical methods is assumed.
Course Prerequisite
Linear algebra
Multivariate calculus
Basic programming ability using Python
Course Goals
By the end of the course, you will be able to:
Learn how to formulate computational problems properly
Learn how to select an effective solution algorithm for a given problem
Learn how to interpret computational results properly
Textbook (Recommended but not required)
Michael T. Heath. Scientific Computing, Second edition, The McGraw-Hill Companies.
Sample syllabus - students will receive the detailed syllabus at the beginning of
the semester enrolled in the course.
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CS 450: Numerical Analysis

Course Description

Numerical solution of mathematical problems arising in computational modeling and data analysis,

including proper problem formulation, selection of effective solution algorithms, and interpretation of

results. First half of course focuses on algebraic problems, including linear and nonlinear algebraic

equations, eigenvalue problems, and optimization. Second half of course focuses on analytic problems,

including numerical integration and differentiation and initial and boundary value problems for differential

equations. Prerequisites include linear algebra, multivariate calculus, and basic programming ability,

preferably using Python. No prior familiarity with numerical methods is assumed.

Course Prerequisite

  • Linear algebra
  • Multivariate calculus
  • Basic programming ability using Python

Course Goals

By the end of the course, you will be able to:

  • Learn how to formulate computational problems properly
  • Learn how to select an effective solution algorithm for a given problem
  • Learn how to interpret computational results properly

Textbook (Recommended but not required)

Michael T. Heath. Scientific Computing, Second edition , The McGraw-Hill Companies.

Sample syllabus - students will receive the detailed syllabus at the beginning of

the semester enrolled in the course.

Course Schedule Week Topic (^1) Scientific Computing 2 Systems of Linear Equations 3 Linear Least Squares 4 Eigenvalue Problems 5 Nonlinear Equations 6 Optimization 7 Midterm 8 Interpolation 9 Numerical Integration and Differentiation 10 Spring break, No class 11 Initial Value Problems for Ordinary Differential Equations 12 Boundary Value Problems for Ordinary Differential Equations 13 Partial Differential Equations 14 Fast Fourier Transform 15 Random Numbers and Stochastic Simulation 16 Final

your official final course grade. Grades that fall directly on a threshold will be rounded up to the higher

letter grade (e.g. 90 percent is an A- not a B+)

Assignments Occurrence Weight Percentage Graded Quizzes (^13) 13% Programming Assignments 13 26% Midterm Exam 1 26% Final Exam 1 35% Total 100% Grading Scale Total (percentage) Grade 90 - 100 (90-93, 93-96, 96-100) A (A-, A, A+) 80 - 90 (80-83, 83-86, 86-90) B (B-, B, B+) 70 - 80 (70-73, 73-76, 76-80) C (C-, C, C+) 60 - 70 (60-63, 63-66, 66-70) D (D-, D, D+) Below 60 F Student Code and Policies

A student at the University of Illinois at the Urbana-Champaign campus is a member of a University

community of which all members have at least the rights and responsibilities common to all citizens, free

from institutional censorship; affiliation with the University as a student does not diminish the rights or

responsibilities held by a student or any other community member as a citizen of larger communities of

the state, the nation, and the world. See the University of Illinois Student Code for more information.

Academic Integrity

All students are expected to abide by the campus regulations on academic integrity found in the Student

Code of Conduct. These standards will be enforced and infractions of these rules will not be tolerated in

this course. Sharing, copying, or providing any part of a homework solution or code is an infraction of the

University’s rules on academic integrity. We will be actively looking for violations of this policy in

homework and project submissions. Any violation will be punished as severely as possible with sanctions

and penalties typically ranging from a failing grade on this assignment up to a failing grade in the course,

including a letter of the offending infraction kept in the student's permanent university record.

Again, a good rule of thumb: Keep every typed word and piece of code your own. If you think you are

operating in a gray area, you probably are. If you would like clarification on specifics, please contact the

course staff.

Disability Accommodations

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soon as possible. If you’re unsure if this applies to you or think it may, please contact the instructor

and Disability Resources and Educational Services (DRES) as soon as possible. You can contact DRES

at 1207 S. Oak Street, Champaign, via phone at (217) 333-1970, or via email at disability@illinois.edu.