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Math 450 Applied Mathematics I (Fall 2009)


 
Instructor Mark Pernarowski 
Textbook Applied Mathematics (3rd ed)
J. David Logan
Office Hours Schedule (Wil 2-236)
Phone 994-5356
Classroom Wil 1-144

Math 450

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Homework/Exams Classnotes/Handouts


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 Grading: The course % is determined by:

   Midterm       M            100 
   Final         F            100
   Homework      HW           200
  _______________________________
                                     400 
 
         % = (M+F+HW)/4

 The final is not comprehensive
 and both the final and midterm
 are take home exams.

 Homework and exam due dates will
 be announced in class and posted
 here at a later date. Exam content
 will be announced in class.

 Midterm due date: TBA
 Final due date: TBA
 
Syllabus: Material covered:

  Class Notes ODE Review
 Chapter 1 Dimensional Analysis
 Chapter 2 Perturbation Methods
 Chapter 3 Calculus of Variations
 
 Time permitting some of Chapter 4.

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.










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  Homework and Exams:



 
 Due Date
 Content  Solutions
Homework 1 Friday, Sept 18 ODE Review HW_1_Solns 
Homework 2 Friday, October 2 Dimensional Analysis HW_2_Solns
Homework 3 Friday, October 16 Regular Perturbation Problems HW_3_Solns 
Midterm 1 Friday, October 23 on HW1-HW3 Midterm 1 Solns
Homework 4 Friday, November 6 Singular perturbations, Asymptotics TBA 
Homework 5 TBA  
Final TBA



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Classnotes/Handouts:

I will post any handouts and class notes here:
  1. Ordinary Differential Equation  (ODE) review (Text Section 1.3). Throughout the course one will need to be able to solve a variety of ordinary differential equation problems based on techniques from Math 274 (formerly Math 225). Things we will review are:
    1. First Order Linear Equations
      • homogeneous
      • nonhomogeneous
      • initial value problems
    2. First Order Nonlinear Equations
      • separable
      • Bernoulli equations
    3. Second Order Constant Coefficient Equations
      • homogenous (distinct, complex, repeated roots)
      • nonhomogeneous - variation of parameters
      • nonhomogeneous - undetermined coefficients
      • initial value problems
    4. Systems of Differential Equations (second order only)
      • homogeneous - real, complex and repeated eigenvalues
      • nonhomogeneous - fundamental matrices, particular solutions

      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. A summary of some physical quantities and their units (MKSA system)
    2. An introduction to dimensional analysis with examples
    3. General theory for unit free laws and the Pi-theorem
    4. Nondimensionalizing (scaling) models: Logistic, Chemostat
  3. Perturbation Theory (Text Chapter 2)
    1. Introductory examples illustrating issues
    2. Summary sheet for Taylor Series
    3. Regular Perturbation Theory/Examples for Algebraic problems
    4. Regular Perturbation Theory/Examples for Initial Value Problems
    5. Regular Perturbation Theory - Nonlinear Oscillations
    6. Asymptotic Expansions
    7. Singular Perturbation Theory/Algebraic problems
    8. Singular Perturbation Theory/Boundary Value Problems- Intro. A casual introduction to boundayer layers and how one finds approximations valid in (inner) and away from (outer) the layer. The ideas of outer and inner approximations and matching are introduced and applied to a single model problem. Some Maple code I used in developing the example is included here.  
      1. Examples of solved problems
      2. Matching Theory - notes on the theory behind matching and why it works
      3. A few examples of method failures - result from incorrect assumptions
    9. Singular Perturbation Theory/Initial Value Problems
      1. Strongly damped oscillator - nondimensionalization/solution/issues
      2. Chemical Reaction Kinetics 
  4. Calculus of Variations (Text Chapter 3) 




 
 
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View Text-only Version Text-only Updated: 11/06/2009
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