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# MATH 3600-100 (8458), Spring 2018

## Applied Numerical Methods

### Syllabus

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, Wednesday, and Friday 12:55-1:50pm, or by appointment.
Web page:
http://www.ohiouniversityfaculty.com/mohlenka/2185/3600.
Class hours/ location:
Monday, Wednesday, Friday 2:00-2:55pm in 314 Morton Hall.
Text:
Introduction to Numerical Methods and Matlab Programming for Engineers, Todd Young and Martin Mohlenkamp. Available at http://www.ohiouniversityfaculty.com/youngt/IntNumMeth/.
Homework:
Each lecture in the text has a few homework problems, which are due at the end of the following class period. Do the homework in a group of 2 or 3 and submit a group solution for each problem. Submission is online through Blackboard; upload a single file (.docx or .pdf) for each problem.
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 four tests, in class, without the aid of the computer (or calculator, notes, etc.). See further test information.
Final Exam:
The final exam is on Monday, April 30, 12:20-2:20pm, in our regular classroom. See further test information.
Attendance:
This is a "lab" class, so your attendance, participation, and collaboration are essential. You are allowed 5 absences (out of 41 classes) without penalty; these include university excused absences for illness, death in the immediate family, religious observance, jury duty, or involvement in University-sponsored activities. Each additional absence will reduce your final average by 0.5%. Your attendance record will be available in Blackboard.
Your grade is based on homework 40%, 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 for each lecture is due at the end of the next class period (skipping test days). Late homework is penalized 10% for each class day (or part thereof) late. You can resubmit a homework to improve your score, but the late penalty will apply.
Smartphones:
During class time, your phone must be off and out of sight. (The mere visible presence of you phone decreases your cognitive performance; see the article and research paper.) You may step out into the hall to use your phone. Violators will first receive a warning and then be marked as half absent.
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). (You do not need to acknowledge me or the textbook.)
• 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.
Responsible Employee Reporting Obligation:
If I learn of any instances of sexual harassment, sexual violence, and/or other forms of prohibited discrimination, I am required to report them. If you wish to share such information in confidence, then use one of the confidential resources listed by the Office of Equity and Civil Rights Compliance.
Learning Resources:

### Schedule (Subject to change)

Week Date Topic/Materials Homework due, Test, etc.
1 Part I: Matlab and Solving Equations
Wed Jan 17 Introduction, Lecture 1: Vectors, Functions, and Plots in Matlab
Fri Jan 19 Lecture 2: Matlab Programs Lecture 1 homework
2 Mon Jan 22 Lecture 3: Newton's Method and Loops Lecture 2 homework
Wed Jan 24 Lecture 4: Controlling Error and Conditional Statements Lecture 3 homework; do problem 3.3 as a Good Problem using the Layout skill
Fri Jan 26 Lecture 5: The Bisection Method and Locating Roots; mybisect.m Lecture 4 homework (drop deadline)
3 Mon Jan 29 Lecture 6: Secant Methods; mysecant.m Lecture 5 homework
Wed Jan 31 Lecture 7: Symbolic Computations; part I review Lecture 6 homework; do problem 6.1 as a Good Problem using Flow (and Layout)
Part II: Linear Algebra
Fri Feb 2 Lecture 8: Matrices and Matrix Operations in Matlab Lecture 7 homework
4 Mon Feb 5 Lecture 9: Introduction to Linear Systems Lecture 8 homework
Wed Feb 7 test information Test through Lecture 7
Fri Feb 9 Lecture 10: Some Facts About Linear Systems Lecture 9 homework
5 Mon Feb 12 Lecture 11: Accuracy, Condition Numbers and Pivoting Lecture 10 homework
Wed Feb 14 Lecture 12: LU Decomposition Lecture 11 homework; do problem 11.1 as a Good Problem using Symbols (and Flow, Layout)
Fri Feb 16 Lecture 13: Nonlinear Systems - Newton's Method Lecture 12 homework
6 Mon Feb 19 Lecture 14: Eigenvalues and Eigenvectors Lecture 13 homework
Wed Feb 21 Lecture 15: An Application of Eigenvectors: Vibrational Modes Lecture 14 homework; do problem 14.1 as a Good Problem using Logic (etc.)
Fri Feb 23 Lecture 16: Numerical Methods for Eigenvalues; part II review (in Lecture 18) Lecture 15 homework
7 Part III: Functions and Data
Mon Feb 26 Lecture 19: Polynomial and Spline Interpolation Lecture 16 homework
Wed Feb 28 test information Test through Lecture 15
Fri Mar 2 Lecture 20: Least Squares Fitting: Noisy Data Lecture 19 homework
8 Mon Mar 5 Lecture 21: Integration: Left, Right and Trapezoid Rules Lecture 20 homework
Wed Mar 7 Lecture 22: Integration: Midpoint and Simpson's Rules; mysimpweights.m Lecture 21 homework; do problem 21.1 as a Good Problem using Intros
Fri Mar 9 Lecture 23: Plotting Functions of Two Variables; mywedge.m; mywasher.m Lecture 22 homework
Spring Break
9 Mon Mar 19 Lecture 24: Double Integrals for Rectangles; mylowerleft.m; mydblsimpweights.m Lecture 23 homework
Wed Mar 21 Lecture 25: Double Integrals for Non-rectangles; mywedge.m Lecture 24 homework; do problem 24.1 as a Good Problem.
Fri Mar 23 Lecture 27: Numerical Differentiation Lecture 25 homework
10 Mon Mar 26 Lecture 28: The Main Sources of Error; part III review Lecture 27 homework
Wed Mar 28 test information Test through Lecture 25 (skipping 17 and 18)
Part IV: Differential Equations
Fri Mar 30 Lecture 29: Reduction of Higher Order Equations to Systems Lecture 28 homework (drop deadline with WP/WF)
11 Mon Apr 2 Lecture 30: Euler Methods; myeuler.m; mymodeuler.m Lecture 29 homework
Wed Apr 4 Lecture 31: Higher Order Methods Lecture 30 homework; do problem 30.1 as a Good Problem using Graphs
Fri Apr 6 Lecture 33: ODE Boundary Value Problems and Finite Differences; myexactbeam.m Lecture 31 homework
12 Mon Apr 9 Lecture 34: Finite Difference Method -- Nonlinear ODE Lecture 33 homework
Wed Apr 11 Lecture 35: Parabolic PDEs - Explicit Method; myheat.m Lecture 34 homework; do problem 34.1 as a Good Problem
Fri Apr 13 Lecture 36: Solution Instability for the Explicit Method; myexpmatrix.m Lecture 35 homework
13 Mon Apr 16 Lecture 37: Implicit Methods Lecture 36 homework
Wed Apr 18 test information Test through Lecture 35 (skipping 17, 18, 26, and 32).
Fri Apr 20 Lecture 38: Insulated Boundary Conditions; myheatdisk.m Lecture 37 homework
14 Mon Apr 23 Lecture 39: Finite Difference Method for Elliptic PDEs; mypoisson.m Lecture 38 homework
Wed Apr 25 Lecture 41: Finite Elements; mywasher.m Lecture 39 homework; do problem 39.1 as a Good Problem
Fri Apr 27 Lecture 42: Determining Internal Node Values; Part IV review; myfiniteelem.m Lecture 41 homework
15 Mon, Apr 30 test information Final Exam 12:20-2:20pm, in our classroom.

Martin J. Mohlenkamp