Course Objective

At the end of this course the student is able to
a) 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
contraints
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

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) for
Calculus 1 is the average 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. Midterm exam or final exam cannot be retaken
separately! More details can be found in the manual on Canvas.

Literature

Adams and Essex, Calculus: A Complete Course, 9th edition, Pearson 2018,
ISBN-10: 0134154363 • ISBN-13: 9780134154367.

Target Audience

1 BA

Additional Information

Attendance for at least 10 out of a total of 14 seminars is mandatory.

Recommended background knowledge

Calculus 1