Analysis in one variable is a beginning course in mathematical analysis.

The theory and its calculus is also fundamental for science and technology.

Course offering missing for current semester as well as for previous and coming semesters

## Content and learning outcomes

### Course contents

No information inserted

### Intended learning outcomes

After completing the course, the student can use calculus in one variable to formulate, solve and analyze problems.

More precisely, the goal means that the student also can

• use the definition of a limit and determine limits;
• formulate and derive properties for maxima, minima and intermediate values of continuous functions;
• use continuous, monotone and invertible functions to solve some equations analytically and others numerically;
• use and understand derivatives for studying graphs, analyze inequalities and solve optimization problems;
• formulate the definition of an integral and analyze integrability;
• determine some integrals by primitive functions;
• use integrals to determine area, volume and length of curves;
• approximate functions with Taylor polynomials;
• solve some differential equations with integrals and others numerically;
• formulate and analyze some applied problems with differential equations;
• analyze infinite series with integrals.

### Course Disposition

No information inserted

## Literature and preparations

### Specific prerequisites

SF1643 Numbers and Functions.

### Recommended prerequisites

No information inserted

### Equipment

No information inserted

### Literature

LTH/Övningar i analys i en variabel.

## Examination and completion

If the course is discontinued, students may request to be examined during the following two academic years.

A, B, C, D, E, FX, F

### Examination

• TEN1 - Examination, 8,0 hp, betygsskala: A, B, C, D, E, FX, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

### Other requirements for final grade

The examination of the course is by a finishing written exam and some smaller written test and projects during the course. The tests and projects give credits for the final exam.

### Opportunity to complete the requirements via supplementary examination

No information inserted

### Opportunity to raise an approved grade via renewed examination

No information inserted

### Examiner

No information inserted

### Ethical approach

• All members of a group are responsible for the group's work.
• In any assessment, every student shall honestly disclose any help received and sources used.
• In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.

## Further information

### Course web

No information inserted

SCI/Mathematics

### Main field of study

Mathematics, Technology

First cycle