Learning outcomes:

This is an essential introductory subject that offers to the students the preliminary knowledge of calculus for economics science students. The aim is to develop basic skills and understanding of notions of differential calculus of one variable functions and function of several variables as well as their application in economic science. The focus is on those elements of a typical college calculus course that are most used in economics.

On successful completion of this module the learner will be able to:

  • Use basic skills of calculus of functions of one variable
  • Use basic skills of calculus of functions of several variables
  • Use MATHEMATICA to address the above topics
  • Understand, apply, and analyze calculus-based economic models


  • Code :             X31
  • Semester :     3rd
  • Effort :              7.5 ECTS
  • Hours :             4 per week
  • Type :                Mathematics
  • Department : Economics
  • Exams :             Yes

Course Contents:

  • Sequences and series. The principle of mathematical induction.

    Functions: algebra of functions, inverse functions, polynomial and rational functions.

    Limits. Continuity, differentiation functions, implicit differentiation, L’Hopital’s rule, tangent. Monotonicity, maximum and minimum values, concavity, symmetry, curve sketching.

    Functions of several variables. Partial differentiation. Directional Derivatives. Total Differential. Jacobian Matrix. Homogeneous Functions. Euler's thorem. Convexity, Implicit Functions Derivatives, Parametric Functions Derivatives, Tangential Plane.

    Unconstrained optimization and optimization under equality constraints.

    Applications to Economic theory:

    • Rate of change, supply and demand curves, finding equilibrium.
    • Present value, Annuity, Logarithmic derivative. Percent rate of change, Marginal cost-revenue-profit, elasticity.
    • Consumer theory (Indifference Curves, Marginal Rate of Substitution, consumer surplus, utility maximisation ),
    • Theory of production (Marginal and Average products, Marginal Rate of Technical Substitution, Production functions, Returns to scale),
    • Cost theory (Revenue, cost and profit, profit maximization).

    All the above topics are illustrated with MATHEMATICA.