## Course Information Package

Course Unit TitleCALCULUS FOR BUSINESS AND SOCIAL SCIENCES
Course Unit CodeAMAT106
Course Unit Details
Number of ECTS credits allocated5
Learning Outcomes of the course unitBy the end of the course, the students should be able to:
1. Explain 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, marginal profit, maximization of profit and minimization of cost).
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. Apply and interpret the Lagrange multipliers method for constrained optimization.
7. Employ the models of exponential growth and decay problems with emphasis to business applications
8. Explain the concept of the indefinite and definite integral
Mode of DeliveryFace-to-face
PrerequisitesAMAT110Co-requisitesNONE
Recommended optional program componentsNONE
Course Contents

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)

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 with emphasis to business applications.

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

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