Syllabus academic year 2011/2012
(Created 2011-09-01.)
Credits: 13,5. Grading scale: TH. Cycle: G1 (First Cycle). Main field: Technology. Language of instruction: The course will be given in Swedish. FMA645 overlaps following cours/es: ??1690, ??1691, FMA415, FMAA01 and FMAA05. Compulsory for: IBYA1, IBYI1, IBYV1, IDA1, IEA1. Course coordinator: Anders Holst,, Mathematics. Assessment: Written test in all subcourses. The first subcourse is graded as Passed och Not passed. The courses Calculus 1 and 2 are when passed graded in a scale from 3.0 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). Parts: 3. Home page:

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

Skills and abilities
For a passing grade the student must


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: curves, 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 an integral. Methods of integration. Riemann sums. Geometrical and other applications of integrals. Improper integrals. Differential equations of first order: linear and separable. Applications. Linear differential equations of second order: solution of homogeneous and certain inhomogeneous equations, with applications. The Taylor and Maclaurin formulae. Expansion of the elementary functions, with applications.

Månsson, J. och Nordbeck, P.: Endimensionell analys, Studentlitteratur 2011, ISBN 9789144056104.
Månsson, J. och Nordbeck, P.: Övningar i endimensionell analys, Studentlitteratur 2011, ISBN 9789144075020.
Additional material provided by the department.


Code: 0107. Name: Algebra.
Higher education credits: 3. Grading scale: UG. Assessment: Written test, with grades Passed and Not passed. Some assignments. Contents: See above, Algebra.

Code: 0207. Name: Calculus 1.
Higher education credits: 6. Grading scale: TH. Assessment: Written test. Contents: See above, Calculus 1.

Code: 0307. Name: Calculus 2.
Higher education credits: 4,5. Grading scale: TH. Assessment: Written test. Contents: See above, Calculus 2.