This course is replaced by MAT3440 – Dynamical systems.

Syllabus/achievement requirements

Elementary Differential Equations with Boundary Value Problems (sixth edition), Edwards and Penney:

Chapter 1. Chapter 2.1, 2.2 Theorem 5 (emphasis on 2nd-order equations), 2.3 p. 131-132 (Theorem 3), 2.5. Parts of chapters 5 and 6, and all of 7.1-7.4

In Sydsæter, Seierstad and Strøm's book "Matematisk analyse - bind 2" (main reference):

• Chapter 4: 4.5
• Chapter 11: 11.1-11.5
• Chapter 12: 12.1-12.5, 12.7

Students that do not understand Norwegian may use the book: Knut Sydsæter et al.: Further mathematics for economic analysis, Chapter 8 and 9, together with the relevant section about convex and concave functions.

Alternative (for students not speaking Norwegian):

Seierstad and Sydsæter, Optimal control theory with economic applications

• chapter 1 – sections 1, 2, 4 – section 5 without the terminal condition (31c). Also excluded: proof of (32b) p.34, example 9 p. 38 and the subsection another terminal condition p.39. – section 6 until p.106 (included). • chapter 2 – section 3 (Assume allways that p0 = 1) – section 5,6 (We only consider the case with one state and one control variable) – section 9 p.142-145 (before the subsection: An existence theorem)

• chapter 3 – section 5

• the relevant information about convex and concave functions.

As a second alternative in English the lecture notes,

LECTURES ON OPTIMAL CONTROL THEORY

may also be used in combination with the exercises in Sydsæter, Seierstad and Strøm, "Matematisk analyse - bind 2" (the relevant theoretical material in The Calculus of Variations and in Optimal Control Theory is contained in the lecture notes.)

The above is a tentative outline which will be updated as the course proceeds.

References:

Edwards & Penney: Elementary Differential Equations with boundary value problems, 2008. Upper Saddle River, N.J. : Pearson Prentice Hall. ISBN: 0-13-600613-2.