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,
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.
Edwards & Penney: Elementary Differential Equations with boundary value problems, 2008. Upper Saddle River, N.J. : Pearson Prentice Hall. ISBN: 0-13-600613-2.
Sydsæter, Seierstad, Strøm: Matematisk analyse - bind 2, 2002 (or newer). 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.