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# Student guide Faculty of Economics A.Y. 2007/08

Mathematics for economics and finance 1
Aim of the course
The course presents the standard tools of infinitesimal and differential calculus for functions in one variable, use of differential calculus for optimisation problems, the first elements of integral calculus, and the first elements of financial calculus, with examples of applications relevant to economics given wherever possible.
The illustration of the above material assumes a prior knowledge of the fundamentals of mathematics, including algebra and analytic geometry. For students who are not proficient in the prerequisites, a parallel remedial course will be offered during the first month.
Syllabus
1. Numbers. Integers and rational numbers. Real numbers. Powers and logarithms. Sets of real numbers, intervals. The real number line and the Cartesian plane. The summation symbol; sum of the terms in a progression.
2.   Functions. Definition of real function of a real variable. Sequences. Simple and compound interest. Linear functions. Equilibrium of the market. Production costs. Point of preference reversal. Revenues and profits. Quadratic and inverse proportionality. Bounded, monotonic functions. Maxima and minima. Elementary functions: power, exponential, logarithmic and trigonometric functions.
3. Limits and continuity. Convergent, divergent and irregular sequences. Compounding and discount factors. Limits of functions. The number "e". Continuous compounding of interest. Calculation of limits. Continuity. Properties of continuous functions: Weierstrass theorems, of intermediate values and zeroes.
4.   Series. Characteristics of a numeric series. Geometric series.
5. Differential calculus and optimisation. Derivative and the tangent. Marginal cost. Differentiation rules. Differential and linear approximation. Elasticity and semi-elasticity. Elasticity of demand. Instantaneous force of interest. Stationary points and optimisation. Fermat's theorem. An efficiency problem: minimum average cost. Maximum turnover. Mean value theorem. Test for monotonicity. Maximum profit. Convexity, concavity and inflection points. Study of the graph of a function.
6.   Integral calculus. Definite integral and area. Differential calculus and integral calculus: fundamental theorem of integral calculus. Primitives and indefinite integral. Elementary primitives.
7. Financial calculus. Compounding and discounting. Accumulation factor, discount factor, reciprocal relation. Normal financial regimes. Equivalent interest rates. Subdivisibility. Fixed income assets.
Examinations
There will be a written examination and an optional oral exam. Passing the "Mathematics 1" exam is a prerequisite for admission to the "Mathematics for economics and finance 2" exam.