Series solution for ordinary differential equations with variable coefficients: Taylor`s and power series. Special s: Gamma, Beta, Bessel and Legendre s. Partial differential equations: method of separation of variables. Applications on partial differential equations: heat equation, wave equation, Laplace equation. Conformal mapping: complex s as mapping, linear fractional mapping, Schwarz – Christoffel mapping.
Mathematics
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| content serial | Description |
|---|---|
| 2 | Week Number 2: Differential equation with variable coefficients, ordinary and singular points, solution about ordinary points. |
| 3 | Week Number 3: Solution about singular points: Regular singular points, the method of Frobenius - Case I. |
| 4 | Week Number 4: The method of Frobenius - Case II and Case III. |
| 5 | Week Number 5: Gamma and Beta functions. |
| 6 | Week Number 6: Lengendre differential equation and Legendre polynomials. |
| 7 | Week Number 7: Bessel differential equation. |
| 8 | Week Number 8: Bessel function of the 1st kind. |
| 9 | Week Number 9: Boundary value problems, partial differential equations and the method of separation of variables. |
| 10 | Week Number 10: Heat equation - heat transfer in a bar. |
| 11 | Week Number 11: Wave equation - vibration of a string. |
| 12 | Week Number 12: Laplace equation and potential fields. |
| 13 | Week Number 13: Conformal mappings - Complex functions as mappings. |
| 14 | Week Number 14: Bilinear transformations – linear fraction transformation. |
| 15 | Week Number 15: Schwarz Christoffel transformation. |
| 16 | Week Number 16: Final Exam. |
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