Undergraduate Numerical Techniques for Atmosphere, Ocean and Earth Scientists: ATSC 409¶
Calendar Entry¶
Web-based introduction to the practical numerical solution of ordinary and partial differential equations including considerations of stability and accuracy. Credit will not be granted for both ATSC 409 and ATSC 506/EOSC 511.
Course Purpose¶
The students completing this course will be able to apply standard numerical solution techniques to the solution of problems such as waves, advection, population growth.
Instructors¶
Prerequisites¶
Solution of Ordinary Differential Equations (MATH 215 or equivalent) AND a programming course. Partial Differential Equations (Math 316 or Phys 312) is recommended. 1
Course Structure¶
This course is not lecture based. The course is an interactive, computer based laboratory course. The computer will lead you through the laboratory (like a set of lab notes) and you will answer problems most of which use the computer. The course consists of three parts. A set of interactive, computer based laboratory exercises, two mini-projects and a final project.
During the meeting times, we will hold short quizzes (just to make sure you are keeping up) and brief presentations to help with technical matters and the more difficult sections of the course.
You can use a web-browser to examine the course exercises. Point your browser to:
Grades¶
Your grades will be calculated in two ways and we will use which ever is higher. 1. Original
Laboratory Exercises 30%
Quizzes 10%
Mini-projects 20%
Project Proposal 5%
Project 30%
Project Oral Presentation 5%
2. Lower Final Project
Laboratory Exercises 45%
Quizzes 10%
Mini-projects 30%
Project Proposal 5%
Project 5%
Project Oral Presentation 5%
Meeting Times¶
1400-1600 Mondays, Room 135, Earth and Oceans Sciences (EOS) Main
Laboratory Problem Sets¶
The laboratory problem sets can be given to either instructor when completed. (We have mail boxes in the Earth and Ocean Sciences Main Office). They may be hand written or typed. You may wish or be asked to include plots and diagrams. You can email us plots instead of printing them. Sometimes, rather than a large series of plots, you may wish to include a summarizing table. If you do not understand the scope of a problem, please ask. The time scales given in the Contents section are based on 7 hours/week additional to class time. Help with the labs is available 1) through piazza on Connect so you can contact your classmates and ask them 2) during the weekly scheduled lab or 3) directly from the instructors. Assignments, mini-projects and the project are expected on time. Late ones will be marked and then the mark will be multiplied by \((0.9)^{\rm (number\ of\ days\ or\ part\ days\ late)}\). (Below we give two dates for each assignment. You should aim for the first one (this would keep you totally up to date). The later one allows a couple of days in case. )
Contents¶
For each laboratory we give an estimate of number of hours. You will need to complete six hours a week to keep up with the course material covered in the quizzes.
Introductory Meeting
Laboratory One
Estimate: 8 hours
Quiz #1 Objectives 2 pertaining to Lab 1 sections Introduction, Discretization, Difference Approximations to the First Derivative
Quiz #2 Objectives pertaining to Lab 1 all sections and Lab 2 sections Introduction, Accuracy of Difference Approximations
Assignment: See web.
Laboratory Two
Estimate: 6 hours
Quiz #2 Objectives pertaining to Lab 1 all section and Lab 2 sections Introduction, Accuracy of Difference Approximations
Quiz #3 Objectives pertaining to Lab 2 all sections and Lab 3 section Linear Systems.
Assignment: See web.
Laboratory Three
Estimate: 8 hours
Quiz #3 Objectives pertaining to Lab 2 all sections and Lab 3 section Linear Systems.
Quiz #4 Objectives pertaining to Lab 3 all sections.
Assignment: See web.
Mini-Project #1
Estimate: 4 hours
Details on web.
Laboratory Four
Estimate: 8 hours
Quiz #5 Objectives pertaining to Lab 4 section Solving Ordinary Diff. Eqns with the Runge-Kutta Method, to end of subsection The Runge-Kutta Tableau
Quiz #6 Objectives pertaining to Lab 4 all sections and Lab 5 section Daisyworld
Assignment: See web.
Laboratory Five
Estimate: 6 hours
Quiz #6 Objectives pertaining to Lab 4 all sections and Lab 5 section Daisyworld
Quiz #7 Objectives pertaining to Lab 5 all sections
Assignment: 4a, 4b, 6-1, 6-2, 6-3
Mini-Project #2
Estimate: 4 hours
Details on web.
Laboratory Seven (do 7 if you have PDE’s)
Estimate: 8 hours
Quiz #8 Objectives pertaining to Lab 7 sections Physical Example, Poincare Waves and Numerical Solution
Assignment: See web.
Laboratory Six (do 6 if you do not have PDE’s)
Estimate: 8 hours
Quiz #8 Objections pertaining to Lab 6 sections Introduction and the Lorenz Equations
Assignment: See web.
Project
Estimate: 16 hours
20 minute presentation to the class
Project report