Yi Hong

The University of Georgia

CSCI 4150/6150: Numerical Simulations in Science and Engineering

Overview: Computationally oriented, covering a wide range of topics that are necessary for numerical simulation in science and engineering. Sequential and parallel numerical methods will be introduced. Available symbolic and numerical software packages (e.g., Matlab, Maple) and visualization tools will be used in the mathematical simulations.

Course Information

  • Class meetings: T, R 11:00am – 12:15pm, W 11:15am – 12:05pm @ Boyd 306

  • Instructor: Yi Hong (yihong -at- cs.uga.edu, office: Boyd 616)

  • Office hours: W 10:00am – 11:00am, R 10:00am – 11:00am, or by appointment

  • Course webpage: http://cobweb.cs.uga.edu/~yihong/CSCI4150-6150-Sp2020.html

Topics

  • Introduction to scientific computing and numerical simulations

  • Number Systems, computer arithmetic, and errors

  • Numerical methods for solving Initial and Boundary Value Problems of Differential Equations

  • Numerical methods for solving Partial Differential Equations

  • Symbolic computation

  • Introduction to high performance computing

  • Speedup and efficiency

  • Introduction to parallel algorithms for solving numerical problems using CUDA for GPUs

  • Visualization tool

Available symbolic and numerical computational packages (such as Matlab, Maple, and CUDA) and visualization tools will be used in the simulations.

Textbook

  • Numerical Mathematics and Computing (Seventh Edition) by Ward Cheney and David Kincaid

  • Additional topics will be discussed in class

Prerequisites

MATH 2250 and CSCI 1301-1301L, or Permission of Department

Grading

  • Exam 1 (20%)

  • Exam 2 (20%)

  • Final Exam (25%)

  • Homework (30%: 6 out of 7 assignments, each 5%)

  • Participation and Attendance (5%)

Graduate students will be asked to do extra problem(s) on the tests and homework and/or a project.

Assignments must be submitted in class or on eLC before 5pm on their due date.

  • Late Policy: 1 day late (10% off), 2 (20% off), 3 (30% off). Late submissions are not accepted after 3 late days.

NO MARKEUP TESTS

Academic Honesty

All students are responsible for maintaining the highest standards of honesty and integrity in every phase of their academic careers. The penalties for academic dishonesty are severe and ignorance is not an acceptable defense.

Tentative Schedule

Date Topic Reading Assignments
Jan 7 (T) Course Introduction
Introduction to Numerical Simulations
-- --
Jan 8 (W) Introduction to Matlab (1) -- --
Jan 9 (R) Introduction to Matlab (2)
Programming Suggestions
Chapter A.1 --
Jan 14 (T) Representation of Numbers in Different Bases (1) Chapter B.1 --
Jan 15 (W) Representation of Numbers in Different Bases (2)
Floating-Point Representation (1)
Chapter B.1
Chapter 1.3
--
Jan 16 (R) Floating-Point Representation (2) Chapter 1.3, C.1 --
Jan 21 (T) Floating-Point Representation (2)
Errors: Absolute and Relative
Chapter 1.3, C.1
Chapter 1.1
--
Jan 22 (W) Loss of significance
Taylor Series (1)
Chapter 1.4
Chapter 1.2
--
Jan 23 (R) Taylor Series (2) Chapter 1.2 Homework 1 Handout
Jan 28 (T) Taylor Series (3) Chapter 1.2 --
Jan 29 (W) Taylor Series (4) Chapter 4.3 --
Jan 30 (R) Taylor Series (5) Chapter 4.3 Homework 1 Due
Homework 2 Handout
Feb 4 (T) Taylor Series (6)
Symbolic Computation: Maple and Matlab
Chapter 4.3
--
--
Feb 5 (W) Symbolic Computation: Maple and Matlab
Initial Value Problems (1)
--
Chapter 7.1
--
Feb 6 (R) Initial Value Problems (2) Chapter 7.2 Homework 2 Due
Homework 3 Handout
Feb 11 (T) Initial Value Problems (3) Chapter 7.3 --
Feb 12 (W) Initial Value Problems (4) Chapter 7.3 --
Feb 13 (R) Initial Value Problems (5)
Systems of ODEs (1)
Chapter 7.3
Chapter 7.4
Homework 3 Due
Feb 18 (T) Systems of ODEs (2) Chapter 7.4 --
Feb 19 (W) Systems of ODEs (3) Chapter 7.4 --
Feb 20 (R) Exam 1
Feb 25 (T) Systems of ODEs (4) Chapter 7.4 Homework 4 Handout
Feb 26 (W) Systems of ODEs (5)
Solving ODEs (1)
Chapter 7.4 --
Feb 27 (R) Boundary-Value Problems (1) Chapter 11.1 --
Mar 3 (T) Boundary-Value Problems (2) Chapter 11.2 Homework 4 Due
Mar 4 (W) Boundary-Value Problems (3) Chapter 11.2 --
Mar 5 (R) Boundary-Value Problems (4) Chapter 11.2 --
Mar 9-27
(M-F)
Spring Break & Class Suspension
Mar 31 (T) Boundary-Value Problems (5) Chapter 11.2 Homework 5 Handout
Apr 1 (W) Linear Systems (1) Chapter 2.2, 2.3 --
Apr 2 (R) Linear Systems (2) Chapter 2.3 --
Apr 7 (T) Linear Systems (3) Chapter 2.3 Homework 5 Due
Apr 8 (W) More on Linear Systems (1) Chapter 8.1 --
Apr 9 (R) More on Linear Systems (2) Chapter 8.1, 8.4 Take-Home Exam 2
Apr 14 (T) More on Linear Systems (3) Chapter 8.4 Exam 2 Due
Apr 15 (W) Partial Differential Equations (1) Chapter 12.1 --
Apr 16 (R) Partial Differential Equations (2) Chapter 12.1 Homework 6 Handout
Apr 21 (T) Partial Differential Equations (3) Chapter 12.1 --
Apr 22 (W) Partial Differential Equations (4) Chapter 12.2 --
Apr 23 (R) Partial Differential Equations (5) Chapter 12.3 Homework 6 Due
May 5 (T) Take-Home Final Exam

Disclaimer

The instructor reserves the right to make changes to the syllabus, including exam dates. These changes will be announced as early as possible.