| Dato | Undervises av | Sted | Tema | Kommentarer / ressurser |
| 16.01.2012 | Terje Sund (TS)
| Kristen Nygaards hus 2116 (Store aud)
| Edwards & Penney (EP) 1.1, 1.2, 1.4
| First-order differential equations and mathematical models. Separable equations.
|
| 18.01.2012 | TS
| Kristen Nygaards 2116 Store aud (KN 2116)
| EP 1.3, 1.5
| Slope fields. Existence and uniqueness. Linear equations
|
| 23.01.2012 | TS
| KN 2116
| EP 1.6, ( 2.1)
| Substitution methods and exact equations.
(Second-order linear equations.)
|
| 25.01.2012 | TS
| KN 2116
| 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, 1.4.66EP Section 1.6: Reducible equations
|
| 30.01.2012 | TS
| KN 2116
| 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).
|
| 01.02.2012 | TS
| KN 2116
| 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.
|
| 06.02.2012 | TS
| KN 2116
| 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.
|
| 08.02.2012 | TS
| KN 2116
| Exercises
| In EP 2.1: 1, 17 21, 24, 32, 33, 38, 40, 43, 51, 52.1.6: 57, 58, 62
|
| 13.02.2012 | TS
| KN 2116
| 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.
|
| 15.02.2012 | TS
| KN 2116
| Exercises
| In EP2.2: 25, (26), 36, 442.3: 22, 232.5: 1, 3, 4, 57
|
| 20.02.2012 | TS
| KN 2116
| SSS 11.2-11.5
| Calculus of Variations. Proof of the Main Theorem
|
| 22.02.2012 | TS
| KN 2116
| Exercises
| In EP:2.5: 10, 61In SSS:4.5: 2, 311.2: 1, 7, 8, 9 (11.3: 1, 2, 3 except the case T=1.) SOLUTIONS
|
| 27.02.2012 | TS
| KN 2116
| SSS 11.3-11.5. EP 5.1
| The case of a free right endpoint (in calculus of variations).First-order linear systems of differential equations.
|
| 29.02.2012 | TS
| KN 2116
| Exercises
| In SSS (text in Norwegian)11.3: 1, 2, 3 except the case T=1.
11.5: 2 (a) and (b).Exam June 2006, Problem 1 (Oppgave 1)
|
| 05.03.2012 | TS
| KN 2116
| EP 5.1-5.3, 5.4
| The method of elimination. Matrices and linear systems. The eigenvalue method.
|
| 07.03.2012 | TS
| KN 2116
| 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.
|
| 12.03.2012 | TS
| KN 2116
| EP 5.3, 5.4, (5.6)
| Wronskians of systems. Solutions of nonhomogeneous systems.
Complex eigenvalues.
(Multiple eigenvalue solutions.)Obligatory Problem Set
|
| 14.03.2012 | TS
| KN 2116
| Exercises. Theory from 5.6.
| EP5.4: 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.)
|
| 19.03.2012 | TS
| KN 2116
| EP 5.6
| Multiple eigenvalue solutions. Defective eigenvalues.
|
| 21.03.2012 | TS
| KN 2116
| Exercises
| 5.6: 2, 3, 7, 15, 16, (21)
|
| 26.03.2012 | TS
| KN 2116
| EP 5.7
| Matrix exponentials.
|
| 28.03.2012 | TS
| KN 2116
| Cancelled (because of midterm exams)
|
|
April 2- April 10: Easter vacation.
| Dato | Undervises av | Sted | Tema | Kommentarer / ressurser |
| 11.04.2012 | TS
| KN 2116
| EP 5.7, 5.8
| Matrix exponentials. Variation of parameters.
|
| 16.04.2012 | TS
| KN 2116
| SSS 12.1-12.4
| Optimal Control Theory. The Maximum Principle (first version). Mangasarian's Theorem
(first version). Examples.
|
| 18.04.2012 | TS
| KN 2116
| Exercises
| EP 5.7: 3, 21, 25, 29, 34, 37. (5.8: 19)
|
| 23.04.2012 | TS
| KN 2116
| SSS 12.3-12.4
| Optimal Control Theory. The Maximum Principle (general version). Mangasarian's Theorem (general version). Arrow's condition.
|
| 25.04.2012 | TS
| KN 2116
| Exercises
| SSS 12.2: 1, 2, 3. EP 5.8: 2, 24
|
| 30.04.2012 | TS
| KN 2116
| EP 7.1-7.3
| Nonlinear systems. Almost linear systems, linearization. Equilibrium solutions and stability. The phase plane: Real eigenvalues.
|
| 02.05.2012 | TS
| KN 2116
| Exercises
| SSS 12.4: 1, 2, 3 (EP 7.2: 9. Also find the linearizations at the critical (equilibrium) points. Determine the type of each critical points.)
|
| 07.05.2012 | TS
| KN 2116
| EP 7.2, 7.3
| Linear and almost linear systems. Linearization. Equilibrium solutions and stability. The phase plane: Complex eigenvalues.
|
| 09.05.2012 | TS
| KN 2116
| Exercises
| SSS 12.4.6 (b). 12.7.1.
Exam June 2006, Oppgave 2.(Exam June 2010, Oppgave 1 )
|
| 14.05.2012 | TS
| KN 2116
| EP 6.1, 6.2, 6.3
| Euler's Method. The improved Euler Method. The Runge-Kutta Method.
|
| 16.05.2012 | TS
| KN 2116
| EP 6.3. Exercises
| EP 7.3: (17,) 29, 30, 33. Exam June 2010, Oppgave 1
Notice that likevektspunkt = critical point (also called equilibrium point.)The following: ProblemSolution to Problem
|
| 21.05.2012 | TS
| KN 2116
| Exercises
| Exam 2011
|