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
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
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
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 o
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
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 n
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. T
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:
Tayl
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:
Intui
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
Famil
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
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 w
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: .
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: .
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:
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 1
13. (a) Find the absolute max and the absolute min of f (x, y) = x4 y4 4mg + 2,
onthesetD=cfw_(x,y): ngg3, Ogyg 2.
(b) Find the absolute max and the absolute min of f (m, y) = x2 y2 2y + l,
on the set
)1.
e.g.2 Find the coordinates of the stationery point of the
curve y=x3 -4x+l . Is the point o more or- min?
2
Solution: y=x 4x+l - (1)
= =2.1t:4
d it
_y=0 =b 2x4=0 =5 x=2
air
Substitute in (1): (2].
THE UNIVERSITY OF SYDNEY
Semester 1, 2017
Information Sheet for MATH1901 Differential Calculus (Advanced)
Websites: It is important that you check both the Junior Mathematics website and the MATH1901
ARENES
CONTENTS
Prior knowledge
Structure of benzene
Thermodynamic stability
Delocalisation
Electrophilic substitution
Nitration
Chlorination
Friedel-Crafts reactions
Further substitution
ARE
3. Chemistry
Complete this table for the atoms listed:
atom name atomic number number 0f number 0f
neutrons electrons
m. I: In: Chlorine _- avg/jg
261 I I 9:
104 Rf It; _ W
[/2 mark per correct row =
T HE U NIVERSITY OF SYDNEY
SCHOOL OF M ATHEMATICS AND STATISTICS
Solutions to Problem Sheet for Week 2
MATH1901: Differential Calculus (Advanced)
Semester 1, 2017
Web Page: sydney.edu.au/science/maths
T HE U NIVERSITY OF SYDNEY
SCHOOL OF M ATHEMATICS AND STATISTICS
Solutions to Problem Sheet for Week 4
MATH1901: Differential Calculus (Advanced)
Semester 1, 2017
Web Page: sydney.edu.au/science/maths
T HE U NIVERSITY OF SYDNEY
SCHOOL OF M ATHEMATICS AND STATISTICS
Solutions to Problem Sheet for Week 5
MATH1901: Differential Calculus (Advanced)
Semester 1, 2017
Web Page: sydney.edu.au/science/maths
The University of Sydney
School of Mathematics and Statistics
Solutions to Problem Sheet 4 (Week 5)
MATH1901: Dierential Calculus (Advanced)
Semester 1, 2016
Topics covered and aims
In lectures last w
7. For what values of the constants a, b, c (with b 6= 0) is the function with formula
f (x) =
x a
bx c
and domain cfw_x 2 R | x 6= c/b
equal to its own inverse? (Hint: It may help to draw the graph.)
The University of Sydney
School of Mathematics and Statistics
Solutions to Problem Sheet 10 (Week 11)
MATH1901: Dierential Calculus (Advanced)
Semester 1, 2016
Topics covered and aims
In lectures last
The University of Sydney
School of Mathematics and Statistics
Solutions to Problem Set 5 (Week 6)
MATH1901: Dierential Calculus (Advanced)
Semester 1, 2016
Topics covered and aims
In lectures last wee
The University of Sydney
School of Mathematics and Statistics
Solutions to Problem Sheet 8 (Week 9)
MATH1901: Dierential Calculus (Advanced)
Semester 1, 2016
Topics covered and aims
In lectures last w