Information for MATH201 students, Autumn 2009

Information on this page is for MATH201 students at both the Loftus campus and the Wollongong campus. The time or date when individual items were placed on the site is indicated within the square brackets following the item.


Rod's availability for answering questions during session are below

I will be generally available at the following times in my office 15.G25 to answer questions on MATH201.

Wednesdays 10.30-12.30

Fridays, 9.30-10.30, 2.30-3.30

I will also be around at other times and you are welcome to ask me a question if you find me. Also, you can email me to make an appointment.

Important dates for MATH201

Mid-session test. Wednesday 29 April (at both Wollongong and Loftus).

Assignment. Will be handed out Wednesday 13 May. Assignment is due Wednesday May 27. (These are for both Wollongong and Loftus).

Studying for MATH201

Lecture attendance is very important.

Mathematics 201 is a course that involves many new ideas and concepts and much more than mere "information collection" is required. There will be a substantial difference in how we approach the subject compared with what you have seen before in calculus. The lectures give you a chance to understand a way of thinking about the material. The lectures give you more opportunities to explore the concepts that underlie MATH201. The lectures will have comments, ideas, examples, illustrations and material that are not in the notes. All of these will help you understand the subject much better than simply reading the notes.

MATH201 places great importance on the logical development of ideas, and how the different ideas from various parts of the course are related to each other. This requires a different mental outlook than simply asking something like "how do I get an answer for this type of integral?" The definitions of the concepts are important and you should know them by heart, as well as understanding their meaning. The course also emphasises the solving of specific problems. Depending upon time, there will be discussion of applications to physics and economics.

To prepare for the exam over the whole session: know and understand the definitions, know the statements of the results and understand them, make sure you can solve the problems set during the session and that you have studied carefully the examples given during the course. Make use of the additional material on this web site, especially the examples. Make sure you have a thorough knowledge of the notes, and of all work done during session.

The following general information about MATH201 may be downloaded in pdf format.

Information and policy documents

Information sheet for MATH201 students (Wollongong Campus) [week 1].
Information sheet for MATH201 students (Loftus Students) [week 1].
Policies and services of the University, Faculty and School [week 1].

MATH201 CONSULTATION TIMES FOR THE STUDY VACATION

Below are consultation times for the study vacation and Monday June 15th.

You are free to see me at other times if I am in my office.

Send me an email on nillsen@uow.edu.au if you need to make an appointment.

Tuesday June 9th: 10.30--11.30 room 15.G25 (Rod's office)

Thursday June 11th: 9.30--11.30 room 15.113

Friday June 12th: 10.30--12.30 room 19.G027

Monday June 15th 10.30--12.30 room 15.G25 (Rod's office)

ANSWERS TO THE 2008 EXAM PAPER

Download answers to the 2008 exam paper.

Examples and material supplementary to the lecture notes

Revision and new ideas [week 1]. This sheet has 3 problems to think about in your study time in weeks 1 and 2.
Supplementary examples 1 [week 1]. These are examples on functions, concerning one-to-one functions, composition, inverses and linear functions. This is revision material
Supplementary examples 2 [week 1]. This example is related to physics and concerns a linear transformation arising in Einstein's theory of special relativity.
Composition (substitution) of functions [week 1]. This illustrates the concept of composition as first applying one function to a point, then applying another function to the point so obtained.
Supplementary example 3 [week 1]. This example is a bit similar to the problem illustrated in Figure 2.2, page 17 of the notes. It is concerned with how a particular function changes a region S (which is a "triangular" region with a curved boundary) in 2 dimensions into a triangle in 2 dimensions, when the function is applied to each point of the S.
Discussion of ellipses [week 2]. Some people have told me they don't know anything about ellipses. You can look at the pdf here on ellipses that tells you all you need to know - basically they are like circles where the radius is not constant and varies a bit as you go around the curve.
The rotation function is linear [week 3]. This example concerns the rotation function in two dimensions. This function is linear and its matrix is calculated.
A worked example on the chain rule [week 4].
Figures depicting the definition of the integral of a function of two variables [week 5].
[week 6].
A worked example on calculating the derivative matrix of a function [week 6]. This example illustrates the two possible approaches to proving that a function is linear: (i) the definition, and (ii) showing that the function is given by a matrix multiplication.
Two worked examples concerning the calculation of double integrals [week 6].
A worked example on calculating the Jacobian [week 6].
A second worked example on calculating the Jacobian [week 6].
Calculating partial derivatives using the chain rule This helps with doing Exercise 33 in Exercises 4.10. [week 6].
Examples on repeated integration [week 7].
A worked example on calculating a double integral by substitution [week 7].
Another worked example on calculating a double integral involving the exponential function, by substitution [week 7].
Yet another worked example on calculating a double integral by substitution [week 7].
Here are some comments on partial derivatives as they relate to thermodynamics (for physics students) [week 8].
Examples on the Divergence Theorem [week 11].
Another example on calculating a surface integral [week 11].
Three examples on calculating surface integrals [week 11].
An example concerning Stokes' Theorem [week 11].
An example on Lagrange multipliers [week 12].
NOTE: examination papers for this subject for 2007 and 2008 are available in electronic form on the University Library website [week 12].

Answers to the exercises in the lecture notes

Answers to Math201 exercises 2.14, 2009[week 3].
Answers to Math201 exercises 3.4, 2009[week 3].
Answers to Math201 exercises 4.10, 2009[week 4].
Answers to Math201 exercises 5.7, 2009[week 6].
Answers to Math201 exercises 6.7 and 7.11, 2009[week 11].
Answers to Math201 exercises 8.4, 2009[week 13].

Tutorial problems and Revision for week 4


Exercises 3.4: 7 (if not done last week), 8, 11
Exercises 4.10: 1, 2, 4, 5, 6
Revision: study the problem and worked solution in Figure 2.2 in the notes. On this webpage, download and study the "discussion of ellipses" and "supplementary example 3".

Tutorial problems and Revision for week 5


Exercises 4.10: 15, 16, 17, 21, 27.
Revision: Memorize the definition of the derivative, given on page 47 of the notes. Write some explanatory lines, in clear and complete sentences and in your own words, to explain how we associate a matrix f'(x) with the derivative of f at x. Explain briefly how we calculate f'(x) in terms of partial derivatives. Your written discussion should be clear, complete and grammatically correct as far as possible.

Tutorial problems and Revision for week 6


Exercises 4.10: 20, 24, 30, 31, 38
Revision: in your own words, in clear and complete sentences, write out a statement of the Chain Rule. If you still don't understand what the chain rule says, ask your tutor. Also, study Figure 4.2 on the polar coordinates transformation.

Tutorial problems and Revision for week 7

The tutors will set some problems for the 2007 test, by way of exercises and revision.

Tutorial problems and Revision for week 8

Exercises 5.7: 1, 2, 4, 5.

Tutorial problems and Revision for week 9

Exercises 5.7: 6, 7, 8, 13.
Exercises 6.7: 1, 2. Revision: make sure you understand the discussion on substitution and the formulas (5.19) and (5.20) in the notes, and do other exercises on integration by substitution.

Tutorial problems and Revision for week 10

Exercises 6.7: 3, 5, 7, 8
Exercises 7.11: 1, 2, 3.
Revision: make sure you understand the definition of the integral of a vector field along a curve, as described in sections 7.1 and 7.2. Make sure you understand and remember Green's Theorem.

Tutorial problems and Revision for week 11

Exercises 7.11: 4, 6, 8.
Revision: make sure you understand how to calculate the normal vectors to a given surface, and how to calculate integrals over a surface.

Tutorial problems and Revision for week 12


Exercises 7.11: 11, 12, 13, 15. Revision: make sure you understand the Divergence Theorem, and study the examples on this theorem and surface integrals on this website.

Tutorial problems and Revision for week 13


Exercises 8.4: 3, 5, 6, 7. Revision: make sure you understand the Divergence Theorem and Stokes' Theorem, and study the relevant examples in the notes and on this website. Make sure you understand Lagrange multipliers.

Test from 2007

Click here, for a copy of the 2007 mid-session test.

Copy of the assignment for Session 1 2009

Click here, for a copy of the assignment. Note that although this is for Wollongong students, the Loftus assignment is the same -- only the handing-in arrangements are different.

STATEMENT ON EXAMINABLE MATERIAL FOR THE TEST

The following is the examinable material for the test next week, WEEK 8.
(a) Sections 2.1 to 4.8 in the notes are examinable.
(b) Section 4.9 in the notes on Implicit Functions is NOT examinable. Problems on implicit functions are NOT examinable.
(c) Sections 4.10 to 5.3 in the notes are examinable (up to and including double/repeated integrals, that is).
(d) Section 5.4 and subsequent sections in the notes are NOT examinable (except for the Exercises in 5.7 that come under the sections above).
(e) The 2007 test paper (available above), gives a good idea of the likely layout and types of problems to be on the test. Note that there will be a question asking about definitions.

Exercises supplementary to those in the lecture notes

Errata in the lecture notes

Rod Nillsen
Coordinator
MATH201
Autumn Session 2009