Mathematics · self-study course
Advanced mathematical methods
Study complex analysis, residues, Fourier series, PDE boundary conditions and convexity through focused lessons.
5 lessons40 quiz questionsAdvanced university
Your learning path
- 01
Holomorphic functions and Cauchy-Riemann equations
A derivative must have the same limit along every complex direction.
Advanced university · Notes · 8 questions - 02
Poles, residues and contour integrals
The coefficient of (z−a)^(−1) in the Laurent expansion is the residue.
Advanced university · Notes · 8 questions - 03
Fourier coefficients and convergence
On [−π,π], distinct integer sine or cosine modes are orthogonal under integration.
Advanced university · Notes · 8 questions - 04
PDE modes, boundaries and initial data
A sine mode for u_t=κu_xx decays as exp(−κk²t).
Advanced university · Notes · 8 questions - 05
Convexity and constrained optimization
Values on a line segment lie below the corresponding chord of function values.
Advanced university · Notes · 8 questions