Undervisningsplan
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  Firstorder 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. (Secondorder 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, 1.4.66 EP Section 1.6: Reducible equations

30.01.2012  TS  KN 2116  EP 2.1, (2.2 Theorem 5, 2.3 Theorem 3)  Secondorder 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.114116, first half of p.117).11.1, 11.2 (SSS=Sydsæter, Seierstad, Strøm, Matematisk Analyse II)  Convex and concave functions and the 2ndderivative test. Calculus of Variations. The Euler equation. The main theorem. 
15.02.2012  TS  KN 2116  Exercises  In EP 2.2: 25, (26), 36, 44 2.3: 22, 23 2.5: 1, 3, 4, 57 
20.02.2012  TS  KN 2116  SSS 11.211.5  Calculus of Variations. Proof of the Main Theorem 
22.02.2012  TS  KN 2116  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

27.02.2012  TS  KN 2116  SSS 11.311.5. EP 5.1  The case of a free right endpoint (in calculus of variations). Firstorder linear systems of differential equations. 
29.02.2012  TS  KN 2116  Exercises  In SSS (text in Norwegian) 
05.03.2012  TS  KN 2116  EP 5.15.3, 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.) 
14.03.2012  TS  KN 2116  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.) 
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 12.112.4  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 12.312.4  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 7.17.3  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.

14.05.2012  TS  KN 2116  EP 6.1, 6.2, 6.3  Euler's Method. The improved Euler Method. The RungeKutta 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: Problem 
21.05.2012  TS  KN 2116  Exercises  Exam 2011 