School of Civil Engineering
CIVL2201 Structural Mechanics
Laboratory Sessions Information, Marking Criteria and Report Writing
This information sheet provides general instructions on how to prepare a laboratory report in Structural Mechanics.
Similar gene
Material Properties of Steel and Concrete
Report from Laboratory Demonstrations on 16 March 2012
As part of the unit of study CIVL2201 Structural Mechanics
NAME: Liang, HUANG
SID: 311152392
DATE OF REPORT: 25 APR 2012
ABSTRACT
This report describes a tens
The University of Sydney
School of Mathematics and Statistics
Answers to MATH2061 Linear Mathematics Exam 2010
1.
(a) 1
(b) Linearly independent.
(c) A plane in 3 dimensional space; x + y z = 0.
(e)
(i)
2
3
1
(ii)
(d)
1
0
0
(i)
1
2
3
3
4
1
0
0
(ii)
2.
(a)
The University of Sydney
School of Mathematics and Statistics
Answers to MATH2061 Linear Mathematics Exam 2009
1.
(a) . the only scalars a1 , a2 , . . . , an that satisfy a1 v1 + a2 v2 + . . . + an vn are
a1 = a2 = . . . = an = 0.
(b) Not linearly indepen
MATH2061 LINEAR MATHEMATICS QUIZ
School of Mathematics & Statistics, University of Sydney
The quiz will be held in lectures on Wednesday, January 23rd. The quiz will
start at 2pm and run for 45 minutes.
The quiz is worth 15% of the marks for the Linear
The University of Sydney School of Mathematics and Statistics Summer School MATH2061: Vector Calculus Quiz Info 2012
Information The quiz will start at 2pm on Monday 13 February, in the lecture The quiz runs for 45 minutes. The quiz is worth 15% of the Ve
The University of Sydney
School of Mathematics and Statistics
Summer School
MATH2061: Vector Calculus
2013
MATH2061 Linear Mathematics and Vector Calculus (Vector Calculus half)
LECTURER:
Ivan Guo Carslaw 807, ivan.guo@sydney.edu.au
COURSE TOPICS:
Line In
T HE U NIVERSITY OF S YDNEY P URE M ATHEMATICS Linear Mathematics 2011
Quiz 1b - Solutions
0 2 0 1. Find the eigenvalues of the matrix 1 1 0. 0 -1 1 a) -1, 1, -2 b) 1, 1, 2 c) 1, 1, -2 d) -1, 1, 2 Solution d)
2. The set S = t 1 | t R is a subspace of R2
The University of Sydney School of Mathematics and Statistics
Solutions to Vector Calculus - Quiz A
MATH2061/2067: Semester 1, 2011
1. Let F = 2x i + y j. Find the flux
C
F n ds, where C is the unit circle,
centre (0, 0), taken once anti-clockwise, and n
T HE U NIVERSITY OF S YDNEY
P URE M ATHEMATICS
Linear Mathematics
2016
Tutorial 3 (Preliminary and extra exercises)
Preliminary exercise
Your tutor will award you a preparation mark for this weeks tutorial if you have made a significant attempt on this qu
The University of Sydney
School of Mathematics and Statistics
Solutions to Tutorial 8
MATH2061: Vector Calculus
Summer School
1. Let F be the vector field F = (2x + sin yz)i + (2y + xz cos yz)j + (2z + xy cos yz)k.
(a) Show that F is conservative and find
T HE U NIVERSITY OF S YDNEY
P URE M ATHEMATICS
Linear Mathematics
2016
Tutorial 2 Solutions
n
o
R2 | y = 4x is a subspace of R2 .
Solution S is clearly non-empty, since 00 satisfies the equation y = 4x and is therefore in S.
a
Now suppose that u =
The University of Sydney
School of Mathematics and Statistics
Exercises 11
MATH2061: Vector Calculus
Summer School, 2016
Preparatory questions (attempt before the tutorial)
1. Using spherical coordinates, write equations which describe the surface of the
The University of Sydney
School of Mathematics and Statistics
Practice session 7
MATH2061: Vector Calculus
1. Evaluate
Z
Summer School
ds if = xy + z and C is the straight line segment from (1, 1, 1) to
C
(2, 2, 5).
2. Describe geometrically the vector f
T HE U NIVERSITY OF S YDNEY
P URE M ATHEMATICS
Linear Mathematics
2016
Tutorial 5
2 0 2
1. Let A = 0 3 0 .
0 0 3
a) Find all the eigenvalues for the matrix and, for each eigenvalue, find a basis for the corresponding eigenspace.
b) Write down a square m
The University of Sydney
School of Mathematics and Statistics
Solutions to Practice session 11
MATH2061: Vector Calculus
Summer School, 2016
1. Evaluate the following surface integral:
ZZ
(z + 2) dS,
S : x 2 + y 2 + z 2 = a2 .
S
Solution: In spherical co-
T HE U NIVERSITY OF S YDNEY
P URE M ATHEMATICS
Linear Mathematics
2016
Tutorial 6
1. A sequence of real numbers is defined by xn+3 = 2xn+2 + xn+1 2xn , with x0 = 0, x1 = 1
and x2 = 1.
xn+2
x
n+1
, and un+1 = Aun .
a) Let un = x
n
Show that A is the matri
The University of Sydney
School of Mathematics and Statistics
Solutions to Exercises 11
MATH2061: Vector Calculus
Summer School, 2016
1. Using spherical coordinates, write equations which describe the surface of the hemisphere x2 + y 2 + z 2 = 1, z 0.
Sol
The University of Sydney
School of Mathematics and Statistics
Exercises 12
MATH2061: Vector Calculus
Summer School, 2016
Preparatory questions (attempt before the tutorial)
1. Compute F and F, and verify that ( F) = 0 for
(a) F = sin x i + cos y j;
(b) F
T HE U NIVERSITY OF S YDNEY
P URE M ATHEMATICS
Linear Mathematics
2016
Tutorial 4 (Preliminary and extra exercises)
Preliminary exercises
Your tutor will award you a preparation mark for this weeks tutorial if you have made a significant attempt on these
T HE U NIVERSITY OF S YDNEY
P URE M ATHEMATICS
Linear Mathematics
2016
Tutorial 1 Solutions
1. Determine whether or not the vector
3
2
1
6 .
5 ,
4 ,
8
7
1
2
1
can be written as a linear combination of the vectors
3
Solution The question asks whether or
T HE U NIVERSITY OF S YDNEY
P URE M ATHEMATICS
Linear Mathematics
2016
Tutorial 1 (Preliminary and extra exercises)
Preliminary exercises
Your tutor will award you a preparation mark for this weeks tutorial if you have made a significant attempt on these
T HE U NIVERSITY OF S YDNEY
P URE M ATHEMATICS
Linear Mathematics
2016
Tutorial 5 (Preliminary and extra exercises)
Preliminary exercise
Your tutor will award you a preparation mark for this weeks tutorial if you have made a significant attempt on this qu
The University of Sydney
School of Mathematics and Statistics
Practice session 8
MATH2061: Vector Calculus
Summer School
1. (a) Find grad f if f (x, y) = x + 2xy 3y 2 .
(b) Find grad g if g(x, y, z) = ex cos(yz 2 ).
1
.
(c) Find if = p
x2 + y 2 + z 2
2. (
T HE U NIVERSITY OF S YDNEY
P URE M ATHEMATICS
Linear Mathematics
2016
Tutorial 4 Solutions
n 4 o
6
2
3 , 3 , 6
1. Let X =
. Find the dimension of Span(X).
2
1
0
Solution Note that the subset containing the first two vectors of X is linearly independent
(
T HE U NIVERSITY OF S YDNEY
P URE M ATHEMATICS
Linear Mathematics
2016
Tutorial 2 (Preliminary and extra exercises)
Preliminary exercises
Your tutor will award you a preparation mark for this weeks tutorial if you have made a significant attempt on these
The University of Sydney
School of Mathematics and Statistics
Solutions to Practice session 9
MATH2061: Vector Calculus
Summer School, 2016
1. Sketch the following regions:
(a) cfw_(x, y) R2 | 1 x 2, x y x
(b) cfw_(x, y) R2 | x = r cos , y = r sin , 0 2,
The University of Sydney
School of Mathematics and Statistics
Solutions to Tutorial 9
MATH2061: Vector Calculus
Summer School
1. The sphere x2 +y 2 +z 2 = 25 has a hole bored through it by the cylinder x2 +y 2 = 4.
Find the volume of that part of the sphe
The University of Sydney
School of Mathematics and Statistics
Solutions to Tutorial 11
MATH2061: Vector Calculus
Summer School, 2016
2
1. If F = y i + y j + xyz k, evaluate
ZZ
S
F n dS where S is the curved surface
of the cylinder x2 + y 2 = 4, 0 z 2, and