Introduction To The Foundations Of Applied Mathematics Answers

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Site contents: Syllabus Matlab Announcements Lecture notes Schedule and homework Links Help info Anonymous Feedback Form

Announcements

[08/16/10] Welcome! Our first meeting is on Monday, Aug. 30. The textbook we are going to use is Mark H. Holmes "Introduction to the Foundations of Applied Mathematics" by Springer. If you have time, please try to familiarize yourself with the material by reading the introduction and prepare for the fruitful work this semester. Hope it will be an enjoyable one!

[09/20/10]Office hours this Tuesday Sept 21 are moved to 10am-12pm.

[09/22/10]Office hours are permanently moved to 10am-12pm.

[09/29/10]Office hours this Thursday Sept 30 are going to be 10am-11am, but I will be available after 12pm as well. Homework 2 solutions have been posted, see the corrected solution to problem 2.6.

[10/25/10]Office hours tomorrow, Tuesday Oct 26, are canceled due to a workshop.

[12/03/10]

Final Exam will be given in class on last day of classes, Dec. 10 and will be due by 5pm on Monday Dec. 20. No extensions will be provided.

Homework and notes

Homework assignments and notes will be posted here as the course progresses.
Reading assignments and selected homework problems will follow our main text: "Introduction to the Foundations of Applied Mathematics" by Mark H. Holmes, Springer.

Homework 1: due in class on Friday Sept 10 - [solution set]

Homework 2: due in class on Friday Sept 24 - [solution set]

Sample Exam 1 - some practice problems for Midterm I.

Sample Exam 1 solutions - practice Midterm I solutions.

Homework 3: due in class on Friday Oct 22 -[solution set]

Homework 4: due in class on Monday November 8 -[solution set]

Homework 5: due in class on Wednesday December 1 --[solution set]Practice questions for the Final Exam

Final Exam - due by 5pm on Monday Dec 20. No extensions!

Final Exam Solutions

Enjoy your break and happy holidays!

Assessment

Your grade in this course will depend on your performance on graded projects and one take-home final exam. Tentative weight of assessment components:
- Projects and homework assignments: 30%
- Midterm exam: 25%
- Final exam: 30%
- Participation: 15%

Letter grade will be determined as follows:

Score above	90%	80%	70%	60%	otherwise
Letter grade	A	B	C	D	F

From time to time practice problems will be given that will not count towards the final grade, unless specifically noted. I strongly encourage all participants to do these exercises in order to gain the necessary grasp of the material and perform well on the exam and graded assingments. I will discuss solutions in class.
I expect all class participants to abide to the rules and regulations specified in the official GMU Honor code.

Tentative schedule

Adobe reader needed to view .pdf files is available here Please note that this schedule is subject to change. Make sure you check this site frequently for updates.

1	[08/30/10] Chapters 1.1, 1.2: Dimension analysis	[09/01/10] Chapter 1.2	[09/03/10] Chapters 1.2, 1.3
2	[09/06/10] Labor day - no class	[09/08/10]	[09/10/10] HW1 due
3	[09/13/10]	[09/15/10]	[09/17/10]
4	[09/20/10]	[09/22/10]	[09/24/10] HW2 due
5	[09/27/10]	[09/29/10]	[10/01/10]
6	[10/04/10]	[10/06/10] Midterm I Review	[10/08/08] Midterm Exam I
7	[10/11/10] Columbus Day break - no class Class meets Tuesday Oct 12	[10/13/10]	[10/15/10]
8	[10/18/10]	[10/20/10]	[10/22/10] HW3 due
9	[10/25/10]	[10/27/10]	[10/29/08]
10	[11/01/10]	[11/03/10]	[11/05/10]
11	[11/08/10]	[11/10/10]	[11/12/10]
12	[11/15/10]	[11/17/10]	[11/19/10]
13	[11/22/10]	[11/24/10] Thanksgiving break - no class	[11/26/10] Thanksgiving break - no class
14	[11/29/10]	[12/01/10]	[12/03/10]
15	[12/06/10]	[12/08/10]	[12/10/10] Final Review

Help info and contacts

If you are looking for help, these are some of your options:

Try coming to my office hours.
If you have conflict with my office hours, talk to me after class or email me, I'll try to make an appointment for you at a different time.
Additional help is available in the Mathematics Tutoring Center, located in the Johnson Center room 344. Hours are posted on the Tutoring Center website.

If you have concerns or suggestions that you'd rather leave anonymous, please use the anonymous feedback form. I need to know what you think in order to make the learning process effective, so any feedback is valuable to me.

About MATLAB

MATLAB is an interactive programming language for general scientific and technical computation with powerful graphics and library functions. We will be using MATLAB environment for some homework problems towards the end of the semester and I expect you to be able to get access to it. Here is some relevant information.
- Some guidelines for accessing and using MATLAB are available here: http://math.gmu.edu/introtomatlab.htm
- A standalone student version of the product is available from Mathworks website for a reasonable price.

Some MATLAB tutorials you might want to read:

MATLAB website and documentation
Basic MATLAB tutorial (U. Michigan)
Somewhat more advanced MATLAB tutorial (U. Michigan)
MATLAB Summary and Tutorial (from U. of Florida)
Gentle introduction to MATLAB (from U. of Washington)
Function handling in MATLAB

Useful links

Every now and then I find interesting information on the web or in press. I'll be putting this stuff here, since it could help some of you to refresh things you might have forgotten or to aid with the general understanding of the course. If you find something useful yourself, please let me know, I'll be really happy to expand this list with your suggestions.

Basic math reference resources:
Partial fractions tutorial
Integration tutorial
Partial derivative examples
A concise Integral Table from Mathwords
Calculus review - formulae you have to remember!
Huge collection of Math related info at Wolfram Mathworld

Software tools available online:
ODE Software: powerful Dfield and PPlane Matlab tools (read instructions!)
DFDEMO: Direction field Java applet
One more direction field Java applet
Phase portrait generator (applet by Prof. Mansfield, PSU)
Studying ODE (applets for dir. fields, solving systems and more, by M. Rychlik)
Differential Equations and Initial Value Problems, applet
Systems of ODEs, applet
ODE solver Solutia (script for solving DE in standard form)

Course notes from different sources
ODE modules from Duke Univ. (TRY THESE!)
S.O.S. Math - nice short Differential Equations course online
S.O.S. Mathematics - CyberExam - sample exams online
Nagle's ODE book: Interactive Differential Equations supplement
1st Order ODEs (nice introductory notes by I. Blank, in .ps format)
Differential Equations Notes (good notes w/lots of examples by B. Ikenaga, in .ps format)
GATech DE course (great notes, by Jason Metcalfe)

Miscellaneous links

You might need to install current version of Ghostview to be able to view .ps files!

ODE Lecture Notes (handwritten notes, more advanced material, by M. Pemberton)
Advanced Differential Equations (extended source of notes on DE by S. Newhouse, in .ps format)
ODE course for Engineers (nice application examples, by J.R. White)
ODE notes (in .pdf, by Peter Wolenski, LSU)
Numerical Solution of ODEs (CSEP electronic book)
Numerical Solution of ODEs (Advanced course on theory of ODE, .ps file)
Numerical Methods (S. Dalziel)
Partial Differential Equations Notes (html notes on PDEs by A. Hood)
Course Notes: ODE, PDE etc (J. Labute at McGill, in .pdf)
Topics in Calculus (has some ODE notes too, by L. Lady)
ODE Notes and Exercises (Maple-based exercises, by P. Monk)
ODE course: lectures, problem sets, exams etc (by J.N. Kutz, U. Wash)
ODE Exams, Worksheets, ... (R.L. Devaney)
Mathematical Notes (.pdf notes on ODE by M. Malek, more theoretical)
PDE & Vector Calculus Lecture Notes (by W. Zakrzewski, Durham UK)
Complex Analysis and Differential Equations (by S.G. Rajeev, Rochester)
Difference Equations to Differential Equations (D. Sloughter)
Linear Methods ... (E.M. Harrell, J.V. Herod)
Hilbert Space Methods for PDEs (R.E. Showalter)
Topics in Integral and Differential Calculus (T. Kawasaki)
ODE Projects (A.C. Heinricher)
Maple Worksheet Repository
Graphical Tools (applets)
Taylor polynomial applets: 1, 2, 3, 4
Java Examples etc. (J. Feldman)
Damped Harmonic Motion, applet
Interactive Math Programs (calculus and DE applets from Dartmouth)
Kepler's Laws, applet
Fourier Synthesis, applet
The Lorenz Equations, applet
Nonlinear Klein-Gordon wave equation (applet by Paul Garrett)
Heat equation, applet
Java calculus, applets
MathServ DE Toolkit
Math Archives: ODEs, PDEs
Math Forum - Differential Equations (notes, problems, puzzles, discussions etc)
Differential Equations and more (calculus.net project)
ODE Project at BU
Sampler of applets (performance analysis, by Paul Garrett, UMN)
Famous Curves Applet Index (spirals, involutes and more)
Math Reference Tables