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 (the necessary material in The Calculus of Variations and in Optimal Control Theory may be found there.)
The above is a tentative outline which will be updated as the course proceeds.
References:
Edwards & Penney: Elementary Differential Equations with boundary value problems, 2009. Upper Saddle River, N.J. : Pearson Prentice Hall. ISBN: ISBN: 0-13-600613-2..
Sydsæter, Seierstad, Strøm: Matematisk analyse - bind 2, 2002. Oslo : Gyldendal akademisk.
Knut Sydsæter et al.: Further mathematics for economic analysis, 2008. Harlow : Financial Times/Prentice-Hall. ISBN: 0-273-71328-0.
Atle Seierstad, Knut Sydsæter: Optimal Control Theory with Economic Application, 1987. Amsterdam : North-Holland. ISBN: 0-444-87923-4.