Course Details

1. Understand the concept of the derivative of a function and calculate the derivatives of polynomial, logarithmic and rational functions.
2. Apply differentiation for: sums, products, quotients, and the chain rule.
3. Calculate and apply in real business problems the second and order derivatives (for minimization and maximisation).
4. Apply derivatives in optimization problems with emphasis in business problems (marginal cost, marginal revenue, and marginal profit). Profit maximization and cost minimization.
5. Calculate the partial derivatives of functions of two or more variables and to apply them for the calculation of the maxima and minima of optimization problems.
6. Understand, apply and interpret the Lagrange multipliers method for constrained optimization.
7. Understand the models of exponential growth and decay problems with emphasis to business applications
8. Understand the concept of the indefinite and definite integral
9. Formulate an optimization problem for a particular production model.

Derivatives

Functions, limits, continuity. The concept of the derivative of a function. Derivatives of polynomial, logarithmic and rational functions.

Derivatives of the product and quotient. The chain rule.

Higher order derivatives (second, third etc)

Analysis of a function

Minimize and maximise a function using the second order derivative criterion.

Applications of derivatives in optimization problems with emphasis in business problems.

Functions of two or more variables.

Maxima-minima. Application in business problems (marginal cost, marginal revenue, marginal profit, exact cost, maximum profit and minimum cost).

The Lagrange multipliers method.

Exponential growth and decay problems

Exponential growth and decay problems with emphasis to business applications.

Anti-derivatives and the concept of the indefinite integral. Integration of simple functions.

Integrals

The concept of the definite integral. The fundamental theorem of calculus. Applications in business problems.

• Barnett R., Ziegler M., Byleen K., College Mathematics for Business, Economics, Life Sciences and Social Sciences. Pearson Prentice Hall 2008

• Anton, H., and Kolman, A., Mathematics with Applications for the Management, Life and Social Sciences, Wiley, 2002.