Week 1 
Function of a Complex
Variable 
Wednesday
Sep 23 
Algebra, complex plane, Argand diagram, de Moivre’s theorem,
trigonometric series 
3

Friday
Sep 25 
Analytic
functions, CauchyRiemann conditions, Riemann sheets, branch
cuts

24.1  24.6



Week 2 
Function of a Complex
Variable 
Monday
Sep 28 
Contour
integrals, Cauchy’s Theorem and integral formula,
Taylor expansion 
24.8  24.11

Wednesday
Sep 30 
Analytic continuation, Laurent series, poles, calculus
of residues 
24.12

Friday
Oct 2 
Contour
integration: Examples 
24.13



Week 3 
Finite Dimensional
Vector Spaces 
Monday
Oct
5 
Contour
integration with branch cuts 
24.13

Tuesday
Oct 6
XHr
1212:50p 
Linear
vector spaces, algebra, linear independence, basis set,
transpose, inner product 
8.1

Wednesday
Oct
7 
Matrix
operations, linear operators, classes of operators, examples

8.28.12

Friday
Oct
9 
Eigenvectors/values, inequalities, GramSchmidt
orthogonalization 
8.13



Week 4 
Finite Dimensional
Vector Spaces 
Monday
Oct 12 
Unitary
operators, eigenvalues/vectors, diagonalization,
characteristic equation

8.13  8.14

Wednesday
Oct 14

Change of basis, orthogonal transformation, eigenproblems 
8.15  8.17

Friday
Oct 16 
Systems of
linear differential equations 
8.18, 9.1



Week 5 
Linear Differential
Equations 
Monday
Oct 19 
Second order DEs, ordinary and singular points,
series
solution 
16.1

Wednesday
Oct 21 
Series solution and Method of Frobenius 
16.2

Friday
Oct 23 
Series expansion around a singular point, Bessel’s equation
and functions 
16.3



Week 6 
Linear Differential
Equations 
Monday
Oct 26 
Missing solutions, logarithmic solution 
16.4

Wednesday
Oct 28 
Legendre's equation and polynomial solutions 
16.6

Friday
Oct 30 
Nonhomogenous problem, families of ODES 
Notes



Week 7 
Infinite Dimensional
Vector Space 
Monday
Nov 2 
Hilbert space, selfadjoint operator, complete and
orthonormal sets 
17.1  17.2

Wednesday
Nov 4 
Eigenfunction expansions 

Friday
Nov 6 
Boundary value problems, SturmLiouville problem 
17.4



Week 8 
Infinite Dimensional
Vector Spaces 
Monday
Nov 9 
Green's
functions 
17.5  17.6

Wednesday
Nov 11 
Gamma
function 
18, Notes

Friday
Nov 13 
Hypergeometric and special functions 
18, Notes



Week 9 
Integral Transforms 
Monday
Nov 16 
Orthogonal
polynomials 
18, Notes

Wednesday
Nov 18 
Fourier
transform, convolution, Parseval relation, uncertainty
principle 
13.1

Friday
Nov 20 
Laplace
transform, an application leading to Abel’s integral
equation 
13.2



Week 10/11 
Integral Transforms 
Monday
Nov 23 
General
approach to the derivation of transform pairs 
Notes

Monday
Nov 30 
Other transform pairs 
Notes

Wednesday
Dec 2 
Applications 
