Lecture notes

Lecture notes will be placed here.

January 18 (#01): Complex plane/Euler's formula
January 23 (#02): Exponential/logarithmic functions
January 25 (#03): Cauchy-Riemann equations
January 30 (#04): Harmonic functions, Cauchy's theorem
February 01 (#05): Cauchy's theorem, Cauchy's integral formula
February 06 (#06): Liouville's theorem, Fundamental theorem of Algebra, Taylor series
February 08 (#07): Analytic continuation
February 13 (#08) : Laurent series, Singularities
February 15 (#09) : Residues, Application of residue theorem to integrals
February 20 (#10) : Application of residue theorem to integrals
February 22 (#11) : Conformal mapping
February 27 (#12) : Heat conduction/Solid Mechanics
March 01 (#13) : Solid Mechanics
March 06 (#14) : Fluid mechanics
March 08 (#15) : Fluid mechanics (Circle theorem), Linear space
March 27 (#16): Liner space, Inner product,Norm, Distance, Best approximation
March 29 (#17): Norm of matrix, Gram-Schmidt orthonormalization
April 03 (#18): Sturm-Liouville system
April 05 (#19): Sturm-Liouville, Eigenvalues
April 10 (#20): Diffusion equations/Laplace equations
April 12 (#21): When the interval is infinite, Method of Weighted Residuals
April 17 (#22): MWR for S-L systems, FEM, weak form
April 24 (#23): FreeFEM++, FDM
April 26 (#24): LU decomposition, Neumann Series, Existence of solution