Undervisningsplan
Dato | Undervises av | Sted | Tema | Kommentarer / ressurser |
17.01.2011 | L. Veseth | Complex functions, related to sections 2.8-2.14 in the textbook. | ||
18.01.2011 | Continues with complex functions and series. Sections 2.6-2.15 in the textbook. | Problems for Wednesday January 26th: Textbook chapter 2: 7.14, 7.16, 9.26, 9.27, 10.21, 10.31, 11.12, 12.11, 14.23, 17.6, 17.22, 17.30. | ||
24.01.2011 | Analytic functions. The Cauchy-Riemann equations. Chapter 14, 14.1-14.2 in the textbook. | The lectures on January 24th and 25th will give a somewhat more comprehensive discussion of paragraphs 14.1-14.3. | ||
25.01.2011 | Integrals of complex functions. Cauchys theorem and Cauchys integral formula (14.3). | |||
31.01.2011 | Cauchys integral formula with examples (14.3). The Taylor series. | The lectures on January 31st and February 1st will give a somewhat more comprehensive discussion of paragraphs 14.3-14.4 in the textbook. | ||
01.02.2011 | The Laurent series with examples (14.4). Zeros and poles of complex functions | Problems for Wednesday February 2nd: Chapter 2: 17.25, 17.28, 17.32. Chapter 14: 1.11, 1.20, 2.27, 2.46, 2.63. | ||
07.02.2011 | The Residue theorem with examples. 14.5 an 14.6 in the textbook. | |||
08.02.2011 | Applications of the Residue theorem. 14.7 in the textbook. Problems 8 and 9 from "extra problems" (see new message). You may drop example 5 and the rest of 14.7. | Problems for Wednesday February 9th: Chapter 14: 3.17, 3.18, 3.19, 3.20, 3.22, 3.23, 4.6, 4.9, 4.11. | ||
14.02.2011 | End of complex analysis. Principal value of an integral. Problems 10 and 11 from "extra problems". Start differential equations, Chapter 8: 8.3 and 8.4. | |||
15.02.2011 | Homogeneous differential equations of second order (8.5). Lecture note will be on the net (in Norwegian). | Problems for Wednesday February 16th: Chapter 14: 6.9, 6.19, 6.28, 7.7, 7.9, 7.11, 7.13. | ||
21.02.2011 | The Euler-Cauchy equation. Inhomogeneous diff. equations (8.6-8.7, lecture note) | |||
22.02.2011 | Continues with inhomogeneous equations. Start Greens functions (lecture note). | Problems for Wednesday February 23rd: Chapter 14: 7.17, 7.24. Chapter 8: 3.3, 3.11, 5.11, problems 12a,b,c from "extra problems". NB! Error in problem 5.11, should be 9y. | ||
28.02.2011 | Greens functions with examples. See lecture note on differential equations. Start on series solutions. | |||
01.03.2011 | Solution of diff. equations in terms of series (Chapter 12, 12.1, 12.2 and 12.11, lecture note). | Problems for Wednesday March 2nd: Chapter 8: 6.3, 6.11, 6.23, 7.17, 7.18, 7.22. | ||
07.03.2011 | Fourier series. Chapter 7, 7.1-7.9. | |||
08.03.2011 | Continues with Fourier series (complex form). Start Fourier transforms (7.12). | Problems for Wednesday March 9th: Chapter 8: 12.16, 12.18, 13.8. Chapter 12: 1.9, 11.2, 11.6, 11.8. | ||
14.03.2011 | Fourier transforms. Chapter 7, 7.12. Also chapter 8, 8.10-8.11. | |||
15.03.2011 | Continues with Fourier transforms and examples. | Problems for Wednesday March 16th: Chapter 7: 5.7, 5.8, 8.16, 9.6, 9.11. | ||
21.03.2011 | Laplace transforms. Chapter 8: 8.8-8.9. | |||
22.03.2011 | Continues with Laplace transforms and examples. | Problems for Wednesday March 23rd: Chapter 7: 9.15, 12.1, 12.6, 12.11, 12.22, 12.25. Chapter 8: 11.14, 11.15. NB! Misprint in problem 12.22, see Eq.(17.4) in chapter 12 for correct definition of the Bessel function. | ||
28.03.2011 | No lectures March 28th, March 29th. No group March 30th. (Home exam). | |||
04.04.2011 | Last lecture on Laplace transforms with examples. | |||
05.04.2011 | Tensors. Highlights from chapter 10, 10.1-10.5. Lecture note (important). | Problem for Wednesday April 6th: Chapter 8: 8.4, 8.5, 8.11, 8.21, 9.25, 9.31, 9.38, 10.15, 11.7. | ||
11.04.2011 | Calculus of variations. Highlights from chapter 9, 9.1-9.5. | |||
12.04.2011 | Start partial differential equations. Chapter 13. Separation of variables (p.619-622) The wave equatin (13.4). | Problemsd for Wednesday April 13th: Laplace: Chapter 8: 10.17, 11.11. Tensors: Chapter 10: 4.2, 4.5, 5.7, 5.9a,b, 5.10, 5.11, 5.13f,g,h. | ||
26.04.2011 | No lecture Tuesday April 26th. | No group Wednesday April 27th. | ||
02.05.2011 | End of wave equation. Example. The diffusion equation (13.3). Solution in terms of Fourier series. | |||
03.05.2011 | Partial diff. equations, non-Cartesian coordinates. 13.5-13.7 (somewhat simplified) | Problems for Wednesday May 4th: Chapter 9: 2.1, 2.5, 3.6, 5.11. Chapter 13: 4.2, 4.5, 4.8. | ||
09.05.2011 | Solution of partial differential equations by use of integral transforms. 13.9 (somewhat extended). | |||
10.05.2011 | Partial differential equations and Greens functions. End of 13.8 (somewhat extended). Orthogonal sets of functions. Lecture notes. Last lecture! | Problems for Werdnesday May 11th: Chapter 13: 5.9, 6.3, 9.5, problem 25 from "extra problems". | ||
18.05.2011 | Problems for Wednesday May 18th: Problems 23 and 24 from "extra problems". Greens functions: Chapter 13, 8.6 and 8.7. Last group. |
Publisert 5. jan. 2011 13:40
- Sist endret 10. mai 2011 17:36