Course content

The course expands on and enhances the analysis from MA1101 with respect to contents, applications, and level of abstraction.
Infinite series is a central topic, with a focus on power series and Taylor expansions.
Another central topic is differential equations.
Numerical aspects associated with these topics, as well as integration and equation solving.
Basic analytic geometry in the plane is covered.
There is an emphasis on rigour.

Learning outcome

1. Knowledge. The student has knowledge of central concepts and results concerning: Series, in particular power series and Taylor series; uniform convergence; analytic geometry in the plane. Moreover, the student is familiar with numerical methods for integration, equation solving, and approximation by polynomials.

2. Skills. The student is able to choose and implement suitable numeral methods for problems involving integration and equation solving, and to estimate the accuracy of the chosen method. The student is able to apply knowledge of series and numerical methods to differential equations. Moreover, the student is able to read and write rigorous mathematical arguments related to the course content, and to extract the main ideas in the argumentation.

Learning methods and activities

Lectures and exercises. Final grade based on written final examination. Retake of examination may be given as an oral examination.

Compulsory assignments

• Exercises

Recommended previous knowledge

The course is based on MA1101 Basic calculus I.

Course materials

Will be announced at the start of the course.

Credit reductions