Analysis II

2019-2020

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).

Method 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.

Literature

1) A Friendly Introduction to Analysis; Single and Multivariable, second
edition, Witold A. J. Kosmala, Pearson. ISBN 0130457965/978-0130457967.
2) Lecture notes, available via Canvas.

Target Audience

1 EOR

Additional Information

We expect that you attend the seminars well prepared! That means that
you have already tried to make the exercises at home! Some exercises
will be treated on the blackboard. You can ask questions about other
exercises to the teaching assistant. An attendance list will be used.

Recommended background knowledge

This course requires knowledge of topics treated in Analysis I.

General Information

Course Code X_400642
Credits 6 EC
Period P4+5
Course Level 100
Language of Tuition English
Faculty Faculty of Science
Course Coordinator dr. ir. R.F. Swarttouw
Examiner dr. ir. R.F. Swarttouw
Teaching Staff dr. ir. R.F. Swarttouw
dr. M.A. Estevez Fernandez

Practical Information

You need to register for this course yourself

Last-minute registration is available for this course.

Teaching Methods Seminar, Lecture
Target audiences

This course is also available as: