Formation/Cours

At the end of the course, the student should be able to:
This calculus interactive course aims at providing an introduction to the mathematical tools for quantitative problem solving in Economics, Business and Finance. It will move back and forth between theory and applications and allow the students to gain an appreciation of the strengths and limitations of mathematical model-building. Emphasis will be on the use of the basic concepts of the theory of functions in the description and solution of problems from economical sciences.
• Understand the concept of “function” in both its graphical and algebraic dimensions,
• Understand the notions of “limit” and of “continuity” and their relevance with respect to functions, • Be able to differentiate polynomials, rational, logarithmic and exponential functions,
• Have knowledge of what is meant by “local extrema” and “inflection points” and know how to evaluate them,
• Acquire the ability to extend this knowledge further to functions of several variables and partial derivatives,
• Apply and interpret all these mathematical notions in various applications in economics and related areas,
• Develop modelling skills: the ability to translate various real-world scenarios into mathematical models. Develop problem solving skills: the ability to analyze complicated problems in a variety of subject areas, and to synthesize solutions to such problems.

Topics will include:
I Functions of one variable : domain, range. Inverse functions .Power, exponential and logarithmic functions. Applications in economics and Business (cost, revenue and profit functions, demand and supply functions, learning curves and logistic curves). • Limits, continuity • Derivatives : differentiation using limits, differentiation techniques . Applications • Graphs using derivatives, asymptotes. Applications

II Functions of several variables (The Codd- Douglas function). Partial derivatives, max-min problems, Lagrange multipliers.
* Detailed outline of the course will be given on the first day of class and will be posted on line.