Course syllabus

Endimensionell analys A1
Calculus in One Variable A1

FMAB45, 5 credits, G1 (First Cycle)

Valid for: 2020/21
Decided by: PLED F/Pi
Date of Decision: 2020-04-01

General Information

Main field: Technology.
Compulsory for: BME1, M1, MD1
Language of instruction: The course will be given in Swedish

Aim

The aim of the course is to give a basic introduction to calculus in one variable. The aim as also to develop the student's ability to solve problems, to assimilate mathematical text and to communicate mathematics.

Learning outcomes

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.
• be familiar with the logical structure of mathematics, in the way it appears e.g. in plane geometry.
• be able to account for the contents of definitions, theorems and proofs.

Competences and skills
For a passing grade the student must

• be able to demonstrate a good algebraic computational ability.
• be able to demonstrate an ability to explain mathematical reasoning in a structured and logically clear way.

Contents

The number concept. Calculation with fractions. Inequalities. Square roots. Curves and equations of degree 2. Geometry in the plane. Analytic geometry. The circle, ellipse, hyperbola. Arithmetic and geometric sums. The binomial theorem. The modulus of a number. Trigonometry. Powers and logarithms. The concept of a function. The properties of the elementary functions: graphs, formulas. Sequences of numbers.

Examination details

Grading scale: TH - (U,3,4,5) - (Fail, Three, Four, Five)
Assessment: Written test comprising theory and problem solving. Computational ability tests. An oral assignment. ONLY STUDENTS WHO PASSED THE TESTS OF COMPUTATIONAL ABILITY AND THE ORAL ASSIGNMENT MAY PARTICIPATE IN THE WRITTEN TEST.

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: 0120. Name: Written Examination.
Credits: 5. Grading scale: TH. Assessment: Written test comprising theory and problem solving. Computational ability tests must be passed before the examination. One assignment (oral and in writing) must be passed before the examination.
Code: 0220. Name: Computational Ability Test 1.
Credits: 0. Grading scale: UG.
Code: 0320. Name: Assignment.
Credits: 0. Grading scale: UG.
Code: 0420. Name: Computational Ability Test 2.
Credits: 0. Grading scale: UG.

Admission

The number of participants is limited to: No
The course overlaps following course/s: FMA410, FMA415, FMA645, FMAA05, FMAA50, FMAA01

Reading list

• Diehl, S: Inledande geometri för högskolestudier. Studentlitteratur, 2015. Chapters P,T, A.
• Övningar i Inledande geometri för högskolestudier. Studentlitteratur, 2015, ISBN: 9789144067865.
• Månsson, J. och Nordbeck, P.: Endimensionell analys. Studentlitteratur, 2011, ISBN: 9789144056104.
• Övningar i endimensionell analys. Studentlitteratur, 2018, ISBN: 9789144127187.

Contact and other information

Course coordinator: Studierektor Anders Holst, Studierektor@math.lth.se
Course administrator: Studerandeexpeditionen, expedition@math.lth.se
Course homepage: http://www.maths.lth.se/course/endimA1ny/
Further information: Calculus in one variable is taught and examined in two versions, track A (the courses Calculus in One Variable A1-A3) and track B (the courses Calculus in One Variable B1-B2) respectively, depending on the student's programme. The goals are the same. The present course belongs to track A. A student who has enrolled in this course may not later enrol in courses from track B. Before the written retake exams it will be possible to retake the tests of computational ability and the oral assignment.