# ELE 3776 Mathematical Analysis

## ELE 3776 Mathematical Analysis

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

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.

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 be 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.

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

__Chapter references to Sydsæter et. al:__

- Multivariable optimization problems for functions of several variables: Ch. 17.1 - 17.6
- Constrained optimization (general Lagrange problems): Ch. 18.1 - 18.4, 18.6 - 18.7
- Implicit differentiation: Ch. 7.1,7.2, 15.1-15.3
- Linear and polynomial approximations. Differentials: Ch. 7.4, 7.5, 15.8, 15.9
- Elasticity: Ch. 7.7, 14.10
- Homogeneous functions: Ch. 15.6
- Non-linear programming: Ch. 20.1-20.3
- Systems of equations: Ch. 15.10, 12.2
- Gaussian elimination: Ch. 12.8
- Matrix and vector algebra: Ch. 12.1 - 12.7
- Determinants and inverse matrices: Ch. 13.1 - 13.8
- Integration: Integration by parts and integration by substitution: Ch. 10.5 - 10.6
- Differential equations: Ch. 11.9, 11.10

The course is taught over 36 hours divided in 30 hours of instruction and 6 hours of problem solving. In addition, there are digital learning resources. 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.

For electives re-sit is normally offered at the next scheduled course. For this course, however, a re-sit is 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.

Higher Education Entrance Qualification

**Disclaimer**

Deviations in teaching and exams may occur if external conditions or unforeseen events call for this.

EXC 2910 Mathematics or equivalent.

Assessments |
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Exam category: School Exam Form of assessment: Written School Exam - pen and paper Exam/hand-in semester: First Semester Weight: 100 Grouping: Individual Support materials: - BI-approved exam calculator
- Simple calculator
- Interest table
Duration: 4 Hour(s) Exam code: ELE37761 Grading scale: ECTS Resit: Examination every semester |

Activity | Duration | Comment |
---|---|---|

Teaching | 30 Hour(s) | |

Feedback activities and counselling | 6 Hour(s) | Review of assignments in plenary |

Prepare for teaching | 114 Hour(s) | |

Student's own work with learning resources | 31 Hour(s) | |

Digital resources | 15 Hour(s) | |

Examination | 4 Hour(s) |

A course of 1 ECTS credit corresponds to a workload of 26-30 hours. Therefore a course of 7,5 ECTS credit corresponds to a workload of at least 200 hours.