Analytical methods in mathematical modeling 4010-MAMa

1. Algorithms – general concepts (2 lectures, 2 exercises):
a. Problem - Model - Algorithm - Implementation
b. Algorithm properties: correctness, complexity, error tolerance, numerical stability
c. Algorithm types: iterative, adaptive, greedy
2. Linear algebra (8 lectures, 8 exercises):
a. Systems of linear equations, Gaussian elimination
b. Matrices, vectors, matrix operations
c. Orthogonality, Euclidean norm, orthogonal projection
d. Matrix factorization, SVD decomposition, matrix conditioning
3. Calculus (6 lectures, 6 exercises):
a. Differential and integral calculus
b. Newton's algorithm
c. Monte-Carlo algorithm
d. Steepest descent algorithm
4. Differential Equations (8 lectures, 8 exercises):
a. Ordinary and partial equations, systems of equations, initial and boundary conditions, etc.
b. Discretization, meshes
c. Galerkin methods
d. Examples of models and their analysis
5. Statistics (6 lectures, 6 exercises):
a. Wstęp probabilistyczny
b. Introduction to Probabilistics
c. Descriptive analysis of data sets (populations) – parameters
d. Estimation of population arameters
e. Verification of statistical hypotheses

The order of issues addressed and the level of detail in their implementation may change slightly.