Review of elementary logic. Declarative statements, quantifiers, predicates, logical connectives. Conjunctions, disjunctions, conditional statements and their negation.
Review of some basic facts in the theory of Riemann integration. Piecewise constant, piecewise continuous, piecewise C1 functions. Riemann integral of bounded real functions on bounded real intervals. Properties of the Riemann integral concept: mean value theorem, linearity, monotonicity, integrability of monotone functions, of continuous functions (with finite discontinuity set), absolute integrability, independence from finite subsets of the domain, fundamental theorem of integral calculus, integro-differential formula, formula of primitives, integration by parts, by substitution, by decomposition, differentiation under the integral sign.
Ordinary linear differential and difference equations: Cauchy’s problem: existence, unicity, continuity with respect to initial conditions and parameters. A geometric presentation of some linear first order differential and difference equations in dimension one and two. Solution of simple nonlinear differential equations by separation of variables. General theory and solution formulas for the linear case, with constant coefficients and time-varying coefficients.
Simple problems of dynamic optimization. Introduction to the calculus of variations and the theory of optimal control. The Euler-Lagrange equation. Pontryagin’s maximum principle. A few direct applications to models of economic growth.