Mathematics 2A03: Mid-Term Test 2
Instructor: Dr. D. Pelinovsky
Date: November 6, 2012, 10:30-11:20
NAME:
STUDENT NUMBER:
Instruction: Textbooks, lecture notes, and McMaster calculators are allowed on the
test. The duration of this test is 50 minutes. The
Math 2A03 Ch. 13 Worksheet
To use Sage you can:
Install Sage on your own computer: go to http:/www.sagemath.org/ and click on the
download link. Follow the instructions for your operating system (Linux, OS X, or Windows).
After starting Sage, either log
Math 2A03 Ch. 14 Worksheet
Plotting functions of 2 variables:
The plot3d function in Sage makes 3D graphs of functions of 2 variables. Type the following
example into an empty cell and evaluate it.
var(x,y)
plot3d(x^2+y^2,(x,-1,1),(y,-1,1),aspect_ratio=[1
MATHEMATICS 2A03 - sample exam
1. Consider the following scalar function of two variables:
f (x, y) = y log(x2 + y 2 ).
(a) Is f continuous at (0, 0)? Prove it.
(b) If f continuously dierentiable at (0, 0)? Prove it.
(c) Compute the linear approximation t
Math 2A03 Ch. 16 Worksheet
2D vector elds:
2D vector eld plots are implemented in Sage via the plot_vector_field function. This
function takes as input a pair of functions of two variables and ranges for the x- and y-axes.
As a rst example, you can plot t