Multivariate Calculus and ordinary differential equations
MATH 1052

Winter 2011
MATH1052/1072
Multivariate Calculus
and
Ordinary Differential Equations
WORKBOOK
Second Semester, 2017
c School of Mathematics and Physics, The University of Queensland, Brisbane QLD 4072, Aus
tralia.
Multivariate Calculus and ordinary differential equations
MATH 1052

Winter 2011
MATH1052 Problem Sheet #5 Solutions
Semester 2, 2017
1. Use the triangle method to sketch the plane x 6y 2z = 6.
This plane has intercepts x = 6 on the xaxis, y = 1 on the yaxis and z = 3 on the
za
Multivariate Calculus and ordinary differential equations
MATH 1052

Winter 2011
MATH1052 Problem Sheet #7 Solutions
Semester 2, 2017
1. Let f : R2 cfw_(0, 0) 7 R be given by
xy 2
,
x2 + y 4
xy sin(x + 1)
f (x, y) =
,
x2 + 2y 2
x2 + 2xy + 2y 2
f (x, y) =
.
3x2 + 2y 2
f (x, y) =
Sh
Multivariate Calculus and ordinary differential equations
MATH 1052

Winter 2011
MATH1052 Problem Sheet #3 Solutions
Semester 2, 2017
1. The ODE xy 00 3y 0 12y/x = 0 has y = x6 as one solution. Use the reduction of order
technique to find another linearly independent solution.
Gue
Multivariate Calculus and ordinary differential equations
MATH 1052

Winter 2011
MATH1052 Problem Sheet #7
Semester 2, 2017
These questions are for practice, and discussion in your tutorial. They will not be
marked and do not have to be handed in.
Topic: Partial Derivatives & Tang
Multivariate Calculus and ordinary differential equations
MATH 1052

Winter 2011
MATH1052 Problem Sheet #1
Semester 2, 2017
These questions are for practice, and discussion in your tutorial. They will not be
marked and do not have to be handed in.
Topics: Equilibrium Solutions, Sl
Multivariate Calculus and ordinary differential equations
MATH 1052

Winter 2011
MATH1052 Problem Sheet #8
Semester 2, 2017
These questions are for practice, and discussion in your tutorial. They will not be
marked and do not have to be handed in.
Topic: Directional Derivatives an
Multivariate Calculus and ordinary differential equations
MATH 1052

Winter 2011
MATH1052 Problem Sheet #6
Semester 2, 2017
These questions are for practice, and discussion in your tutorial. They will not be
marked and do not have to be handed in.
Topic: Contours and Cross Section
Multivariate Calculus and ordinary differential equations
MATH 1052

Winter 2011
MATH1052 Problem Sheet #4
Semester 2, 2017
These questions are for practice, and discussion in your tutorial. They will not be
marked and do not have to be handed in.
Topic: Conic Sections
1. Without
Multivariate Calculus and ordinary differential equations
MATH 1052

Winter 2011
MATH1052 Problem Sheet #3
Semester 2, 2017
These questions are for practice, and discussion in your tutorial. They will not be
marked and do not have to be handed in.
Topic: Second Order ODEs
1. The O
Multivariate Calculus and ordinary differential equations
MATH 1052

Winter 2011
MATH1052 Problem Sheet #6 Solutions
Semester 2, 2017
1. Sketch the contours f = 9, 0, 9, 18 of the function f (x, y) = 9y 2 x2 . Label each of the
contours and determine all x and y intercepts.
z = f
Multivariate Calculus and ordinary differential equations
MATH 1052

Winter 2011
MATH1052 Problem Sheet #1 Solutions
Semester 2, 2017
1. What is the order of each of these differential equations?
d2 g
(a) 2 + sin = 0 second order.
dt
l
(b) y 0 (x) = y 2 first order.
(c) y 2
d3 y d
Multivariate Calculus and ordinary differential equations
MATH 1052

Winter 2011
MATH1052 Problem Sheet #2 Solutions
Semester 2, 2017
1. Solve the following initial value problems.
(a)
dy
= cos t, y() = 2. You can integrate directly to obtain the general solution
dt
y = sin t + c.
Multivariate Calculus and ordinary differential equations
MATH 1052

Winter 2011
MATH1052 Problem Sheet #5
Semester 2, 2017
These questions are for practice, and discussion in your tutorial. They will not be
marked and do not have to be handed in.
Topic: Equations of Lines and Pla
Multivariate Calculus and ordinary differential equations
MATH 1052

Winter 2011
MATH1052 Problem Sheet #8 Solutions
Semester 2, 2017
1. Find the gradient of f at the specified point:
a) f (x, y) = (x + y) sin xy at (0, 1),
b) f (x, y) = sin(xy) + cos(xy) at (, 1),
c) f (x, y) = x
30594/01 Comply with infection control policies and procedures in animal work  Written Assessment
MATH 101

Fall 2017
Australian Veterinary Association
Guidelines for
Veterinary Personal
Biosecurity
February 2013
Preface 1
1. Executive summary
2
2. Introduction
3
2.1 Background and objectives
3
3. Zoonotic disease
30594/01 Comply with infection control policies and procedures in animal work  Written Assessment
MATH 101

Fall 2017
Question 1: Research and list four classes of infectious microorganisms
Question 2: In the additional resources you will find the Guidelines for Veterinary
Personal Biosecurity document from the AVA
The STeps To Long
Division
ivi  The number inside The house wiTh The number
ouTsi e of The house
* I i I  The number ouTside of The house b The number on
Top 0? The house Y
The number inside The hou
Maths Quiz
1. Calculate 438 296
2. Which number is nearest to 450?
350, 398, 515, 630 or 750
3. 549 x 6
4. 268 x 63
5. 180 3
6. Michael bought 7 packs of 8 chocolate bars. How many chocolate bars did
Word problems
1. 15 children are at a party. 3 go home. The others share
48 sweets. How many do they each get?
2. 9 groups of 9 children go to a sports day. 7 are sick. How
many children take part?
3.
Questions simultaneous equations
1. 1000 tickets were sold. Adult tickets cost $8.50, children's cost $4.50, and a total of
$7300 was collected. How many tickets of each kind were sold?
2. A woman is
Word problems
1. Kelsey had 20 stickers. She bought 14 stickers from a store in
the mall and got 10 stickers for her birthday. Then Kelsey gave 2
of the stickers to her sister and used 21 to decorate
Data Independence
DBMS Languages and Interfaces
The DBMS Environment
Classification of DBMSs
Module 8
Database Architecture
INFS1200 / INFS7900
Introduction to Information Systems
Data and Knowledge E
Relational Query
Basic SQL DDL and DML
The Select Statement
Module 7
SQL
INFS1200 / INFS7900
Information Systems
Data and Knowledge Engineering Group
School of Information Technology and Electrical En
Design Guidelines
Functional Dependency
Normalization
Properties of Decomposition
Module 6
Functional Dependencies
and Normalization
INFS1200 / INFS7900
Information Systems
Data and Knowledge Engineer