General Information
| Course Code | X_400636 |
|---|---|
| Credits | 6 EC |
| Period | P2 |
| Course Level | 100 |
| Language of Tuition | English |
| Faculty | Faculty of Science |
| Course Coordinator | dr. S.D. Barthel |
| Examiner | dr. S.D. Barthel |
| Teaching Staff |
dr. S.D. Barthel |
|
Part of programme(s)
Bachelor
Premaster
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Practical Information
You need to register for this course yourself. The (de)registration deadlines can be found on VU.nl
| Teaching Methods | Seminar*, Written partial exam, Lecture |
|---|
*You cannot select a group yourself for this teaching method, you will be placed in a group.
Target audiences
This course is also available as:
Course Objective
At the end of this course the student is able toa) determine if a series is convergent or divergent, using several tests
(like the comparison test, ratio test, alternating series test)
b) work with power series (find the radius of convergence, differentiate
or integrate termwise)
c) find the Taylor series of several functions (like exp(x), sin(x),
cos(x), ln(1+x), etc)
d) calculate dot products, cross products, vector projections, distances
in R^3
e) calculate partial derivatives, also using the chain rule
f) find extreme values of functions of two variables, with and without
constraints
g) compute double integrals, also using polar coordinates
g) calculate with complex numbers
h) solve several first- and second-order differential equations
(separable equations, first-order linear equations, second-order linear
equations with constant coefficients).
Course Content
Series, vectors in R^2 and R^3, real functions of several variables,complex numbers, differential equations.
Topics that will be treated are:
1) sequences, series, power series, Taylor series
2) vectors, dot product, cross product, vector projection, distances in
R^3
3) partial derivatives, chain rule, gradients
4) extreme values, Lagrange multiplier method
5) double integrals, polar coordinates
6) complex numbers
7) first and second order differential equations
Additional Information Teaching Methods
Lectures (3 x 2 hours per week) and seminars (2 x 2 hours per week).Attendance for at least 10 out of a total of 14 seminars is mandatory.
Method of Assessment
There is a midterm exam and a final exam. The final grade (G) is theaverage of the midterm exam (M) and final exam (F): G=(M+F)/2. There is
one retake which covers all topics for the midterm exam and the final
exam. The midterm exam or final exam cannot be retaken separately.
Literature
Adams and Essex, Calculus: A Complete Course, 9th edition, Pearson 2018,ISBN-10: 0134154363 • ISBN-13: 9780134154367.