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Week 1 |
Function of a Complex
Variable |
|
Wednesday
Sep 24 |
Algebra, complex plane, Argand diagram, de Moivre’s theorem,
trigonometric series |
3
|
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Friday
Sep 26 |
Analytic
functions, Cauchy-Riemann conditions, Riemann sheets, branch
cuts
|
24.1 - 24.6
|
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|
|
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Week 2 |
Function of a Complex
Variable |
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Monday
Sep 29 |
Contour
integrals, Cauchy’s Theorem and integral formula,
Taylor expansion |
24.8 - 24.11
|
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Tuesday
April 1
X-Hr
12-12:50p |
Analytic continuation, Laurent series, poles, calculus
of residues |
24.12
|
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Wednesday
Oct 1 |
Contour
integration: Examples |
24.13
|
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Friday
Oct 3 |
Contour
integration with branch cuts |
24.13
|
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|
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Week 3 |
Finite Dimensional
Vector Spaces |
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Monday
Oct 6 |
Linear
vector spaces, algebra, linear independence, basis set,
transpose, inner product |
8.1
|
|
Wednesday
Oct 8 |
Matrix
operations, linear operators, classes of operators, examples
|
8.2-8.12
|
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Friday
Oct 10 |
Eigenvectors/values, inequalities, Gram-Schmidt
orthogonalization |
8.13
|
|
|
|
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Week 4 |
Finite Dimensional
Vector Spaces |
Monday
Oct 13 |
Unitary
operators, eigenvalues/vectors, diagonalization,
characteristic equation
|
8.13 - 8.14
|
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Wednesday
Oct 15
|
Change of basis, orthogonal transformation, eigenproblems |
8.15 - 8.17
|
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Friday
Oct 17 |
Systems of
linear differential equations |
8.18, 9.1
|
|
|
|
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Week 5 |
Linear Differential
Equations |
|
Monday
Oct 20 |
Second order DEs, ordinary and singular points,
series
solution |
16.1
|
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Wednesday
Oct 22 |
Series solution and Method of Frobenius |
16.2
|
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Friday
Oct 24 |
Series expansion around a singular point, Bessel’s equation
and functions |
16.3
|
|
|
|
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Week 6 |
Linear Differential
Equations |
|
Monday
Oct 27 |
Missing solutions, logarithmic solution |
16.4
|
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Wednesday
Oct 29 |
Legendre's equation and polynomial solutions |
16.6
|
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Friday
Oct 31 |
Nonhomogenous problem, families of ODES |
Notes
|
|
|
|
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Week 7 |
Infinite Dimensional
Vector Space |
|
Monday
Nov 3 |
Hilbert space, self-adjoint operator, complete and
orthonormal sets |
17.1 - 17.2
|
|
Tuesday
Nov 4
X-Hr
12-12:50p |
Eigenfunction expansions |
17.3
|
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Wednesday
Nov 5 |
No class |
|
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Friday
Nov 7 |
Boundary value problems, Sturm-Liouville problem |
17.4
|
|
|
|
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Week 8 |
Infinite Dimensional
Vector Spaces |
|
Monday
Nov 10 |
Green's
functions |
17.5 - 17.6
|
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Wednesday
Nov 12 |
Gamma
function |
18, Notes
|
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Friday
Nov 14 |
Hypergeometric and special functions |
18, Notes
|
|
|
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Week 9 |
Integral Transforms |
|
Monday
Nov 17 |
Orthogonal
polynomials |
18, Notes
|
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Wednesday
Nov 19 |
Fourier
transform, convolution, Parseval relation, uncertainty
principle |
13.1
|
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Friday
Nov 21 |
Laplace
transform, an application leading to Abel’s integral
equation |
13.2
|
|
|
|
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Week 10 |
Integral Transforms |
|
Monday
Nov 24 |
General
approach to the derivation of transform pairs |
Notes
|
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Monday
Dec 1 |
Other transform pairs |
Notes
|
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Wednesday
Dec 3 |
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