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                              Math 450/451:   Applied Math I-II    (Spring 2024)

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               Math 450XXXX

 

  INSTRUCTOR:   Mark Pernarowski (Schedule)
  TEXTBOOK:  

Applied Mathematics (4rth ed)    -  J. David Logan

  •   Chapter 1 Dimensional Analysis and Scaling
  •   Chapter 3 Perturbation Methods
  •   Chapter 4 Calculus of Variations
  LOCATION:
 

MWF 10-10:50 , Wil 1-143

  GRADE:  

Grades will be recorded in D2L. The course % will determined as follows:

 

 

 

 

 

 

 

 

 

 

 

HOMEWORK:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

NOTES 

 

 

 

 

 

 

 

 

 

 

 
                         Percent     Due Date     
 
Midterm
 
M
25%
 March 22
Wil 1-143 in class
 (takehome)
 
Final
 
F
25%
 May 6
Wil 1-143 10-11:50am
 (takehome)
 
Homework
 
HW
50%
below
   
 
 
 
 
100
     

 

Conversion to letter grade:

A A- B+ B B- C+ C C- D F
90-100 87-89 84-86 80-83 77-79 74-76 70-73 67-69 60-66  

 

Homework and due dates will be posted here as class develops. Homework assignments will have varied lengths and difficulty hence will have different raw scores. The HW% for the final grade will be the % from the sum of all the raw HW scores:

           
  M450       Due Date   
 
Homework 1
  Dimensional Analysis       
Wed, September 13
  Homework 2   Regular Perturbation - Algebraic   Mond, October 2
  Homework 3   Regular Perturbation - ODE   Friday, October 13
  Homework 4   Singular Perturbation Theory   Friday, November 3
  Homework 5   Calculus of Variations   Friday,November 17
  Midterm  

Take home due in class -  link

  Friday, October 20
  Final  

 Take home due in class - link

   

 

  M451       Due Date   
 
Homework 6
  Calculus of Variations - Applications  
  January 26    
  Homework 7   Generalized Fourier Series      February 9        
  Homework 8   Green's Functions      February 26
  Homework 9   PDE intro solutions      April 1
  Homework 10   PDE models,Random Walks, Series      April 15
           
  Midterm   Fourier, Greens, Distributions     March 22
  Final         Monday May 6, 10-11:50am
           Holy Grail - 3 questions

 

 

Periodically I will post handwritten and/or typeset lecture notes here.

 

M450 Notes:

1. Dimensional Analysis (Text Chapter 1)

  1. Dimensional Analysis Introductory examples. and Similarity Solns.
  2. Dimensional Analysis Theory
  3. Scaling in differential equations (nondimensionalization)

2. Perturbation Theory (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 example, Chemical Model example

3. Calculus of Variations (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. Principle of Least Action
  6. Higher Dimensional Problems
    1. Spring-Pendulum example
    2. Geodesics
  7. Isoperimetric Constraints - example

 

M451 Notes:

1. Function Expansions

  1. Generalized Fourier Series
  2. Sturm Liouville Theory

2. Green's Functions

  1. Introduction to Green's Functions
  2. Fredholm Integral Equations (no HW on this)
  3. Distributions introduction

3. Partial Differential Equations

  1. Introduction and Examples
  2. Series Solutions
  3. Conservation Laws
  4. Multivariate Calculus Review
  5. Diffusion and Random Walks
  6. Method of Characteristics
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      Holidays:
     
First Day of School Wednesday, January 17th 
Presidents Day (no classes, offices closed) Monday, February 19
Spring Break (no classes, offices open) March 11-15
University Day (no classes, offices open) Friday, March 29
Last Day of Classes Friday, May 2
Last Day of Finals Thursday, May 9