Math 450/451 Applied Mathematics

 Instructor Mark Pernarowski Textbook Applied Mathematics (3rd ed) J. David Logan Office Hours Schedule (Wil 2-236) Phone 994-5356 Classroom Rob Hall 307 MWF 10:00-10:50am

### Homework/Exams

### Classnotes/Handouts

 ` Grading: The course % for each of M450 and M451 is determined by:   Final         F            100   Homework      HW           200  _______________________________                              300          % = (F+HW)/3 The final is comprehensive. The Final is a take home exam and due at the date indicated below.  Final: TBA (take-home) Homework due dates and exam dates will be announced in class and posted here at a later date. Exam content will also be announced in class.` ` Syllabus: Material for the M450/M451 sequence will be selected from: Class Notes ODE Review Chapter 1 Dimensional Analysis Chapter 2 Perturbation Methods Chapter 3 Calculus of Variations Chapter 4 Eigenvalue Problems, Green's Functions Chapter 6 Partial Differential Equations Chapter 7 Wave Phenomena Chapter 8 Models of Continua Homework: Assigned homework and some of their solutions will be posted below as the course develops. Homework scores will vary depending on their length and difficulty. The raw scores will be summed, and converted into a % to yield the 200 points in the final grade.`

Classnotes for M450/M451:

1. Ordinary Differential Equation review (Text 1.3,2.2)
1. First Order Linear Equations
2. First Order Nonlinear Equations
3. Second Order Constant Coefficient
4. Systems of Equations (second order only) and some additional Review Problems We  may at some point also need a review of Laplace Transform techniques Other than your previous text, and class notes you may want to consider looking at the review drafted by Paul Dawkins at Lamar University, TX

2. Dimensional Analysis (Text Section 1.1-1.2)

1. Dimensional Analysis Introductory examples. and Similarity Solns. Here's a unit summary sheet
2. Dimensional Analysis Theory
3. Scaling in differential equations (nondimensionalization)

Homework and Exams for M450:

Below are the homework assignments and take-home exams. In the "Sample" column I will occasionally post old versions of similar assignments and their solutions. These should help augment your notes with more worked examples.

 Class Due Date Content Solutions HW 1 M450 Wed. Sept. 17 ODE Review HW 2 M450 Mond., Oct 2 Dimensional Analysis HW 3 M450 Wed. Oct 18 Regular Perturbations Midterm M450 Frid. Oct 27 Is a takehome exam. You may use, class notes, posted notes and the text. You may not use electronic devices (including internet) nor may you discuss the problems with other students. If you need clarification about a problem, you may ask me. Dimensional Analysis - Buckingham Pi theorem Nondimensionalizing an ODE(s) system Regular expansions of f(x,epsilon)=0 Regular expansion of a system  Regular expansion of an IVP HW 4 M450 Poincare Lindstedt method, asymptotics, singular root approximations, Singular boundary value prob. HW 5 M450 Wed. Nov 29 Nonlinear BVP, functional First Variations, Simple Euler Lagrange equations. Final M450 Frid, Dec 8 Is on HW 4-5 (TAKEHOME GIVEN OUT FRI DEC 4 IN CLASS1 HW 6 M451 Frid, Jan 26 Problems with Natural Boundary Conditions (NBC) for Lagrangians L=L(x,y,y')   and L=L(x,y,y',y'') tex HW_7 M451 Frid, Feb 9 Isoperimetric problems, Geodesics and multiple dependent variables. HW_8 M451 Frid, Feb 28 Fourier Series and Sturm Liouville Problems HW_9 M451 Frid, March 23 Integral Equations and Greens Functions HW_10 M451 Frid, April  13 Distributions Final M451 Wed, April 25 Is a takehome exam. You may use, class notes, posted notes and the text. You may use electronic devices for calculations but you may not discuss the problems with other students. If you need clarification about a problem, you may ask me. Is on HW 6-10 and intro PDE methods