THE UNIVERSITY OF SYDNEY
Math1901 Differential Calculus (Advanced)
Semester 1
2013
Tutorial Week 2
1. (This question is a preparatory question and should be attempted before the tutorial.
Answers are provided at the end of the sheet please check your work
The University of Sydney
School of Mathematics and Statistics
Problem Set 3 (Week 4)
MATH1901: Differential Calculus (Advanced)
Semester 1, 2016
Topics covered and aims
In lectures last week:
General definition of a function f : A B.
Domain, codomain, a
The University of Sydney
School of Mathematics and Statistics
Solutions to Problem Sheet 2 (Week 3)
MATH1901: Differential Calculus (Advanced)
Semester 1, 2016
Topics covered and aims
In lectures last week:
Roots of complex numbers.
Complex exponential
The University of Sydney
School of Mathematics and Statistics
Solutions to Problem Sheet 1 (Week 2)
MATH1901: Differential Calculus (Advanced)
Semester 1, 2016
Topics covered and aims
In lectures last week:
Set notation, and number systems N Z Q R C, int
The University of Sydney
School of Mathematics and Statistics
Solutions to Problem Set 3 (Week 4)
MATH1901: Differential Calculus (Advanced)
Semester 1, 2016
Topics covered and aims
In lectures last week:
General definition of a function f : A B.
Domain
8026A Semester 1 2013
The University of Sydney
School of Mathematics and Statistics
MATH1902
Linear Algebra (Advanced)
June 2013
Lecturer: Holger Dullin
Time Allowed: One and a half hours
Family Name: . . . . . . . . . . . . . . . . . . . . . . . . . . .
Semester 1
1. (a)
2012
MATH1902 Long Answer Solutions
1
2
1
1 1 2
1
2
1
2
1
0 3 3
1
3
1 0 1
0 1
1
1
1
(2 marks)
Putting z = t yields y = 1 t, x = 1 + t, and the general solution is
(x, y, z) = (1 + t, 1 t, t)
as t ranges over the reals.
(1 mark)
(b) In ad
THE UNIVERSITY OF SYDNEY
Math1901 Differential Calculus (Advanced)
Semester 1
2013
Tutorial Solutions Week 9
1. (This question is a preparatory question and should be attempted before the tutorial. Answers are provided at the end of the sheet please check
8026A SEMESTER 1 2011
THE UNIVERSITY OF SYDNEY
SCHOOL OF MATHEMATICS AND STATISTICS
MATH 1902
LINEAR ALGEBRA (ADVANCED)
June 2011 LECTURER: D. Easdown
TIME ALLOWED: One and a half hours
Family Name: .
Other Names:
r._._._._.
This examination has two secti
8026A SEMESTER 1 2012
THE UNIVERSITY OF SYDNEY
SCHOOL OF MATHEMATICS AND STATISTICS
MATH 1902
LINEAR ALGsssA (ADVANCED)
June 2012 Lsorosss: D. Eesdown
TIME ALLOWED: One and a half hours
Family Name: .
Other Names:
.
.
MARKERS USE
ONLY
This examination has
The University of Sydney
School of Mathematics and Statistics
Sample Quiz 1
MATH1903: Integral Calculus and Modelling (Advanced)
Semester 2, 2015
Lecturers: Florica-Corina Crstea and Anne Thomas
Family name:
Other names:
SID:
Day:
Time:
Room:
Signature:
P
The University of Sydney
School of Mathematics and Statistics
Problem Sheet 2 (Week 3)
MATH1901: Dierential Calculus (Advanced)
Semester 1, 2016
Topics covered and aims
In lectures last week:
Roots of complex numbers.
Complex exponential function ez = e
The University of Sydney
School of Mathematics and Statistics
Problem Sheet 2 (Week 3)
MATH1901: Differential Calculus (Advanced)
Semester 1, 2016
Topics covered and aims
In lectures last week:
Roots of complex numbers.
Complex exponential function ez =
THE UNIVERSITY OF SYDNEY
Math1901 Differential Calculus (Advanced)
Semester 1
2013
Tutorial Solutions Week 6
(These preparatory questions should be attempted before the tutorial. Answers are provided at
the end of the sheet please check your work.)
1. Let
THE UNIVERSITY OF SYDNEY
Math1901 Differential Calculus (Advanced)
Semester 1
Tutorial Solutions Week 13
2013
1. (This question is a preparatory question and should be attempted before the tutorial. Answers are provided at the end of the sheet please chec
THE UNIVERSITY OF SYDNEY
Math1901 Differential Calculus (Advanced)
Semester 1
Tutorial Solutions Week 3
2013
1. (This question is a preparatory question and should be attempted before the tutorial. Answers are provided at the end of the sheet please check
THE UNIVERSITY OF SYDNEY
Math1901 Differential Calculus (Advanced)
Semester 1
Tutorial Solutions Week 10
2013
(These preparatory questions should be attempted before the tutorial. Answers are provided at
the end of the sheet please check your work.)
1. Sk
THE UNIVERSITY OF SYDNEY
Math1901 Differential Calculus (Advanced)
Semester 1
Tutorial Solutions Week 4
2013
1. (This question is a preparatory question and should be attempted before the tutorial. Answers are provided at the end of the sheet please check
THE UNIVERSITY OF SYDNEY
Math1901 Differential Calculus (Advanced)
Semester 1
2013
Tutorial Solutions Week 11
1. (This question is a preparatory question and should be attempted before the tutorial. Answers are provided at the end of the sheet please chec
The University of Sydney
MATH1901/1906 Differential Calculus (Advanced)
Semester 1
Assignment 1
2013
This assignment is due by 4:00pm on Thursday, 16 May 2013. It
should be posted in the locked collection boxes on the verandah of
Carslaw Level 3. These bo
MAXIMA AND MINIMA:
-TURNING POINTS / POINTS OF INFLECTIONGRAPH OF A FUNCTION y=f(x)
-EXAMPLES:
1. The number of the newspaper copies distributed is given by
minimum number of copies distributed from 1995 to 2002.
= 50
200 + 10000, where t is in years. Fi
The University of Sydney
School of Mathematics and Statistics
Problem Sheet 4 (Week 5)
MATH1901: Differential Calculus (Advanced)
Semester 1, 2016
Topics covered and aims
In lectures last week:
Intuitive concept of a limit.
Formal definition of limits i
The University of Sydney
School of Mathematics and Statistics
Problem Sheet 9 (Week 10)
MATH1901: Differential Calculus (Advanced)
Semester 1, 2016
Topics covered and aims
In lectures last week:
Taylors Theorem.
Curves in R2 and R3 .
After completing th
The University of Sydney
School of Mathematics and Statistics
Problem Sheet 6/7 (Week 7/8)
MATH1901: Differential Calculus (Advanced)
Semester 1, 2016
Note: The quiz was held in tutorials in Week 7. Therefore this problem sheet covers material
covered in
The University of Sydney
School of Mathematics and Statistics
Problem Sheet 1 (Week 2)
MATH1901: Differential Calculus (Advanced)
Semester 1, 2016
Topics covered and aims
In lectures last week:
Set notation, and number systems N Z Q R C, interval notatio
The University of Sydney
MATH1902 Linear Algebra (Advanced)
Semester 1
Exercises for Week 3
2017
Preparatory exercises should be attempted before coming to the tutorial. Questions labelled with
an asterisk are suitable for students aiming for a credit or
The University of Sydney
MATH1902 Linear Algebra (Advanced)
Semester 1
Longer Solutions to Selected Exercises for Week 1
11.
2017
6
8
d
By Pythagoras d = 82 + 62 = 10 . If is the angle to the horizontal then cos =
6/10 , yielding an angle 53 . Thus the re
The University of Sydney
MATH1902 Linear Algebra (Advanced)
Semester 1
5.
Longer Solutions to Selected Exercises for Week 4
2017
We have
QP QR =
2i + j + 3k i + 2j k = 7i + 5j + 3k .
Hence the area of the triangle P QR is
7i 5j 3k
83
=
.
2
2
6.
(i) Obse
The University of Sydney
MATH1902 Linear Algebra (Advanced)
Semester 1
Longer Solutions to Selected Exercises for Week 6
2017
1.
Making each expression equal to 0 produces the point P (2, 1, 4), and equal to 1
produces the point Q(5, 1, 5). A vector in th
The University of Sydney
MATH1902 Linear Algebra (Advanced)
Semester 1
7.
Longer Solutions to Selected Exercises for Week 3
2017
(i) First observe that QP = 2i + 2j + k and QR = i + 2j + 2k , yielding
QP QR = 2 + 4 + 2 = 8 > 0 ,
so that P QR is acute (n