Part I:
-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.
Part II:
-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)

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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.