Mathematical Analysis, 15 credits

Main field of study

Course level

Advancement level

Course offered for

• Bachelor´s Programme in Statistics and Data Analysis

Entry requirements

• General entry requirements for undergraduate studies
  and
  Social Studies, English and Mathematics corresponding to the level in Swedish upper secondary education (Samhällskunskap 1b or 1a1 and 1a2, Engelska 6, Matematik 3b or 3c)
• At least 37 ECTS credits passed from semester 1 and 2 Bachelor´s Programme in Statistics and Data Analysis

Intended learning outcomes

On completion of the course, the student should be able to
- read and interpret mathematical text
- use definitions of central concepts and central approaches
- use arithmetical rules for limits, derivatives, primitive functions and integrals for functions in one variable
- analyse functions in one variable and draw conclusions about the properties of functions
- use standard techniques to determine primitive functions and definite integrals
- draw expressions for, and calculate, geometric quantities
- solve the differential equations of the 1st order
- use Taylor expansions to approximate functions with polynomial
- perform convergence studies of generalised integrals (one variable calculus)
- use certain concepts of multivariable analysis.

Course content

One variable calculus: Algebraic operations. Equations. Differences. Absolute value. Actual and complex numbers. Binomial theorem. Functions of an actual variable. Polynomial. Exponential and logarithm functions. Trigonometric functions. Limit. Derivative and continuity. Derivation rules. Properties of continuous functions. Extreme value. Largest and smallest value. Function study. Primitive function. Integration with geometric applications such as area, arc length, area of rotation, volume of rotation. Generalised integrals. Taylor's formula. Maclaurin expansion of elementary functions with application to limit calculations. Differential equations of the first order. Control of results and partial results
Multivariable analysis: Graphical interpretation of functions in two variables. Partial derivatives. Stationary points. Double integrals. Variable exchanges

Teaching and working methods

The teaching takes the form of lectures and teaching sessions. The students should also study independently.

Examination

The course is examined via two written examinations. Detailed information can be found in the study guide.

Grades

Other information

Planning and implementation of a course must take its starting point in the wording of the syllabus. The course evaluation included in each course must therefore take up the question how well the course agrees with the syllabus. The course is carried out in such a way that both men´s and women´s experience and knowledge is made visible and developed.

Planning and implementation of a course must take its starting point in the wording of the syllabus. The course evaluation included in each course must therefore take up the question how well the course agrees with the syllabus. 

The course is conducted in such a way that there are equal opportunities with regard to sex, transgender identity or expression, ethnicity, religion or other belief, disability, sexual orientation and age.

If special circumstances prevail, the vice-chancellor may in a special decision specify the preconditions for temporary deviations from this course syllabus, and delegate the right to take such decisions.

Department