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                              Math 450/451 Applied Mathematics
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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
Math 450

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 Grading: The course % for each of
M450 and M451 is determined by:

   Final         F            100
  Homework      HW           200

         % = (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.


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        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)
  1. Perturbation Theory (Text Chapter 3)
    1. Introductory Problems
    2. Regular Perturbation Problems - algebraic
    3. Regular Perturbation Problems - Systems and Integrals
    4. Regular Perturbation Problems - ordinary differential equation
    5. Regular Perturbation Problems - nonlinear oscillations
    6. Asymptotics
    7. Singular Perturbation Theory - algebraic 
    8. Singular Perturbation Theory - BVP intro
    9. Singular Perturbation Theory - BVP Matching
    10. Singular Perturbation Theory - BVP worked examples
    11. Singular Perturbation Theory - BVP Matching failure
    12. Singular Perturbation Theory - IVP Oscillator exampleChemical Model example
  2. Calculus of Variations (Text Chapter 4) 
    1. Calculus of Variations - Introduction
    2. Calculus of Variation - 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
  3. Eigenvalue Problems, Integral Equations and Green's Functions  (Text Chapter 5)
    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
  4. Partial Differential Equations (Text Chapter 6)
    1. Introductory examples, definitions, concepts.
    2. Multivariate Calculus Overview
    3. Conservation Laws and Constituitive Relations
    4. Diffusion as Random Walks
    5. Series Solutions for PDE's
    6. Method of Characterisitics - introduction

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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







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.
  1. Dimensional Analysis - Buckingham Pi theorem
  2. Nondimensionalizing an ODE(s) system
  3. Regular expansions of f(x,epsilon)=0
  4. Regular expansion of a system 
  5. Regular expansion of an IVP

HW 4


  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



HW 6


 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 


View Text-only Version Text-only Updated: 4/16/2018
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