Math 413: Modern Applied Mathematics I (Fall 2009)

5:55pm - 7:10pm, TR, S & T I, Room 242

Instructor: Daniel M. Anderson (231 Science and Technology I, 703-993-1482, danders1@gmu.edu)
Office Hours: Tuesday 4:30-5:30PM, Thursday 4:30PM-5:30PM, and by appointment.
Text: Introduction to Applied Mathematics by G. Strang (Welllesley Cambridge Press, 1986)
Prerequisites: A grade of C or better in Math 203 and Math 214/216. This includes sufficient recall of matrix algebra (Math 203) and ordinary differential equations (Math 214 or 216).
Course Goals: In this course we will investigate a variety of mathematical methods within the areas of matrix algebra and differential equations and apply these techniques to equilibrium models in both discrete and continuous systems.
Exams: There will be one midterm exam and one final exam.
Homework There will be weekly assignments that count towards your grade. Some of these assignments will require the use of Matlab and/or Maple. More details to follow.
Grading Policy:: Homework = 50%; Midterm exam = 25%; Final Exam = 25%
In general, 90%-100% = A, 80%-89% = B, 70%-79% = C, 60%-69% = D, below 60% = F. Plus and minus grades will correspond to approximately 3% below or above these cutoff values (e.g. 87%--89% =B+, 80%--83% = B-). I reserve the right to lower the curve, but will not raise the curve.
Topics Covered: Chapter 1 (1.1-1.6): Linear Systems: Gaussian Elimination; Positive Definite Matrices; Minimum Principles, Least Squares; Eigenvalues -- Matrices and ODEs; Further Matrix Theory; Chapter 2 (2.1-2.5): Equilibrium Models -- Discrete Case: Applications Framework; Constraints and Lagrange Multipliers; Electrical Networks; Structural Equilibrium.; Chapter 3 (3.1-3.6): Equilibrium Models -- Continuum Case: Discrete vs. Continuum Models; Differential Equations of Equilibrium; Laplace's Equation and Potential Flow; 3D Vector Calculus; Electricity and Magnetism; Equilibrium of Fluids and Solids; Transport Equations; Navier--Stokes Equations; Bernoulli Equation; Calculus of Variations
Important Dates:: Tuesday, October 12, Fall Recess (no Tuesday classes, Monday classes meet on Tuesday); Tuesday, October 27 Midterm Exam; Thursday, December 10 (our last day of class); Thursday, December 17, 4:30am--7:15pm Final Exam; See see Registrar's calendar for other important dates
Final Exam: The final exam will be an in-class exam and must be taken at the scheduled time. Exceptions are allowed only with a Dean's permission, by University rules.
Honor System: It is expected that each student in this class will conduct himself or herself within the guidelines of the Honor Code. All academic work should be done with the level of honesty and integrity that this University demands.

Using computers at George Mason
Some Help With Matlab
Matlab Introduction [ PDF] (posted 8/28/09)
Additional Notes on Linear Algebra [ PDF] (posted 10/1/09)
Homework Assignments: HW1 (Due: Tuesday, September 8) (1.2):1,4,9,10,11; HW2 (Due: Tuesday, September 15) (1.3):1,2,3,6,8; HW3 (Due: Thursday, September 24) (1.4):1,2,10,11; HW4 (Due: Thursday, October 1) (1.5):1,2,3,13; HW5 (Due: Thursday, October 8) (1.6):2,3,7,8,9; HW6 (Due: Tuesday, October 20) (2.1):2,3,4,11; HW7 (Due: Thursday, November 5) (2.2):1,2,3a,b,7; HW8 (Due: Thursday, November 19) Network Problem, details explained in class; HW9 (Due: Tuesday, December 1) (3.1):1,2,4,6,12 [NOTE: use bc. u(0)=0,w(1)=0 on problems 1 and 2 and boundary conditions u(0)=0,u(1)=0 on problem 12]
To Daniel M. Anderson's Homepage