100% Original, Plagiarism Free, Tailored to your instructions

Order Now!

Department of Computer and Mathematical Sciences

Department of Computer and Mathematical SciencesAssignment # 2
You are expected to work on this assignment prior to your tutorial in the week of
January 18th, 2016. You may ask questions about this assignment in this tutorial.
At the beginning of your tutorial in the week of January 25th, 2016 you will be asked
to hand in the assignment. NO ASSIGNMENTS will be accepted at the end of the
tutorial or after the tutorial. Assignments MUST BE submitted ONLY in the tutorial you
are registered for.
A. Readings: 1. Lecture notes: LW2
2. Readings: Marsden & Tromba, Vector Calculus, 6e.
Ch 4.3, Ch 7.1- 7.2.
3. Vector Fields (Notes).
B. Problems:
1. Sketch the vector fields
(x, y) = !
i + x
(x, y) = (x, x2 )
Hint: Plot vectors at several key points along y = ±x and scale the vector field.
2. Show that the curve !
c(t) = (t2, 2t !1, t ), t > 0 is a flow line of the velocity vector
(x, y, z) = (y +1, 2,
3. Find and draw the flow lines of the velocity vector field
(x, y) = (!2y,
Hint: Write the Cartesian equation of the family of flow lines, eliminating the
4. Determine whether or not each of the given vector fields is conservative.
If the vector field is conservative, find a potential function for the field.
(x, y) = (x2 + y2 )
i ! 2x
(x, y) = (2x + ycos xy, x cos xy !1)
5. The conservative field is also called the gradient field. Prove that direction!f is
the direction in which f is increasing the fastest.
6. Find the mass of the thin wire if its linear density is given by f.
a) The wire has the form of a semicircle
c(t) = (a, asint, acost), a > 0, 0 ! t !! , f (x, y, z) = xy
b) The wire is the parabola
y = x2, z = 0; from A(0, 0, 0), to B(1,1, 0), f (x, y, z) = x + y + z
c) The wire has been bent in the shape of the polar graph r =!, 0 !! !

And the density at the point (!,! ) is 2! .
7. Find the work done by the force field
(x, y, z) = (x, y) when a particle is moved
along the straight-line segment from (0,0,1) to (3,1,1).
8. Evaluate each of the following Integrals
a) x dy ! ydx,
c(t) = (cost, sint), 0 ” t ” 2!
(x, y, z) = y
i + 2x
+ y
c(t) = t
i + t2 !
j + t3 !
k, 0 ” t “1

Our Service Charter

  1. Excellent Quality / 100% Plagiarism-Free

    We employ a number of measures to ensure top quality essays. The papers go through a system of quality control prior to delivery. We run plagiarism checks on each paper to ensure that they will be 100% plagiarism-free. So, only clean copies hit customers’ emails. We also never resell the papers completed by our writers. So, once it is checked using a plagiarism checker, the paper will be unique. Speaking of the academic writing standards, we will stick to the assignment brief given by the customer and assign the perfect writer. By saying “the perfect writer” we mean the one having an academic degree in the customer’s study field and positive feedback from other customers.
  2. Free Revisions

    We keep the quality bar of all papers high. But in case you need some extra brilliance to the paper, here’s what to do. First of all, you can choose a top writer. It means that we will assign an expert with a degree in your subject. And secondly, you can rely on our editing services. Our editors will revise your papers, checking whether or not they comply with high standards of academic writing. In addition, editing entails adjusting content if it’s off the topic, adding more sources, refining the language style, and making sure the referencing style is followed.
  3. Confidentiality / 100% No Disclosure

    We make sure that clients’ personal data remains confidential and is not exploited for any purposes beyond those related to our services. We only ask you to provide us with the information that is required to produce the paper according to your writing needs. Please note that the payment info is protected as well. Feel free to refer to the support team for more information about our payment methods. The fact that you used our service is kept secret due to the advanced security standards. So, you can be sure that no one will find out that you got a paper from our writing service.
  4. Money Back Guarantee

    If the writer doesn’t address all the questions on your assignment brief or the delivered paper appears to be off the topic, you can ask for a refund. Or, if it is applicable, you can opt in for free revision within 14-30 days, depending on your paper’s length. The revision or refund request should be sent within 14 days after delivery. The customer gets 100% money-back in case they haven't downloaded the paper. All approved refunds will be returned to the customer’s credit card or Bonus Balance in a form of store credit. Take a note that we will send an extra compensation if the customers goes with a store credit.
  5. 24/7 Customer Support

    We have a support team working 24/7 ready to give your issue concerning the order their immediate attention. If you have any questions about the ordering process, communication with the writer, payment options, feel free to join live chat. Be sure to get a fast response. They can also give you the exact price quote, taking into account the timing, desired academic level of the paper, and the number of pages.

Excellent Quality
Zero Plagiarism
Expert Writers

Instant Quote

Instant Quote
Single spaced
approx 275 words per page
Urgency (Less urgent, less costly):
Total Cost: NaN

Get 10% Off on your 1st order!