# MATH6103 & MATH6500

### Syllabus

The syllabus outlines many of the learning outcomes of the course.

MATH6103 Syllabys PDF

MATH6500 Syllabys PDF

### Lecture Notes

TOC PDF

Lecture 1 PDF Week 1

Lecture 2 PDF

Lecture 3 PDF

Lecture 4 PDF Week 2

Lecture 5 PDF (9/10/12 - Please read example 2.3, we missed this due to the fire alarm!)

Lecture 6 PDF

Lecture 7 PDF Week 3

Lecture 8 PDF

Lecture 9 PDF

Lecture 10 PDF Week 4

Lecture 11 PDF

Lecture 12 PDF Week 5

Lecture 13 PDF

Lecture 14 PDF

Lecture 15 PDF Week 6

Lecture 16 PDF

Lecture 17 PDF

Lecture 18 PDF Week 7

Lecture 19 PDF

Lecture 20 PDF

Lecture 21 PDF Week 8

Lecture 22 PDF

Lecture 23 PDF Note: In lectures I think I mistakenly put p(x) as q(x) i.e. in hand written notes p and q are the other way round! Sorry!

Lecture 24 PDF Week 9

Lecture 25 PDF

Lecture 26 PDF

Lecture 27 PDF Week 10

Lecture 28 PDF End of lecture notes

Download the complete **Differential and Integral Calculus lecture notes 'book'** here PDF.

Don't forget to refer to your hand written notes from lectures. They are probably the best (useful) notes you will have!

### Extra Notes

Complex numbers: quick overview PDF

Limits example PDF

Limits example: making a function continuous PDF

Tangent line example: tangent of y=f(x) at x=c PDF

Logarithms and exponentials example PDF

Integration with partial fractions example PDF

Integration by parts - definite integral example PDF

Integration speed, distance and acceleration - physics example PDF

Integration application - area bounded by curves example PDF

Numerical Integration - trapezium rule example PDF

Differential Equations - 1st order ODE constant coefficient when r=\lambda PDF

Differential Equations - 2nd order ODE constant coefficient when r=\lambda_1=\lambda_2 PDF

Differential Equations - 2nd order ODE constant coefficient IVP when p(x)=constant PDF

Differential Equations - 2nd order ODE constant coefficient BVP PDF

Differential Equations - 2nd order ODE constant coefficient when p(x) is mixed sum of functions PDF

NEW - Differentiation application: real life example Exam Q PDF

NEW - Exponential growth and decay Exam Q PDF

### Homework Sheets

Homework sheets are handed out on Tuesdays and work will be collected on the following Tuesday. No late submissions please!

- Homework 1 PDF Solutions 1 PDF
- Homework 2 PDF Solutions 2 PDF
- Homework 3 PDF Solutions 3 PDF
- Homework 4 PDF Solutions 4 PDF
- Homework 5 PDF Solutions 5 PDF
- Homework 6 PDF Solutions 6 PDF
- Homework 7 PDF Solutions 7 PDF - Deadline extended
- Homework 8 PDF Solutions 8 PDF - Not assessed

You can collect your sheet 8 scripts and all other scripts that you have not taken already from the mathematics office (room 610, 25 Gordon street) early in the second term (January). Please e-mail me if you would like to know your grades or average.

### Past Exam Papers

Solutions for past three years exam papers (department policy) are made available on the MATH 6103 Moodle page, click here. Note that the solutions are no longer made available at the maths office! Note that MATH6103 and MATH6500 exam papers are exactly the same, just the code on the front differs. You can find past exam papers online from the library website here.

### Exam Ruberics

- The ruberics are printed on top of the first page before question 1 in case you forget.
- The difference between MATH6103 and MATH6500: If you are doing MATH6103, you are sitting a non calculator paper. If you are sitting MATH6500, you are allowed to bring your calculator to the exam, not that it will help you.
- You are presented with 7 questions in the paper. Only the best 5 answers will count. You are encouraged to answer all 7 if you have time, if not, read the questions and pick the 5 questions you can answer best first!
- The exam is 2 hours long.
- There is no formula book or formula sheet. Make sure you revise properly!

### Some good tips

- Get good rest the night before the exam and have a good meal to help you think clearly!
- Do not try to 'cram' anything half an hour or an hour before the exam. Relax, your subconcious knows more than your concious mind!
- Read all the exam questions properly before attempting to answer them. Explain your thoughts if you struggle to answer the question, you may gain some marks!
- Start every new question number (e.g. Q1, Q2 etc.) on a new page!
- Clearly label question attempted at the top of the page and on the front of the answer book
- Write clearly, starting a new equation on a new line, like we did on the board during lectures. Please don't try to cram everything within a few lines, ask for more paper if needed!
- Explain what you are doing where possible.
- Stay calm and good luck!

### Revision Class

The revision class is scheduled for Wednesday 20th March 2013 at 1PM in Roberts 309.

In the meantime, if you have any questions feel free to e-mail me or if you would like to see me, send me an e-mail and we can arrange a time to meet.

### Recommended Texts

Although I do not think you require a text book for the course, it can be a good idea to have one to refer to and try extra examples. Here are a few (in no particular order):

Croft, Davison and Hargreaves, Introduction to Engineering Mathematics (Addison-Wesley)

Advancing Maths for AQA: Pure Core 1 & 2 (C1 & C2) (Advancing Maths for AQA 2nd edition)

Advancing Maths for AQA: Pure Core 3 & 4 (C3 & C4) (Advancing Maths for AQA 2nd edition)

Advancing Maths for AQA: Further Pure 1 (FP1) (Advancing Maths for AQA 2nd edition)

For Complex Numbers: AQA GCE Further Pure Mathematics Unit 2 text book PDF

For Differential equations: AQA GCE Further Pure Mathematics Unit 3 text book PDF

Schaum's Outline of Advanced Mathematics for Engineers and Scientists (Schaum's Outline Series)

Schaum's Outline of Calculus, 5ed: Schaum's Outline of Calc, 5ed (Schaum's Outline Series)

Anton, Bivens and Davis, Calculus: Late Transendentals 10ed (Wiley)