Mathematics for Economics II
Universidad Carlos III de Madrid
Area of Study
Business Administration, Economics, Mathematics
Taught In English
Course Level Recommendations
ISA offers course level recommendations in an effort to facilitate the determination of course levels by credential evaluators.We advice each institution to have their own credentials evaluator make the final decision regrading course levels.
Recommended U.S. Semester Credits3
Recommended U.S. Quarter Units4
Hours & Credits
COMPETENCES AND SKILLS THAT WILL BE ACQUIRED AND LEARNING RESULTS.
This subject provides the quantitative instruments that are needed to pose and analyze economic
problems with the aid of a formal model. In working toward the above goal the student will acquire the following competences and skills.
Regarding the contents of the course, the student will be able to:
- Extend the concepts of one variable functions to several variables.
- Understand the basic tools of calculus with several variables.
- Pose and solve static optimization problems.
- Apply all the above concepts to economic problems.
We classify the competences in two groups: specific competences and generic competences or skills.
Regarding the specific competences, the student will be able to:
- Solve linear systems of equations and determine the number of parameters in the solution.
- Understand the fundamental concepts involved in the calculus of functions of several variables: differentiability, chain rule, implicit differentiation.
- Describe the qualitative properties of the functions of several variables, such as growth, concavity and convexity.
- Approximate a function of several variables using the Taylor polynomial.
- Pose and solve static optimization problems, with and without restrictions using the first and second order conditions.
Pertaining the general competences or skills, in the class the student will develop:
- The ability to address economic problems by means of abstract models.
- The ability to solve the above formal models.
- The ability to interpret and classify the different solutions and apply the appropriate conclusions to social contexts.
- The ability to use the basic tools that are need in the modern analysis of economic problems.
Through out the course, the student should maintain:
- An inquisitive attitude when developing logical reasoning, being able to tell apart a proof from
- An entrepreneurial and imaginative attitude towards the cases studied.
- A critical attitude towards the formal results and their applicability in social contexts.
DESCRIPTION OF CONTENTS: PROGRAMME
The course consist of two parts: Linear algebra and optimization of several variable functions.
Linear algebra: Properties of matrices and determinants. Systems of linear equations.
Functions of several variables: Continuity. Calculus of several variables: partial derivatives. Differentiable functions. Convexity. Implicit differentiation. Optimization. Extreme points. Constrained optimization. First and second order conditions. Comparative statics. Application to economic models.
LEARNING ACTIVITIES AND METHODOLOGY
The course lectures will be based on combining theoretical explanations with several practical exercises. The students should attempt to solve the exercises by themselves, before they are addressed in class.
Student participation is considered very important in order to acquire the skills needed to pose and solve economic models.
The final grade is the weighted average of the final exam and the class grade. The final exam is the same for all the Mathematics for Economics II groups and consists of practical exercises and theoretical questions. The class grade is determined by each professor and is based on quizzes done in the classes.
Ordinary exam: The final grade is the weighted average of 60% the grade in the final exam and 40% the class grade.
Extraordinary exam: The final grade is the maximum of the following grades:
a) A weighted average consisting of 60% the grade in the final exam and 40% the class grade.
b) The grade in the final exam.
% end-of-term-examination: 60
% of continuous assessment (assigments, laboratory, practicals): 40
- R. E. Larson, R. P. Hostetler y B. H. Edwards Calculus (Volumen II). English edition, McGraw Hill.
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Please note that there are no beginning level Spanish courses offered in this program.
Courses and course hours of instruction are subject to change.
Eligibility for courses may be subject to a placement exam and/or pre-requisites.
Credits earned vary according to the policies of the students' home institutions. According to ISA policy and possible visa requirements, students must maintain full-time enrollment status, as determined by their home institutions, for the duration of the program.
ECTS (European Credit Transfer and Accumulation System) credits are converted to semester credits/quarter units differently among U.S. universities. Students should confirm the conversion scale used at their home university when determining credit transfer.
Please reference fall and spring course lists as not all courses are taught during both semesters.
Availability of courses is based on enrollment numbers. All students should seek pre-approval for alternate courses in the event of last minute class cancellations
Please note that some courses with locals have recommended prerequisite courses. It is the student's responsibility to consult any recommended prerequisites prior to enrolling in their course.