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MATH241 03xx: Calculus III

MATLAB Assignment 1

9/23/15

Solve the following exercises with MATLAB. Turn in a printout of what you typed into Matlab and the printouts of the plot windows for those questions asking you to plot. Solutions to be returned to your TA by the beginning of discussion on Thursday, 9/29.

For information about Matlab, computers location, and MATLAB tutoring, go to the Math. Dept. undergraduate resources web page:

http://www-math.umd.edu/undergraduate/resources.html.

1.    Please read the guide to MATLAB for MATH241, Part 1 by Justin Wyss-Gallifent,which you can find by clicking on the following link http://www2.math.umd.edu/ pnandori/1.pdf

You do not have to turn in anything for exercise 1, but pelase read this guide.

2.    (1 point each) Define the vectors ~a = 2~i +~j + 3^~k ^~b = −3~i +~j + 2^~k

(a)      Find the projection of ^~b onto ~a

(b)      Find a unit vector perpendicular to both ~a and ^~b.

(c)      Find the sine of the angle between ~a and ^~b.

3.    (1 point) Define four points P = (2,−1,3), Q = (0,7,9), R = (4,−9,−3) and S = (7,−6,−6) and then with two subtractions and one dot product all on one Matlab line show that the line through P and Q is perpendicular to the line through R and S.

4.    (2 points) Define four points P = (5,0,2), Q = (1,1,1), R = (0,1,−2) and S = (1,−2,−1). Find the distance from S to the plane containing the other three points.

√

5.    Define the vector valued function r(t) = sint~i + sint~j +      2cost^~k.

(a)      (1 point) Find the tangent vector T(t)

(b)      (2 points) Find the acceleration vector r⁰⁰(π/4)

6.    Plot each of the following. Set the view so that we can see all significant features.

(a)      (1 point) The function f(x) = (x + 1)²(x − 1)(x − 2)³.

(b)      (1 point) The vector valued function r

(c)      (2 point) The line segment joining (1,−1,1) and (−2,3,4). Hint: Write this line segment as a vector-valued function (d) (2 points) The plane x + 2y + 3z = 11.