# MAT1110 - Calculus and linear algebra

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## Course content

MAT1110 gives an introduction to the theory of functions of several variables with emphasis on differentiation, integration, and interative, numerical methods. The course also contains introductions to MATLAB, series, and linear algebra in Euclidean spaces. MAT1110 is a natural continuation of MAT1100 and a basis for MAT1120.

## Learning outcome

After having completed the course:

• you can parametrize curves and surfaces and use these representations to create graphical figures and to compute arc length, line integrals and surface area
• you know the definition of double and triple integrals, can calculate such integrals by means of different coordinate representations, and use them to solve practical problems
• you can solve theoretical and practical optimization problems with and without constraints
• you are familiar with the completeness property of Euclidean spaces, know how they form a foundation for numerical methods, and can write programs in MATLAB or Python to find zeros and fixed points of functions.
• you master Gauss elimination, are familiar with the concepts of linear independence and basis, and can find eigenvalues and eigenvectors and use them to analyze practical problems from both an analytical and a numerical perspective
• you know what it means for a series to converge, can use tests to decide convergence and find domains of convergence, and can determine the Taylor series of a function
• you can carry out simple mathematical arguments and computations and present them in a clear and coherent way with suitable notation and terminology

Students who are admitted to study programmes at UiO must each semester register which courses and exams they wish to sign up for in Studentweb.

## Prerequisites

### Formal prerequisite knowledge

In addition to fulfilling the Higher Education Entrance Qualification, applicants have to meet the following special admission requirements:

One of these:

• Mathematics R1
• Mathematics (S1+S2)

And and in addition one of these:

• Mathematics (R1+R2)
• Physics (1+2)
• Chemistry (1+2)
• Biology (1+2)
• Information technology (1+2)
• Geosciences (1+2)
• Technology and theories of research (1+2)

The special admission requirements may also be covered by equivalent studies from Norwegian upper secondary school or by other equivalent studies. Read more about special admission requirements (in Norwegian).

### Recommended previous knowledge

MAT1100 - Calculus. Students who haven´t carried out MAT-INF1100 - Modelling and computations may have to use some extra time to study the software in use.

## Overlapping courses

The overlap between the 3 courses MAT1012 - Mathematics 2, MAT1100 - Calculus, MAT1110 - Calculus and linear algebra is 10 credits in total; you get 20 credits for these 3 courses.

10 credits with MAT110.

## Teaching

4 hours of lectures and 2 hours of problem solving in plenum per week. In addition there will be individual exercise solving sessions during the week, with guidance available.

## Examination

Two compulsory assignments need to be passed within given deadlines to be allowed to take the final exam.

There will be a digital midterm exam and a final written exam at the end of the semester which both add up to the final grade. Both exams are compulsory and have to be taken in the same semester.

Midterm exam counts for 1/3 and the final exam counts for 2/3. The final grade is based on the total score and a general impression after the final examination.

### Language of examination

Subjects taught in English will only offer the exam paper in English.

You may write your examination paper in Norwegian, Swedish, Danish or English.

### Resit an examination

This course offers both postponed and resit of examination. Read more:

### Withdrawal from an examination

It is possible to take the exam up to 3 times. If you withdraw from the exam after the deadline or during the exam, this will be counted as an examination attempt.

### Special examination arrangements

Application form, deadline and requirements for special examination arrangements.

## Evaluation

The course is subject to continuous evaluation. At regular intervals we also ask students to participate in a more comprehensive evaluation.

10

Bachelor

Every spring

Every spring

Norwegian

## Contact

Department of Mathematics