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 |
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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
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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:
Classnotes/Handouts:
I will post any handouts and class notes here:
- 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:
- First Order Linear Equations
- homogeneous
- nonhomogeneous
- initial value problems
- First Order Nonlinear Equations
- separable
- Bernoulli equations
- Second Order Constant Coefficient Equations
- homogenous (distinct, complex, repeated roots)
- nonhomogeneous - variation of parameters
- nonhomogeneous - undetermined coefficients
- initial value problems
- 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.
- Dimensional Analysis (Text Section 1.1-1.2)
- A summary of some physical quantities and their units (MKSA system)
- An introduction to dimensional analysis with examples
- General theory for unit free laws and the Pi-theorem
- Nondimensionalizing (scaling) models: Logistic, Chemostat
- Perturbation Theory (Text Chapter 2)
- Introductory examples illustrating issues
- Summary sheet for Taylor Series
- Regular Perturbation Theory/Examples for Algebraic problems
- Regular Perturbation Theory/Examples for Initial Value Problems
- Regular Perturbation Theory - Nonlinear Oscillations
- Asymptotic Expansions
- Singular Perturbation Theory/Algebraic problems
- 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.
- Examples of solved problems
- Matching Theory - notes on the theory behind matching and why it works
- A few examples of method failures - result from incorrect assumptions
- Singular Perturbation Theory/Initial Value Problems
- Strongly damped oscillator - nondimensionalization/solution/issues
- Chemical Reaction Kinetics - not covered in class
- Calculus of Variations (Text Chapter 3)
- Functionals, function spaces and functional minimization - introduction and examples
- Introductory theory for functional minimization: Normed spaces, Local minima definition, admissible variations, Gateaux variations, necessary conditions for minima
- Euler-Lagrange Equations -- in progress.
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