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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 Wil 1-115
MWF 10am

Math 450

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Homework/Exams Classnotes/Handouts


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 Grading: The course % for each of
M450 and M451 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 and Final due dates and
details will 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.













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 Homework and Exams for M450:


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

 
Samples Due Date
Content  Solutions
 
Homework 1 sample / soln Sept 16 ODE Review HW_1_Solns
Homework 2 sample / soln Oct 7 Dimensional Analysis HW_2_Solns
Homework 3 ------ Hints sample / soln Oct 21 Regular Perturbations HW_3_Solns

Midterm  sample / solns Oct 28 HW1-HW3 above Midterm Solns
Homework 4 sample / solns Nov 9 Singular perturbation, Asymptotics,
Poincare Lindstedt
HW_4_Solns
Homework 5 sample / solns Nov 21 Singular BVP HW_5_Solns
Homework 6 sample / solns Dec 7 Calculus of Variations I HW_6_Solns
Final sample / solns Dec 14, 11am HW4-HW6 above  Final Solns



Homework and Exams for M451:

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

 
Samples Due Date
Content  Solutions
 
Homework 7 sample / solns Jan 27 Calculus of Variations II HW_7_Solns
Homework 8 (errata) sample / solns Feb 22 Inner product spaces, Fourier series, SLP HW_8_Solns
Homework 9 sample / solns Feb 29 Integral equations HW_9_Solns
Midterm 1 sample / solns March 7 HW7-9 above Midterm Solns
Homework 10 sample / solns March 30 Greens Functions, Distributions HW_10_Solns
Homework 11 sample / solns April 20 Partial Differential Equations HW_11_Solns
Final sample / solns April 30 HW10-11 above Final Solns



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Classnotes for M450/M451:


  1. Ordinary Differential Equation review (Text Section 1.3). 
    1. First Order Linear Equations
    2. First Order Nonlinear Equations
    3. Second Order Constant Coefficient Equations
    4. Systems of Differential Equations (second order only) and some additional Review Problems
    5. 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. Here's a unit summary sheet. For some more examples you can look at an old homework assignment here.
    2. Dimensional Analysis Theory
    3. Scaling in differential equations (nondimensionalization).
  3. Perturbation Theory (Text Chapter 2)
    1. Perturbation Theory Introduction
    2. Taylor Series Summary Sheet
    3. Regular Perturbation Theory - Algebraic
    4. Regular Perturbation Theory - Differential Equations
    5. Regular Perturbation Theory - Oscillations
    6. Asymptotics
    7. Singular Perturbation Theory - Algebraic
    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.  
    9. Singular Perturbation Theory - Examples of solved problems
    10. Singular Perturbation Theory - Matching Theory
    11. Singular Perturbation Theory - Examples of Failure

  4. Calculus of Variations (Text Chapter 3) 
    1. Introduction to functionals and related minimization problems
    2. Functional Optimization Theory
    3. Euler-Lagrange equations - Necessary conditions for minima
    4. Natural Boundary Conditions
    5. Higher Dimensional Problems
      1. Spring-Pendulum example
      2. Geodesics
    6. Isoperimetric Constraints - example
  5. Eigenvalue Problems, Integral Equations and Green's Functions  (Text Chapter 4)
       1. Function expansions in L2[a,b] using orthogonal sets: generalized fourier series
       2. Regular Sturm Liouville problems and related eigenfunction expansions
       3. Fredholm Integral Equations
       4. Green's Functions 
       5. Distributions
  6. Partial Differential Equations
    1. Introductory definitions, solutions, examples
    2. Multivariable Calculus review
    3. Conservation Laws and Constituitive Relations
    4. Diffusion as Random Walks
    5. Series Solutions for PDEs
    6. Laplace Transform Methods
    7. Method of Characteristics
    8. Reaction Diffusion Equations








 
 
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View Text-only Version Text-only Updated: 4/23/2012
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