Syllabus year 2006

CALCULUS IN ONE VARIABLEFMA410
Matematik, endimensionell analys

Credits: 8. Grading scale: TH. Compulsory for: B1, C1, D1, E1, F1, I1, K1, L1, M1, MD1, N1, Pi1, V1, W1. Course coordinator: Director of Studies, Lars_Christer.Boiers@math.lth.se, Matematik. Assessment: Written examination. Parts: 2. Homepage: http://www.maths.lth.se/matematiklth/vitahyllan/vitahyllan.html.

Aim
Knowledge goals:

After passing the course the student should:

- have a general understanding of what is meant by mathematical theory,

- have acquired knowledge about such mathematical concepts and methods in one variable calculus that are used for the study of mathematical models in applications.

Skill goals:

After passing the course the student should

- have good algebraic computational skills,

- be able to without difficulties perform computations with elementary functions, derivatives and integrals,

- have acquired ability to read mathematical texts and interpret formulae,

- obtained good skills in the use of mathematical concepts and methods and in the construction of mathematical models.

Attitude goals:

After passing the course the student should

- have developed confidence concerning computations and in the application of mathematical theory,

- have no fear and feel confident in using mathematics in whatever context in which it is natural.

Contents
Part 1.

The concept of a function. Properties of the elementary functions: curves, formulas, elementary limits. Sequences: recursion and induction. Limits with applications: asymptotes, the number e, series. Continuous functions. Derivatives: definition and properties, applications. Derivatives of the elementary functions. Properties of differentiable functions: the mean value theorem with applications. Curve sketching. Local extrema. Optimisation. Complex numbers and polynomials.

Part 2.

The concept of primitive function. Simple integration methods: partial integration and change of variable. Partial fractions. Definition of integral. Integration methods. Riemann sums. Geometric and other applications of integrals. Generalized integrals. Differential equations of first order: linear and with separable variables. Linear differential equations. Solving homogeneous and certain inhomogeneous equations. Applications. The Taylor and Maclaurin formulae. Expansion of elementary functions. The importance of the remainder term. Applications of Maclaurin expansions.

Literature
Persson, A. & B÷iers, L-C.: Analys i en variabel, chapters 0-9, appendices A-B. Studentlitteratur 2003. ISBN 91-44-02056-2

Parts

Code: 0197. Name: Calculus in One Variable 1.
Credits: 4. Grading scale: UG. Assessment: Written test. Contents: See above, part 1.

Code: 0297. Name: Calculus in One Variable 2.
Credits: 4. Grading scale: UG. Assessment: Written test. Contents: See above, part 2.