Yi Hong
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.