Welcome to MAT 2440, Spring 2014.
In the differential equation part of the course we will use the book
Edwards & Penney: Elementary Differential Equations with boundary value problems, 2009 (sixth edition, or newer). Upper Saddle River, N.J. Pearson Prentice Hall.
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 Optimal Control Theory we shall use the book
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 who 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 reading 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.
The (free) lecture notes,
LECTURES ON OPTIMAL CONTROL THEORY
should also provide the necessary material in Calculus of Variations and in Optimal Control Theory.
The above is a tentative outline which will be updated as the course proceeds.