Introduction to Algebraic Coding Theory
Supplementary material for Math 336 Cornell University
Sarah A. Spence
Contents
1 Introduction 2 Basics 2.1 Important code parameters . . 2.2 Correcting and det
2012-2013 Winter Term 2
MATH 317 Calculus IV - Section 202
Practice Midterm 1
1. Consider the curve with the parametrization
2 4 2 3/2
r(t) = (t ,
t , 2t),
3
t0
(a) Find the length of the curve from t
MATH 317 Assignment 3
Due Tuesday, March 8, 2016 in class
You must show your work to get full marks. Hand in this question sheet with your
assignment.
!
! x
1 $
1. Consider the vector field shown belo
MATH 317 Assignment 2
Due Friday, January 29, 2016 in class
You must show your work to get full marks.
1. If two objects travel through space along two different curves, it is often
important to know
Textbook Practice Problems
The following problems from the exercises at the end of each section of the textbook are
recommended for practice. Try to do as many of them as you can. Odd-numbered
questio
MATH 317 Midterm 2 Topics
Midterm Exam:
Tuesday, March 22, 2016
3:304:50
Calculators are allowed.
Textbook sections:
16.1 16.5
Vector Fields, Line Integrals and the Fundamental Theorem, Greens Theorem
MATH 317 Midterm 1 Topics
Midterm Exam:
Tuesday, February 16, 2016 3:304:50
Calculators are allowed. The following formulas will be provided:
T(t ) =
r (t )
r (t )
N(t ) =
T(t )
T(t )
B(t ) = T(t ) N(
MATH 317 Assignment 5
Due Friday, April 8, 2016 in class
You must show your work to get full marks. (Do not use Maple unless indicated.)
1. Find an equation of the tangent plane to the surface with pa
MATH 317 Midterm 2 Sample Questions
!
1. Sketch the vector field F(x, y) = ( x +1) i + y j . Based on your sketch, how would you describe
all the flow lines in this vector field?
!
2. Suppose that F i
MATH 317 Sample Midterm Questions
1. Consider the plane curve with parametric equations
x(t) = t 2sin t, y(t) = 1 cost, 0 t 4 .
a. Compute
dy
d2y
and
.
dx
dx 2
b. At what points does the curve have a
MATH 317 Assignment 4
Due Friday, April 1, 2016 in class (no fooling!)
You must show your work to get full marks. Some questions indicate that you should use
Maple. (Do not use Maple for any other que
Suppose that four ants sit on the corners of a square with side length L. Let
~x1 , ~x2 , ~x3 , ~x4 be the position vectors of the four ants and suppose that each one
travels with constant speed in th
SOLUTION TO QUIZ 1
Question 1. Find a parametrization of the intersection of x2 + y 2 = 4
and the surface z = xy.
Solution: Any points on the cylinder x2 + y 2 = 4 can be written as (2 cos t, 2 sin t,
Quiz 2 Solutions, Math 317
October 1, 2017
Problem 1. Suppose an object moves so that its acceleration is given by
~a = h 3 cos t, 2 sin t, 0i
and suppose that at t = 0 the object is located at (3, 2,
Suppose that a particle of mass m is acted on by a central force whose
magnitude is proportional to 1/rd for some integer d. That is
F=
mC
rd+1
r
where r = |r| and C is a positive constant. In the cas
MATH 317 Assignment 1
Due Tuesday, January 19, 2016 in class
You must show your work to get full marks.
1.
Consider the curve with parametric equations x = et , y = e2t (t R)
a. Sketch the curve by ha
15.1 Vector Fields
CHAPTER 15
VECTOR CALCULUS
Vector Fields
15.1
(page 554)
(page 554)
A vector field assigns avector to each point (x, y) or (x, y, 2). In two dimensions F(x, y) = M(x, ~ ) i + N ( xy
2012:2013 Winter Term 2 S o Ind" To ms
MATH 31? Calcuns EV . Sectiun 282
Prantice Midterm 1
1. Consider the curve with the parametrization
4 2.
W) = (t2, mgr? 2t), t a 0
(a) Find the length of the
l olmtrom9 l
Math 317 . Second l\/lidterrn
Mar 15, 2013
Name: Student ID: M_.W._m,_u.
Instructor: ._ Section: W_.m_r._W . -
1. Do not open this exam until you are told to do so.
2. SPECIAL INS
(imam
Math 317 1* irst Midterm
Feb 1, 2013
Name: W Student ID:
Instructor: W_WWW Section:
'1. Do not open this exam until you are told to do so.
2. SPECIAL INSTRUCTIONS: No books, notes, or calc
MATH 317
HMW 1
End of week 1
Solutions HMW1: Questions 5 and 6 of Exercises 13.1.
1. (4 points) Find a vector function for the curve of intersection of x2 + y 2 = 9 and y + z = 2.
Solutions:
We have:
Midterm
Math 317
Section 102
Student Number
Name
No books, notes or calculators are allowed.
Problem 1 (25 points): Answer true or false to the following questions. No explanation is required.
1. The
Midterm
Math 317
Name
February 14th, 2007
Student Number
No books, notes or calculators are allowed.
Problem 1 (10 points): Consider the curve with the parameterization
+
*
2 4 2 3/2
t , 2t .
r(t) = t
Midterm
Math 317
Section 102
Student Number
Name
No books, notes or calculators are allowed.
Problem 1 (25 points): Consider the curve with the parameterization
r(t) = ti + t2 j + tk
for < t < .
1. (1
SOLUTIONS TO HOMEWORK ASSIGNMENT #2
1. The position of a particle is given by r(t) = 3 cos t, 4 cos t, 5 sin t , where > 0.
(a) Find the velocity vector v(t).
(b) Find the acceleration vector a(t).
(c
SOLUTIONS TO HOMEWORK ASSIGNMENT # 3
1. Find the velocity and position vectors for all time if:
(a) a(t) = j time, v(0) = v(0) =< 1, 1, 1 > and r(0) =< 0, 0, 1 > .
(b) a(t) = t, t2 , cos 2t v(0) =< 1,
SOLUTIONS TO MIDTERM #1, MATH 317
1. (9 marks) Answer true or false to the following questions by putting either true or false
in the boxes. If the answer is true give a proof or valid reason, and if