# ELE 3776 Mathematical Analysis

## ELE 3776 Mathematical Analysis

Course code:
ELE 3776
Department:
Economics
Credits:
7.5
Course coordinator:
Robert Gunder Hansen
Product category:
Bachelor
Portfolio:
Bachelor - Electives
Semester:
2019 Autumn
Active status:
Active
Teaching language:
Norwegian/English
Course type:
One semester
Introduction

Mathematical analysis is an advanced math course that is based on the first-year course in mathematics.

Learning outcomes - Knowledge

The course deepens and extends mathematical analysis techniques from the basic course in the first year.

During the course students shall acquire knowledge of:

• 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.
• Selected topics in linear algebra, where students learn vector and matrix arithmetic, Gaussian elimination, determinants, Cramers rule and matrix inversion.
• 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.
Learning outcomes - 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.
General Competence

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

Course content

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
Teaching and learning activities

The course is taught over 45 hours divided in 39 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.

Software tools
No specified computer-based tools are required.

For electives re-sit is normally offered at the next scheduled course. For this course, however, resit it offered in both semesters. If an elective is discontinued or is not initiated in the semester it is offered, re-sit will be offered in the electives ordinary semester.

Qualifications

Higher Education Entrance Qualification.

Required prerequisite knowledge

EXC 2910 Mathematics or equivalent.

Exam categoryWeightInvigilationDurationSupport materialsGroupingComment exam
Exam category:
Submission
Form of assessment:
Written submission
Exam code:
ELE37761
ECTS
Internal and external examiner
Resit:
Examination every semester
100Yes4 Hour(s)
• BI-approved exam calculator
• Simple calculator
• Interest table
Individual
Exams:
 Exam category: Submission Form of assessment: Written submission Weight: 100 Invigilation: Yes Grouping (size): Individual Support materials: BI-approved exam calculator Simple calculator Interest table Duration: 4 Hour(s) Comment: Exam code: ELE37761 Grading scale: ECTS Resit: Examination every semester
Type of Assessment:
Ordinary examination
Total weight:
100
Workload activityDurationType of durationComment student effort
Teaching39Hour(s)
Review of assignments in plenary6Hour(s)
Prepare for teaching120Hour(s)
Self study31Hour(s)
Examination4Hour(s)
Expected student effort:
 Workload activity: Teaching Duration: 39 Hour(s) Comment:
 Workload activity: Review of assignments in plenary Duration: 6 Hour(s) Comment:
 Workload activity: Prepare for teaching Duration: 120 Hour(s) Comment:
 Workload activity: Self study Duration: 31 Hour(s) Comment:
 Workload activity: Examination Duration: 4 Hour(s) Comment: