Syllabus academic year 2007/2008
CALCULUSFMA645

Higher education credits: 13,5. Grading scale: TH. Level: G1 (First level). Language of instruction: The course will be given in Swedish. FMA645 overlap following cours/es: ??1690, ??1691, FMA415, FMAA01, FMAA05, FMA415, FMAA01 och FMAA05. Compulsory for: IBYA1, IBYI1, IBYV1, IDA1. Course coordinator: Director of Studies, Lars-Christer Böiers, Lars_Christer.Boiers@math.lth.se, Matematik. Assessment: Written test in all subcourses. The fiirst 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). In the subcourse Algebra some oral assignments should be completed. Parts: 3. Home page: http://www.maths.lth.se/matematiklth/vitahyllan/vitahyllan.html.

Aim
The course aims at giving a basic treatment of one-dimensional calculus. Particular emphasis is on the role 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

Contents
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: curves, formulas, limits. Limits with applications: asymptotes, 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. Optimisation.

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.

Literature
Dunkels, A m.fl.: Mot bättre vetande i Matematik. Studentlitteratur. ISBN: 9789144322520.
Persson, A & Böiers, L-C: Analys i en variabel. Studentlitteratur 2001. ISBN: 9789144020563.
Övningar till Analys i en variabel, Matematikcentrum, KFS AB Lund.

Parts

Code: 0107. Name: Algebra.
Higher education credits: 3. Grading scale: UG. Assessment: Written test, with grades Passed och 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.