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 Syds?ter, Seierstad and Str?m'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 Syds?ter 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 Syds?ter, 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 Syds?ter, Seierstad and Str?m, "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.
Syds?ter, Seierstad, Str?m: Matematisk analyse - bind 2, 2002 (or newer). Oslo : Gyldendal akademisk.
Knut Syds?ter et al.: Further mathematics for economic analysis, 2008. Harlow : Financial Times/Prentice-Hall. ISBN:?0-273-71328-0.
Atle Seierstad, Knut Syds?ter: Optimal Control Theory with Economic Application, 1987. Amsterdam : North-Holland. ISBN:?0-444-87923-4.