School of Mathematics and Statistics
Summer School 2016
Information Sheet SS1003
General Information about Summer School Courses offered by the School can be found
on the Summer School Web page.
http://www.maths.usyd.edu.au/u/UG/SS/
SS1003 Integral Calculus and Modelling (Summer School)
General Information
The unit of study MATH1003 Integral Calculus and Modelling is offered at the
Summer School as SS1003.
The Exercises and Course Notes used will be essentially the same as those used in
the regular course.
Website http://www.maths.usyd.edu.au/u/UG/SS/SS1003/
Lecturer Dr Bob Crossman: bobc@maths.usyd.edu.au : Room 527 Carslaw
Course Notes
NR O’Brian, CJ Durrant and DJ Galloway. Integral Calculus and Modelling. School of
Mathematics and Statistics, University of Sydney, Sydney, NSW, Australia, 2010.
The course notes have essentially not changed for the last few years. They are the
same notes used in Semester 2 MATH1003. Recent previous editions of the notes are
suitable.
The notes are now available for purchase at Kopystop, 55 Mountain St Broadway,
phone: 9211 2733. Please note that Kopystop will be closing at 3pm on Tuesday 22nd
December 2015 and re-opening on Wednesday 13 January 2016.
An extract of the first section of the notes will be available via a link on the website for
the first two weeks
Exercises

The Exercises and Objectives (E1-E12) sheets will be available on the SS1003
website before the day’s lectures. It is intended that they be read and attempted
before the next day’s tutorial which will cover similar topics

The Tutorial sheets (T2-T12) will be handed out in each tutorial on days 2 to 12.
All the exercises from both the Exercises and Objectives sheets and the Tutorial sheets
are an essential component of the course. They should be attempted before accessing
the solutions which will be posted on the website on a daily basis.
They will essentially be the same as the Exercises used in Semester 2, 2015 in
MATH1003.
Tutorials
Tutorials are held every day following the lecture and will generally focus on material
covered the previous day in the lecture. They will be conducted using Board Format.
Before the Tutorial, you should have attempted the preceding Exercises and Objectives
Sheet.
T1: Room 451
T2: Room 452
T3: Room 453
Alex Casella
Alexander
Chalmers
Student Surname
Chen
To G
James
Gregory
T5: Room 359
Cherry
Ballangan
T6: Room 361
Pantea
Pooladvand
Student Surname
N to V
W to Z
A to
Capa
T4: Room 454
Van Nguyen
Li to M
H to La
Students will be allocated to their tutorial in the first lecture using the alphabetical
breakdown by Family Name above.
Tutorial attendance will be recorded but not count quantitatively towards the
assessment.
Assessment
The final mark for this unit will be calculated as follows:
70%: Examination will cover material in the course notes, the 11 Tutorial sheets, the 12
Exercise and Objective sheets, the 2 assignments and the 2 quizzes. It is tentatively
scheduled for 1:50 pm Tuesday 23rd February 2014, in one or both of Rooms 350/351.
The format is half Multiple Choice questions and half Extended Answer. Further details
will be posted towards the end of the course.
15%: Quiz 1 – will be conducted in the lecture at 2pm Monday 1st Feb and based on
material covered in Tutorial Sheets 2, 3, and 4 and Exercise Sheets 1, 2, and 3 .
15%: Quiz 2 – will be conducted in the lecture at 2pm Monday 15th Feb based on
material in Tutorial Sheets 6, 7, 8 and 9 and Exercise Sheets 5, 6, 7 and 8.
Better Mark: The better mark principle will apply to each of the two quizzes individually.
If the pro- rata performance on the exam is greater than that on a quiz, that quiz mark
will be replaced by the pro-rata exam mark out of 15.
Quizzes will be held at 2pm in the lecture on that day. Because of the use of the
better mark principle, there will be no special consideration given for
circumstances which cause a quiz to be missed.
Passing Final Grades: are returned within one of the following bands:

High Distinction (HD), 85--100: representing complete or close to complete
mastery of the material;

Distinction (D), 75--84: representing excellence, but substantially less than
complete mastery;

Credit (CR), 65--74: representing a creditable performance that goes beyond
routine knowledge and understanding, but less than excellence; and

Pass (P), 50--64: representing at least routine knowledge and understanding
over a spectrum of topics and important ideas and concepts in the course.
A student with a passing or higher grade should be well prepared to undertake further
studies in mathematics on which this unit of study depends.
Assignments
Two assignments will be set and available from the website. Assignments do not count
quantitatively towards your final mark. They are intended to provide a source of
feedback. They will be promptly marked with comment where relevant and returned
before the corresponding quizzes.

Assignment 1 is based on material in Tutorials 2, 3 and 4 and is due at the start
of the tutorial on Monday 25th Jan. It is specifically intended to assist in
preparation for Quiz 1.

Assignment 2 is based on material in Tutorials 6, 7 and 8 and is due at the start
of the tutorial on Monday 8th Feb. It is specifically intended to assist in preparation
for Quiz 2.
.
Timetable
Week
Day
Week 1
Week 2
Week 3
Week 4
Week 5
Week 6
week 7
1
2
3
4
5
6
7
8
9
10
11
12
Mon 11 Tues 12 Mon 18 Tues 19 Mon 25 Wed 27 Mon 1 Tues 2 Mon 8 Tues 9 Mon 15 Tues 16 Tue 23
Exercises
E1
E2
E3
E4
E5
E6
E7
E8
E9
E10
E11
E12
exam
Tutorial
T2
T3
T4
T5
T6
T7
T8
T9
T10
T11
T12
Assignment
A1 due A1 ret
A2 due A2 ret
Quiz
Q1 in lec
Q2 in lec
Consultation
I will be generally available for consultation on Mondays from 5 to 6 pm in Room 527. If
possible, please indicate in advance if you will be attending. I am also available at other
times on Mondays and Tuesdays by appointment.
Communication
Communication will generally be by announcements in lectures and information posted
on the website. It is your responsibility to regularly check the website. Email is the best
way to contact the Lecturer or your Tutor.
Dr Bob Crossman, January 2016
Week Topic Content Guidelines
Changes and omissions will be advised during the course
Week 1
Riemann sums Upper and lower Riemann sums
Definition of definite integral
Non-positive functions
Difference between upper and lower sums
Definite integral: Evaluation of integrals
Theory & applications Estimation of integrals and sums
Properties of the definite integral
Fundamental Theorem Part II
Week 2
Further applications Areas and volumes by slicing
Integration by substitution I
Volumes by shells
Further applications Integration by parts
Indefinite integral Fundamental Theorem Part I
Functions defined by integrals
Week 3
Log & exp functions Natural logarithm
Natural exponential
General forms
Introduction to Properties of models
models and DEs Direction fields
Visualization of solution curves
Week 4
First-order DEs I Classification of differential equations
Separable equations
Integration by substitution II
First-order DEs II Models including growth and decay
Partial fractions
Week 5
First-order DEs III Linear equations
Examples and models
Further examples Radio-active dating
and models Flow and mixing problems
Week 6
Higher-order equations Second-order homogeneous linear
Boundary conditions
Factorization, equal root case
Systems of equations Reduction to second-order
Predator-prey systems
SHM, growing and damped oscillations