# 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