• This web page describes an activity within the Department of Mathematics at Ohio University, but is not an official university web page.
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# MATH 3600-100 (6115), Spring 2015

## Applied Numerical Methods

Catalog Description:
A survey of numerical methods for engineering, science and mathematics students. Topics include: solutions of systems of linear and nonlinear equations, eigenvalues, numerical differentiation and integration, and numerical solution of ordinary and partial differential equations. The topics will be posed in a setting of problems intended for engineering students using MATLAB. The course will simultaneously introduce numerical methods, programming techniques, problem solving skills and the Matlab language, in a lecture-lab format.
Desired Learning Outcomes:
• The ability to use MATLAB as a programming tool to solve common engineering and scientific problems.
• Understand and know how to apply common numerical methods for solving equations and linear systems, integration and differential equations.
• The ability to define and understand the practical consequences of issues such as convergence, stability, computational cost, and error propagation as they apply to various numerical problems.
Prerequisites:
MATH 3400 Elementary Differential Equations.
Instructor:
Martin J. Mohlenkamp, mohlenka@ohio.edu, (740)593-1259, 315-B Morton Hall.
Office hours: Monday 3:05-4pm, Wednesday 3:05-4pm, and Friday 10:45-11:40am, or by appointment.
Web page:
http://www.ohiouniversityfaculty.com/mohlenka/20152/3600.
Class hours/ location:
Monday, Wednesday, Friday 4:10-5:05pm in 314 Morton Hall.
Text:
Introduction to Numerical Methods and Matlab Programming for Engineers, Todd Young and Martin Mohlenkamp. Available at http://www.math.ohiou.edu/courses/math3600.
Homework:
Each lecture in the text has a few homework problems, which are due two class days after we cover that lecture. Do the homework in a group of 2 or 3 and submit a single solution for your group.
Good Problems:
About once a week, one homework problem is designated a Good Problem. These problems will be graded both on content and on presentation. The idea is to practice writing mathematics regularly but in small pieces.
Tests:
There will be three mid-term tests, in class, without the aid of the computer (or calculator, notes, etc.).
Final Exam:
The final exam is on Monday, April 27, at 4:40 pm. The exam is cumulative, but the questions on Parts I, II, and III will be based closely on the questions that appear on the tests for those parts.
Attendance:
This is a "lab" class, so your attendance, participation, and collaboration are essential. Each class you attend earns you 0.25% toward your final grade, up to a maximum of 9%. Since there are 41 classes, this allows for 5 absences, including university excused absences for illness, death in the immediate family, religious observance, jury duty, or involvement in University-sponsored activities. Your attendance record will be available in Blackboard.
Your grade is based on attendance 9%, homework 41%, each test 10% and the final exam 20%. An average of 90% guarantees you at least an A-, 80% a B-, 70% a C-, and 60% a D-.
Late work:
Homework is due by the end of class. Late homework is penalized 5% for each class day (or part thereof) late. You can resubmit a homework to improve your score, but the late penalty will apply.
Tests, final exam:
You may not give or receive any assistance during a test or the exam, including but not limited to using notes, phones, calculators, computers, or another student's solutions.
Homework:
• If your group receives any help on the homework, you must acknowledge in writing what help you received and from whom or what source (including internet links).
• It is permitted to have a student who has already taken this course explain a homework problem to you; however, it is not permitted to look at their written work or programs.
• It is permitted to search the internet for help on homework problems. It is not permitted to look at (or contribute to) any postings of solutions to the specific homework problems for this class. (If you find posted solutions, please send me the link.)
A minor, first-time violation of this policy will receive a warning and discussion and clarification of the rules. Serious or second violations will result in a grade penalty on the assignment. Very serious or repeated violations will result in failure in the class and be reported to the Office of Community Standards and Student Responsibility, which may impose additional sanctions. You may appeal any sanctions through the grade appeal process.
Special Needs:
If you have specific physical, psychiatric, or learning disabilities and require accommodations, please let me know as soon as possible so that your learning needs may be appropriately met. You should also register with Student Accessibility Services to obtain written documentation and to learn about the resources they have available.
Learning Resources:

## Schedule

Subject to change.
Week Date Topic/Materials Homework/Test etc.
1 Part I: Matlab and Solving Equations
Mon Jan 12 Introduction, lecture 1: Vectors, Functions, and Plots in Matlab
Wed Jan 14 lecture 2: Matlab Programs Good Problem using the Layout skill:
Write your mathematical autobiography.
Include
• your current interests and future goals,
• why you are taking this class,
• your preferred learning style(s) as determined by the VARK questionaire, and
• whatever else is relevant or interesting.
Fri Jan 16 lecture 3: Newton's Method and Loops lecture 1 homework
2 Mon Jan 19Martin Luther King, Jr. Day holiday, no class
Wed Jan 21 lecture 4: Controlling Error and Conditional Statements lecture 2 homework
Fri Jan 23 lecture 5: The Bisection Method and Locating Roots; mybisect.m lecture 3 homework; do problem 3.3 as a Good Problem (still using the Layout skill); (drop deadline)
3 Mon Jan 26 lecture 6: Secant Methods; mysecant.m lecture 4 homework
Wed Jan 28 lecture 7: Symbolic Computations; part I review lecture 5 homework; do problem 5.2 as a Good Problem using Flow (and Layout)
Part II: Linear Algebra
Fri Jan 30 lecture 8: Matrices and Matrix Operations in Matlab lecture 6 homework
4 Mon Feb 2 lecture 9: Introduction to Linear Systems lecture 7 homework
Wed Feb 4 lecture 10: Some Facts About Linear Systems lecture 8 homework
Fri Feb 6 part I study guide Test on Part I (lectures 1-7)
5 Mon Feb 9 lecture 11: Accuracy, Condition Numbers and Pivoting lecture 9 homework
Wed Feb 11 lecture 12: LU Decomposition lecture 10 homework
Fri Feb 13 lecture 13: Nonlinear Systems - Newton's Method lecture 11 homework; do problem 11.1 as a Good Problem using Symbols (and Flow, Layout)
6 Mon Feb 16 lecture 14: Eigenvalues and Eigenvectors lecture 12 homework
Wed Feb 18 lecture 15: An Application of Eigenvectors: Vibrational Modes lecture 13 homework; do problem 13.1 as a Good Problem
Fri Feb 20 lecture 16: Numerical Methods for Eigenvalues; part II review (in lecture 18) lecture 14 homework
7 Part III: Functions and Data
Mon Feb 23 lecture 19: Polynomial and Spline Interpolation lecture 15 homework; do problem 15.1 as a Good Problem using Logic
Wed Feb 25 lecture 20: Least Squares Fitting: Noisy Data lecture 16 homework
Fri Feb 27 lecture 21: Integration: Left, Right and Trapezoid Rules lecture 19 homework
Spring Break
8 Mon Mar 9 part II study guide Test on Part II (lectures 8-16)
Wed Mar 11 lecture 22: Integration: Midpoint and Simpson's Rules; mysimpweights.m lecture 20 homework
Fri Mar 13 lecture 23: Plotting Functions of Two Variables; mywedge.m; mywasher.m lecture 21 homework
9 Mon Mar 16 lecture 24: Double Integrals for Rectangles; mylowerleft.m; mydblsimpweights.m lecture 22 homework; do problem 22.1 as a Good Problem
Wed Mar 18 lecture 25: Double Integrals for Non-rectangles; mywedge.m lecture 23 homework
Fri Mar 20 lecture 27: Numerical Differentiation lecture 24 homework
10 Mon Mar 23 lecture 28: The Main Sources of Error; part III review lecture 25 homework
Part IV: Differential Equations
Wed Mar 25 lecture 29: Reduction of Higher Order Equations to Systems lecture 27 homework; do problem 27.1 as a Good Problem using Intros
Fri Mar 27 lecture 30: Euler Methods; myeuler.m; mymodeuler.m lecture 28 homework (drop deadline with WP/WF)
11 Mon Mar 30 lecture 31: Higher Order Methods lecture 29 homework
Wed Apr 1 part III study guide Test on Part III (lectures 19-25, 27, and 28)
Fri Apr 3 lecture 33: ODE Boundary Value Problems and Finite Differences; myexactbeam.m lecture 30 homework
12 Mon Apr 6 lecture 34: Finite Difference Method -- Nonlinear ODE lecture 31 homework
Wed Apr 8 lecture 35: Parabolic PDEs - Explicit Method; myheat.m lecture 33 homework; do problem 33.1 as a Good Problem using Graphs
Fri Apr 10 lecture 36: Solution Instability for the Explicit Method; myexpmatrix.m lecture 34 homework
13 Mon Apr 13 lecture 37: Implicit Methods lecture 35 homework
Wed Apr 15 lecture 38: Insulated Boundary Conditions; myheatdisk.m lecture 36 homework; do problem 36.1 as a Good Problem
Fri Apr 17 lecture 39: Finite Difference Method for Elliptic PDEs; mypoisson.m lecture 37 homework
14 Mon Apr 20 lecture 41: Finite Elements; mywasher.m lecture 38 homework
Wed Apr 22 lecture 42: Determining Internal Node Values; Part IV review; myfiniteelem.m lecture 39 homework; do problem 39.1 as a Good Problem
Fri Apr 24 Review, part IV study guide lecture 41 homework
15 Mon, Apr 27 Final Exam 4:40-6:40pm, in our classroom.

Martin J. Mohlenkamp
Last modified: Fri Apr 10 17:17:39 EDT 2015