# FIN 3515 Mathematical Analysis

FIN 3515 Mathematical Analysis

Responsible for the course
Robert Hansen

Department
Department of Economics

Term
According to study plan

ECTS Credits
7,5

Language of instruction
Norwegian

Introduction
Mathematical analysis is an advanced math course that is based on the first-year course in mathematics, and is a mandatory part of the bachelor's programme in finance. The course is conducted during the second year.

Learning outcome
Acquired Knowledge
The course deepens and extends mathematical analysis techniques from the basic course in the first year. In this context, emphasis is on functional analysis of both the single and the multivariable case. In the multivariable case various techniques for constrained optimization will be examined, also for the case when the constrained condition is given by inequalities. The course also examines selected topics in linear algebra, where students learn vector and matrix arithmetic, Gaussian elimination, determinants, Cramer’s rule and matrix inversion. The course also discusses various integration techniques such as partial integration and integration by substitution. Techniques for the solution of simple first order differential equations will also be reviewed.

Acquired Skills
After completing the course the student will have acquired skills and training in calculus and linear algebra that can be used in secondary economics courses at the final bachelor's and master's level. The course also aims to train students in the construction and analysis of simple economic models. In addition, students will gain a deeper understanding of mathematical concepts through the ability to solve more sophisticated mathematical problems than in the freshman course, and furthermore improve the ability of formal and analytical solution of various problems. Specifically, the students will be trained in using techniques from optimization theory to formulate and solve multivariable optimization problems, both purely theoretical problems, and applied problems in economics. From integration theory and solution of differential equations, students will be able to formulate and solve dynamic models, for example in application of economic theory. Using knowledge of linear algebra, students will be able to formulate and solve linear equations in a compact and efficient manner. Students will also get trained in how to transform a non-linear model to a linear model, and to choose the solution technique that is most appropriate to solve a given problem. Generally, students develop skills in being able to understand mathematical problems and choose appropriate strategies to solve them.

Reflection
The course will strengthen the students' ability of analytical thinking and ability to reflect on the results and calculations.

Prerequisites
EXC 2910 Mathematics or equivalent.

Books:
Sydsæter, Knut and Peter Hammond. 2012. Essential mathematics for economic analysis. 4th ed. Pearson Education. Utvalgte deler, se kursbeskrivelsen

Course outline
Chapter references to Sydsæter et. al:

 1. Multivariable optimization problems for functions of several variables Ch. 13.1 - 13.6 2. Constrained optimization (general Lagrange problems) Ch. 14.1-14.4, 14.6, 14.7 3. Implicit differentiation Ch. 7.1,7.2, 12.1-12.3 4. Linear and polynomial approximations. Differentials Ch. 7.4, 7.5, 12.8, 12.9 5. Elasticity Ch. 7,7, 11.8 6. Homogeneous functions Ch. 12.6 7. Non-linear programming Ch. 14.8, 14.9 8. Systems of equations Ch. 12.10, 15.1 9. Gaussian elimination Ch. 15.6 10. Matrix and vector algebra Ch. 15.1 - 15.5, 15.7 11. Determinants and inverse matrices Ch. 16.1 - 16.8 12. Integration: Integration by parts and integration by substitution Ch. 9.4 – 9.6 13. Differential equations Ch. 9.8, 9.9

Computer-based tools
No specified software tools are required in this course.

The course is taught over 51 hours divided in 45 hours of instruction and 6 hours of problem solving. Extensive problem solving is emphasized, and part of each the teaching session will be used on this. It is important that students attend the lectures well prepared by having a try at the tasks before the lectures.

Work requirements
During the course the students will be given a mandatory assignment. The assignment will be given 14 days before the deadline, and must be completed and submitted individually. After the papers have been filed, the students will be given feedback as the solution is reviewed in the lectures. The task must be approved for the student to be allowed to sit the final exam.

Recommended time use:
 Activity Time Participation in lectures 45 Attendance at problem solving lectures* 6 Preparation for lectures 100 Work requirements 23 Preparation for the exam 22 Exam 4 Total recommended time spent 200
* The problem solving lectures will be integrated with the ordinary lectures.

Coursework requirements
In order to sit for final examination students must submit and get approved an individual assignment.

Examination
A four hour indivivual examination concludes the course.

Examination code(s)
FIN 35151 Written exam, counts 100% of the grade in FIN 3515 Mathematical Analysis, 7.5 credits.

Examination support materials
Interest tables and BI-approved exam calculator. TEXAS INSTRUMENTS BA II Plus ™
Examination support materials at written examiniations are explained under examination information in the student portal @BI. Please note use of calculator and dictionary. https://at.bi.no/EN/Pages/Exa_Hjelpemidler-til-eksamen.aspx

Re-sit examination
A re-examiniation is iffered every term.
Students who do not get approved their mandatory assignment or who have not met the work requirement in the course are not allowed to take the exam. This means that they must take the course once again. Students who do not achieve a Pass for the written exam or who want to improve their grade, must re-sit for the examination later to complete the course.