Course syllabus

# Matematisk analys

Calculus

## FMAA50, 13,5 credits, G1 (First Cycle)

## General Information

## Aim

## Learning outcomes

## Contents

## Examination details

## Admission

## Reading list

## Contact and other information

Calculus

Valid for: 2020/21

Decided by: PLED F/Pi

Date of Decision: 2020-04-01

Compulsory for: IBYA1, IBYI1, IBYV1, IDA1, IEA1

Language of instruction: The course will be given in Swedish

The course aims at giving a basic treatment of one-dimensional calculus. Particular emphasis is put on the role which this plays in applications in different areas of technology, in order to give the future engineer a good foundation for further studies.

Knowledge and understanding

For a passing grade the student must

- within the framework of the course with confidence be able to handle elementary functions of one variable, including limits, derivatives and integrals
- be able to set up and solve some types of linear and separable differential equations that are important in the applications
- be able to give a general account of, and illustrate the meaning of, mathematical concepts in calculus in one variable that are used to construct and study mathematical models in the applications.

Competences and skills

For a passing grade the student must

- be able to demonstrate a good ability to carry out algebraic calculations, and be able to compute with complex numbers
- in connection with problem solving be able to demonstrate an ability to independently choose and use mathematical concepts and methods of one-dimensional analysis, and to construct and analyse simple mathematical models
- in the context of problem solving be able to integrate knowledge from different parts of the course
- be able to demonstrate an elementary ability to explain the solution of a mathematical problem within the course, in a well structured way and with clear logic.

*Algebra:*

Algebraic computations. Functions, equations, inequalities and modulus of a number. Complex numbers. Powers and logarithms. Trigonometry. Curve sketching: elementary functions and second degree curves.

*Calculus 1:*

Complex numbers and polynomials. The concept of a function. Properties of the elementary functions: graphs, formulas, limits. Limits with applications: the number e, series. Continuous functions. Derivatives: definition and properties, applications. Differentiation of the elementary functions. Properties of differentiable functions: the mean value theorem with applications. Curve sketching. Local extreme values. Optimization.

*Calculus 2:*

Primitive functions. Partial integration and change of variable. Partial fractions. Definition of the Riemann integral. Methods of integration. Riemann sums. Geometrical and other applications of integrals. Improper integrals. Differential equations of first order: linear and separable with applications. Linear differential equations of second order: solution of homogeneous and certain inhomogeneous equations, with applications. The Taylor and Maclaurin formulae. Power series expansions of the elementary functions, with applications.

Grading scale: TH - (U,3,4,5) - (Fail, Three, Four, Five)

Assessment: Written tests on all subcourses. The first subcourse is graded as Passed or Not passed. The subcourses Calculus 1 and 2 are graded on a scale from 3.0 (passed) to 6.0 in steps of 0.1. The final grade is the integer part of the mean of these two grades (at most 5).
Oral presentation that must be approved before the student may participate in the exam on the subcourse Algebra.

The examiner, in consultation with Disability Support Services, may deviate from the regular form of examination in order to provide a permanently disabled student with a form of examination equivalent to that of a student without a disability.

Parts

Code: 0117. Name: Algebra.

Credits: 3. Grading scale: UG. Assessment: Written test, with grades Passed and Not passed. Some assignments. Contents: See above, Algebra.

Code: 0217. Name: Calculus 1.

Credits: 6. Grading scale: TH. Assessment: Written test. Contents: See above, Calculus 1.

Code: 0317. Name: Calculus 2.

Credits: 4,5. Grading scale: TH. Assessment: Written test. Contents: See above, Calculus 2.

The number of participants is limited to: No

The course overlaps following course/s: FMA415, FMAA01, FMAA05, FMA410, FMA645

- Månsson, J. och Nordbeck, P.: Endimensionell analys. Studentlitteratur, 2011, ISBN: 9789144056104.
- Övningar i endimensionell analys. Studentlitteratur, 2018, ISBN: 9789144127187.
- Dunkels, A m.fl.: Mot bättre vetande i matematik. Studentlitteratur, 2002, ISBN: 9789144019192.

Director of studies: Studierektor Anders Holst, Studierektor@math.lth.se

Course administrator: Studerandeexpeditionen, expedition@math.lth.se

Course homepage: http://www.maths.lth.se/course/analHbg/