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Universitet
Skills for the mathematical engineers
Course Information
| Course | Skills for the mathematical engineers | Code | MMUK1106 |
|---|---|---|---|
| Directions | 70540202 – Mathematical Engineering (Master) | Semester | 1 |
| Type of subject | Compulsory | Taught Language | English |
| Lectures | 30 | Practical Lessons | 46 |
| Subject Teacher | Umid Karimov | Independent Work | 104 |
| Total Hours | 180 | Credits | 6 |
Lectures
| Code | Topic | Material |
|---|---|---|
| L1 | Introduction to Mathematical Engineering and PDEs. | Download |
| L2 | Classifying PDEs Elliptic, Parabolic and Hyperbolic. | Download |
| L3 | Introduction to first-order PDEs. Method of characteristics and solutions. | Download |
| L4 | Solving second-order linear PDEs. Separation of variables method. | Download |
| L5 | Explanation of boundary conditions and initial conditions. | Download |
| L6 | Introduction to Fourier series and Fourier transforms. | Download |
| L7 | Overview of finite difference methods. | Download |
| L8 | Solving the heat equation using numerical methods. | Download |
| L9 | Finite difference and finite element approaches for elliptic PDEs. | Download |
| L10 | Numerical methods for solving hyperbolic PDEs. | Download |
| L11 | Norms and Banach Spaces. Hilbert Spaces. | Download |
| L12 | Bilinear forms and the Lax-Milgram Theorem. | Download |
| L13 | Distributions and Sobolev Spaces. | Download |
| L14 | Compactness and Embeddings. | Download |
| L15 | Green’s identities. | Download |
Practical Lessons
| Code | Topic | Material |
|---|---|---|
| S1 | Real-Life Motivation: PDEs in Engineering. | Download |
| S2 | Hands-on Classification of PDEs: Elliptic, Parabolic, Hyperbolic. | Download |
| S3 | Method of Characteristics – worked examples. | Download |
| S4 | Numerical implementation of MoC in MATLAB. | Download |
| S5 | Separation of variables for heat and wave equations. | Download |
| S6 | Numerical experiments with separation of variables. | Download |
| S7 | Dirichlet, Neumann and Robin boundary conditions. | Download |
| S8 | Applying initial/boundary conditions in FD schemes. | Download |
| S9 | Computing Fourier expansions of periodic functions. | Download |
| S10 | Fourier series approximation and PDE solving. | Download |
| S11 | Explicit and implicit schemes for 1D PDEs. | Download |
| S12 | Coding finite difference schemes. | Download |
| S13 | Stability analysis of numerical schemes. | Download |
| S14 | Programming heat equation solvers. | Download |
| S15 | Finite difference stencils on paper. | Download |
| S16 | Laplace and Poisson solvers (Jacobi, Gauss–Seidel). | Download |
| S17 | Finite difference schemes for the wave equation. | Download |
| S18 | Wave equation solvers in MATLAB/Python. | Download |
| S19 | Norms, inner products, orthogonality. | Download |
| S20 | Variational problems and Lax–Milgram theorem. | Download |
| S21 | Weak formulations and Galerkin discretization. | Download |
| S22 | Embedding theorems and compactness. | Download |
| S23 | Green’s identities and weak formulations. | Download |