-Real Analysis- Functions, Sets and Sequences of real numbers
-Functions-definition and proofs
Composite function, Real valued function, One to one function, Maximum/minimum functions, Inverse function, Increasing/decreasing functions, Characteristic function, Even/odd functions, Concave/convex, Quasi-concave/quasi-convex functions
-Set: Open/closed sets, Convex sets, Bounded sets, Compact sets, Level sets, Superior/inferior sets- some properties and proofs
-Intermediate value theorem of real analysis
-Continuity and differentiability of functions
-Sequences of real numbers- limit of sequences, Convergent/divergent sequence, Bounded sequence, Monotone sequence, Operations of convergent/divergent sequences, Cauchy sequence.
-Topics in integration and differential equations (rules of transformation, differentiation, solution techniques)
Qualitative theory (phase plane analysis, stability for nonlinear systems)
-Calculus of variation (Euler equation, transversality condition)
-Control theory (maximum principle, variable final time, infinite horizon)
-Dynamic programming (Bellman equation, envelope theorem, multiple variables)
1. Advanced Microeconomic Theory, Geoffrey A. Jehle, Philips J. Reny
2. Further Mathematics for Economic Analysis Sydsaeter, Knut, Peter Hammond, AtleSeierstad, and Arne Ström, Prentice Hall, 2008.
3. Mathematics for Economists – by Carl Simon and Lawrence Blume. W. W. Norton and Company, 1994
4. Applied Intertemporal Optimization, Wälde, Klaus, , http://www.waelde.com/aio : Lecture Notes, University of Glasgow, 2009.
5. Intriligator, M. D (1971) Mathematical Optimization and Economic Theory, Prentice- Hall, N.J.