Math 577: Mathematical Modeling
Problem Set 1
Spring 2014
Assigned Tues Jan 14
Due Thurs Jan 23
Dimensional analysis, scaling and self-similar solutions
0. Reading: Logan, Chapter 1: Section 1.1 (1.1.11.1.4) and Section 1.2 (1.2.1).
1. Logan, Section 1.1.
Math 577: Mathematical Modeling
Spring 2014
Problem Set 6
Due Thurs Mar 6
Assigned Thurs Feb 27
Perturbation methods for weakly-nonlinear oscillator problems
0. Reading: Logan, sections 3.1.2 and 3.1.3.
1. For each problem use the Poincare-Lindstedt expan
Math 577: Mathematical Modeling
Problem Set 5
Spring 2014
Assigned Thurs Feb 13
Due Thurs Feb 20
Boundary Layers and Slender-body Asymptotics for Laplaces Equation
-1. Test #1 : Tuesday, Feb 25, in-class, covering the course material so far (HWs 14, Lectu
Math 577: Mathematical Modeling
Problem Set 4
Spring 2014
Assigned Thurs Feb 6
Due Thurs Feb 13
ODE Boundary Layer Problems
-1. Test #1: (Date to be decided) in-class, covering the course material so far (HWs 14, Lectures 1
9, Logan, Chaps 1, 3: scaling a
Math 577: Mathematical Modeling
Problem Set 2
Spring 2014
Assigned Thurs Jan 23
Due Thurs Jan 30
Scaling and Nondimensionalization
0. Reading: Logan section 1.2.
1. Logan, Section 1.2.3 Exercises, page 40, problem 1.
2. Logan, Section 1.2.3 Exercises, pag
Math 577: Mathematical Modeling
Problem Set 7
Spring 2014
Assigned Thurs Mar 6
Due Thurs Mar 20
Fast/slow dynamical systems and Chemical reaction kinetics
0. Reading from Logan: Sections 2.5.1-2 and 3.4.1-2
(and 1.3.2, 2.1-2.3 if needed for further backgr
Math 577: Mathematical Modeling
Problem Set 11
Spring 2014
Assigned Thurs Apr 10
Due Fri Apr 25, 5:00pm
Conservation laws and wave phenomena (II) [optional extra credit]
-2. This is an optional problem set. It is not required for your course grade; you ma
Math 577: Mathematical Modeling
Problem Set 8
Assigned Thurs Mar 20
Spring 2014
Due Thurs Mar 27
Introduction to the Calculus of Variations
0. Reading: Logan Chapter 4, sections: 4.1, 4.2.2, 4.3, 4.5.1, 4.4.
1. Use the Euler-Lagrange equation to solve pro
Math 577: Mathematical Modeling
Spring 2014
Problem Set 3
Due Thurs Feb 6
Assigned Thurs Jan 30
Regular/Singular Perturbation Problems
-1. Computer-Assisted Algebra Policy : You may always use Maple or Mathematica (or other computer software) to help chec
Math 577: Mathematical Modeling
Problem Set 10
Assigned Wed Apr 3
Spring 2014
Due Fri Apr 10
Conservation laws and wave phenomena (I)
-2. Test 2: In class on Tuesday, April 15.
-1. This is the nal regular (required) homework set. I will determine the A/B/
Math 577: Mathematical Modeling
Spring 2014
Problem Set 9
Due Thurs Apr 3
Assigned Thurs Mar 27
Intermediate Calculus of Variations
-1. Test #2: Apr 8 or 10 (to be determined by vote) in-class, covering SOME of the course material
since the rst exam (HWs