| Dato | Undervises av | Sted | Tema | Kommentarer / ressurser |
| 14.01.2013 | Terje Sund (TS) | FYS (Store Fysikk Auditorium) | Edwards & Penney (EP) 1.1, 1.2, 1.4 | First-order differential equations and mathematical models. Separable equations. |
| 18.01.2013 | TS | VB 1 (Vilhelm Bjerknes Auditorium 1) | EP 1.3, 1.5 | Slope fields. Existence and uniqueness. Linear equations |
| 21.01.2013 | TS | Store Fysikk Auditorium | EP 1.6, ( 2.1) | Substitution methods and exact equations. (Second-order linear equations.) |
| 25.01.2013 | TS | VB 1 | Exercises (Problem Session) and Section 1.6: Reducible equations. | Exercises 1.1.10, 1.1.30, 1.1.45, 1.2.18, 1.4.5, 1.4.18, 1.4.35, 1.4.53, 1.4.66
EP Section 1.6: Reducible equations
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| 28.01.2013 | TS | FYS | EP 2.1, (2.2 Theorem 5, 2.3 Theorem 3) | Second-order linear equations. General solutions. Wronskians. Uniqueness. Characteristic equations. Nonhomogeneous linear equations (emphasis on equations of second order). |
| 01.02.2013 | TS | VB1 | Exercises | In EP
1.3: 1, 11, 12, 16, 23, 30, (32) 1.5: 22, 25, (31) 1.6: 1, 5, (57, 58, 62) Exercises in parenthesis will only be done if there is enough time. |
| 04.02.2013 | TS | FYS | EP 2.2 Theorem 5, 2.3 Theorem 3, 2.5 | Repeated roots, complex roots. Nonhomogeneous linear equations. Undetermined coefficients, with emphasis on equations of second order. Variation of parameters. |
| 08.02.2013 | TS | VB1 | Exercises | In EP
2.1: 1, 17 21, 24, 32, 33, 38, 40, 43, 51, 52. 1.6: 57, 58, 62 |
| 11.02.2013 | TS | VB1 | SSS 4.5 (pp.114-116, first half of p.117).11.1, 11.2 (SSS=Sydsæter, Seierstad, Strøm, Matematisk Analyse II) | Convex and concave functions and the 2nd-derivative test. Calculus of Variations. The Euler equation. The main theorem. |
| 15.02.2013 | TS | FYS | Exercises | In EP
2.2: 25, (26), 36, 44 2.3: 22, 23 2.5: 1, 3, 4, 57 |
| 18.02.2013 | TS | VB1 | SSS 11.2-11.5 | Calculus of Variations. Proof of the Main Theorem |
| 22.02.2013 | TS | FYS | Exercises | In EP:
2.5: 10, 61 In SSS: 4.5: 2, 3 11.2: 1, 7, 8, 9 (11.3: 1, 2, 3 except the case T=1.) SOLUTIONS
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| 25.02.2013 | TS | VB1 | SSS 11.3-11.5. EP 5.1 | Other endpoint conditions, in particular the case of a free right endpoint (in calculus of variations).
First-order linear systems of differential equations. |
| 01.03.2013 | TS | FYS | Exercises | In SSS (text in Norwegian) |
| 04.03.2013 | TS | VB1 | EP 5.1-5.3, 5.4 | The method of elimination. Matrices and linear systems. The eigenvalue method. |
| 08.03.2013 | TS | FYS | Exercises. Theory from 5.3 and 5.4 | EP
5.1: 8, 21; 5.3: 21; 5.4: 17, (24) + General solutions of linear first order systems. The eigenvalue method. |
| 11.03.2013 | TS | VB1 | EP 5.3, 5.4, (5.6) | Wronskians of systems. Solutions of nonhomogeneous systems. Complex eigenvalues. (Multiple eigenvalue solutions.) |
| 15.03.2013 | TS | FYS | Exercises. Theory from 5.6. | EP
5.4: 24, 20; 5.6: 1, (2) (you may use the method of elimination on 5.6: 1 and 2) From 5.6: Multiple eigenvalue solutions.(Defective eigenvalues.) |
| 18.03.2013 | ----- | FYS | ------ | Midterm exams: No lecture |
| 22.03.2013 | --- | VB1 | --- | Midterm exams: No problem session |
March 25- April 2: Easter vacation.
| Dato | Undervises av | Sted | Tema | Kommentarer / ressurser |
| 05.04.2013 | TS | VB1 | EP 5.6 | Multiple eigenvalue solutions. Defective eigenvalues. |
| 08.04.2013 | TS | FYS | Exercises | 5.6: 2, 3, 7, 15, 16, (21) |
| 12.04.2013 | TS | VB1 | EP 5.7 | Matrix exponentials. |
| 15.04.2013 | TS | FYS | EP 5.7, 5.8 | Matrix exponentials. Variation of parameters. |
| 19.04.2013 | TS | VB1 | SSS 12.1-12.4 | Optimal Control Theory. The Maximum Principle (first version). Mangasarian's Theorem (first version). Examples. |
| 22.04.2013 | TS | FYS | Exercises | EP 5.7: 3, 21, 25, 29, 34, 37. (5.8: 19) |
| 26.04.2013 | TS | VB1 | SSS 12.3-12.4 | Optimal Control Theory. The Maximum Principle (general version). Mangasarian's Theorem (general version). |
| 29.04.2013 | TS | FYS | Exercises | SSS 12.2: 1, 2, 3. EP 5.8: 2, 24 |
| 03.05.2013 | TS | VB1 | SSS 12.7 | Proof of Mangasarian's Theorem. Arrow's Theorem. Examples. |
| 06.05.2013 | TS | FYS |
Exercises EP 7.1-7.3 |
12.4: 1, 2, 3 Nonlinear and almost linear systems of differential equations. Isolated critical points. Linearized systems. |
| 10.05.2013 | TS | VB1 | EP 7.2, 7.3 |
Nonlinear systems. Almost linear systems, linearization. Equilibrium solutions and stability. The phase plane: Real eigenvalues. Complex eigenvalues. |
| 13.05.2013 | TS | FYS |
Exercises. (+ some theory from EP. 7.3) |
EP 7.2: 9. Also find the linearizations at the critical (equilibrium) points. Determine the type of each critical points. Linear and almost linear systems. Linearization. Equilibrium solutions and stability. The phase plane: Complex eigenvalues. |
| 24.05.2013 | TS | VB1 |
Exercises. Theory from EP 7.3 |
(Linear and almost linear systems. Linearization. Equilibrium solutions and stability. The phase plane: Complex eigenvalues.) EP 7.3: (17,) 29, 30, 33. Exam June 2010, Oppgave 1 Notice that likevektspunkt = critical point (also called equilibrium point.) (The following: Problem
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| 27.05.2013 | TS | FYS | Exercises |
Final session before the exam. |