Analysis II

COURSE OBJECTIVE
At the end of this course the student is able to
a) Solve some first order (linear or with separable variables) and second order (with constant coefficients) differential equations.
b) Use some convergence tests for (power-)series (comparison test, limit test, ratio test, integral test).
c) Calculate the interval of convergence of a power/Taylor series.
d) Determine if a function of several variables is continuous and/or differentiable.
e) Calculate the extreme values of a function of several variables.
f) Calculate a double or triple integral (if needed with a change of variables)

COURSE CONTENT
In this course we treat sequences and series of functions, functions of
two variables and multiple integration. We also discuss differential
equations of first and second order. The topics are:
a) Differential Equations of first order (separable equations and linear equations) and second order (linear with constant coefficients).
b) Sequences of functions. Pointwise and uniform convergence.
c) Series, Power series and Taylor series. Pointwise and uniform convergence.
d) Basic topology in Eucledian spaces.
e) Functions of several variables (continuity, differentiability, optimization, Taylor series)
f) Multiple integration (double and triple integrals, change of variables, improper integrals)

TEACHING METHODS:
Lectures (2x2 hours per week) and seminars (1x2 hours per week).

TYPE OF ASSESSMENT
There will be a midterm exam at the end of period 4 and a final exam at the end of period 5. Details about the topics treated in each exam and the calculation of the final grade will be published in Canvas. If your grade is not sufficient, it is possible to make the resit about all topics in the spring semester. It is not possible to resit just the midterm or final exam