Some common errors in hw2

Here are some comments on hw2:

 

General comment 1:

 

From now, I'm going to be strict about asking that you show all your work. 
Not enough work = 0 score. As a guide, if I can't do that vector norm in my 
head, then I expect you to show me the intermediate steps on paper. Don't 
just write a formula immediately followed by the answer. If you plot a graph 
or vector field, you must include explanation of your reasoning.

 

Basically I'm addressing those of you who are doing calculations or plots in 
wolfram or desmos, and then just copying out the results. Like the whole 
bunch of you that drew completely identical - but totally wrong - graphs for 
7b.

 

General comment 2:

 

Be careful that you copy out the formulas correctly from the book, and from 
one line of your work to the next. And use the right formula. Sometimes 
people were using r instead of r', or r'' instead of |r''| or whatever.

 

Scoring:

 

I marked questions 1 (4 points), 3 (6 points), 5 (4 points), 7 (2 points), 8 
(1 point) and up to 3 participation marks = 20 points total.  I don't have 
time to mark every question, so the 'participation' mark helps people who may 
have omitted a graded question but worked on others.

 

Comments on individual questions:

 

1a. Computation of normal vector - you can do it geometrically in 2D - but 
make sure the sign is right. Many of you who tried to compute it from the 
definition got hopelessly tangled up in the algebra.

b. The normal vector should be unit length - that's a check if you found it 
by computing.

c. Also the normal direction changes at every point of the curve - so don't 
reuse the same one at different points.

 

3 a. Very messy, lots of algebraic mistakes, and mistakes that propagated - 
the real answer will not be very messy so use some common sense in homework. 
If it starts getting bad, you probably made a mistake.

b. There are different formulas to compute things - some may be easier for 
some problems

c. Remember to use quotient rule to take derivative of a quotient function, 
i.e. Derive then make unit is NOT the same as make unit then derive.

d. Curvature and torsion are scalars! Not vectors. If you forget  | | (norm) 
in your formula, this should alert you to your mistake.

e. Example of common incorrect formula mistake: computing t' x n (instead of 
t x n) for b. That's of course why some of you got zero binormal; n is 
parallel to t'.

 

5. a. The center of mass formula involves ds, so if you used dt, you need to 
make sure |r'| is in integral.

b. A lot of wrong formulas used here: e.g.

b1. Rho is not derived, nor is x, y or z.

b2. On the other hand, for finding mass, you don't use |r'|^2 or an integral 
over |r'|

b3. Center of mass is a vector, not a scalar! It has three vector components. 
It's not just a number.

 

7-8 I ignored it this time, but from now on make sure you write some 
sentences explaining your thought processes.

 

I think you'll get these back on Monday. Good luck with the midterm! Study 
hard!