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 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). 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.) 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. 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: Problem 21.05.2012 TS KN 2116 Exercises Exam 2011
Published Jan. 2, 2012 8:16 PM - Last modified May 23, 2012 6:22 PM