Calculus 2

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 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 partial derivatives, also using the chain rule e) find extreme values of functions of two variables, with and without contraints
f) calculate with complex numbers
g) solve several first- and second-order differential equations (separable equations, first-order linear equations, second-order linear equations with constant coefficients).

COURSE CONTENT
Series, Real functions of Several Variables, Differential equations.

Topics that will be treated are:
1) Sequences, Series, Power Series, Taylor Series
2) Partial Derivatives, Chain Rule
3) Extreme Values
4) Double Integrals, Polar Coordinates
5) Complex Numbers
6) First and Second Order Differential Equations

TEACHING METHODS
Lectures (3x per week) and tutorials (2x per week)

TYPE OF ASSESSMENT
Midterm exam and Final exam. More details can be found in the manual on Canvas.

RECOMMENDED BACKGROUND KNOWLEDGE
Calculus 1