Math
560/561 - Applied Math I/II
| Textbook |
Principles
of Applied
Mathematics, James Keener (not required but highly recommended) |
| Instructor |
Mark
Pernarowski |
| Grading |
Your grade will
be based strictly on homework assignments. The raw score for
each
assignment will vary. If P is the
percentage of the sum of all the raw scores then your letter grade
will be determined from:
| 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 |
0-59 |
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Assignments must be written in a clear and logical fashion. |
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| Homework |
Homework 1
: Inner Product Spaces, Linear
Algebra, Fredholm Alternative |
Due: 9/18/12 |
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Homework 2:
Operator theory and adjoints |
Due: 10/11/12 |
|
Homework 3:
Distributions and Greens functions |
Due:
11/1/12 |
|
Homework 4:
Eigenfunction expansions and Calculus of Variations (intro) |
Due:
12/11/12 |
|
Homework 5: Calculus of Variations, single
and multivariate, and geodesics |
Due:
1/24/13 |
|
Homework 6:
Constraints, Transversality, Convexity, Multivariate, Mechanics |
Due: 2/26/13 |
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| Notes |
Inner product
spaces,
bases, coordinates, Gram Schmidt, Least Squares |
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Eigenvalues, self
adjoint,
diagonalization, maximum principle |
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Subspaces,
Projections and the
Fredholm Alternative for Matrices |
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Least
Squares and Normal Equations |
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Hilbert
Spaces and Operators |
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Functional 101,
Adjoints and
Fredholm Alternative |
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Operator
Inverses |
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Distributions
(useful
old notes here) |
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Greens
functions |
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Sturm
Liouville Theory
(LaTex
Overview notes) |
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Sturm
Liouville Applications |
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Calculus of
Variations
- Introduction |
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Calculus of
Variations - Theory,
issues, NBC, L(x,y,y') and L(x,y,y',y'') |
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Calculus
of Variations -
Multi-variable L(x,y1,y1',y2,y2',...) introduction |
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Calculus of
Variations -
Geodesics
and Isoperimetric
Problems
and Transversality |
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Calculus of
Variations -
Convexity, Sufficiency, Existence and Convexity overview |
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Calculus of Variations -
Several independent variables. |
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Calculus of Variations -
Least Actions and Hamiltonian
Mechanics (not yet complete) |
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