# Resources

This page has selected resources for some important areas of mathematics.

Additional resources for the 2 unit Mathematics and the Extension 1 Bridging Courses are below.

## Algebra skills

- The Maths Learning Centre algebra workshop notes are available here.

An Algebra Refresheris an algebra workbook (with answers) producted by staff from the Department of Mathematical Sciences and the Mathematics Learning Support Centre at the University of Loughborough. Go to the Mathcentre homepage and search for 'Algebra Refresher'. They also have resource materials by topic and maths videos.

## Differential calculus

- The Mathematics Learning Centre has published a workbook called Introduction to Differential Calculus which looks at the concept of a derivative and the rules of differentiation.
- The Mathcentre has an extensive range of notes and videos on differentiation. For a list of their differentiation notes by topic and a list of the maths videos available follow the links from the Mathcentre Homepage. The math video on the chain rule is particularly useful. There are two workbooks for revision of differentiation on this site: "Basic Differentiation – A Refresher" and "A Calculus Refresher". These workbooks were developed by staff from the Department of Mathematical Sciences or Mathematics Education Centre at the University of Loughborough and contain lots of exercises with answers.
- The UBC Online calculus homepage.

On this homepage are the course notes of the introductory differential calculus course at the University of British Columbia. They give a very good introduction to the derivative including interactive graphs to aid visualisation.

## Integration

- The Mathematics Learning Centre has published two workbooks on integration. The first one Introduction to Integration: Part 1 The Antiderivative looks at integration as the reverse of differentiation. The second Introduction to Integration: Part 2 The Definite Integral looks at the Definite Integral as a limit of a sum and its applications.
- The Mathcentre has an extensive range of notes and videos on integration. For a list of their integration notes by topic and list of the maths videos available follow the links from the Mathcentre Homepage.
- www.ugrad.math.ubc.ca/coursedoc/math101/notes/

These are the course notes of the introductory integration course at the University of British Columbia. They give a very good introduction to the Definite Integral including interactive graphs to aid visualisation. - On this site is a collection of modules put together by the University of Tennessee.

http://archives.math.utk.edu/visual.calculus/4/index.html

Its tutorials on integration and its applications include animations to illustrate mathematical concepts. It uses the plug-ins Flash and Live math.

## Additional resources: 2 unit Mathematics Bridging Course

- Day 1: Functions

Solutions to selected exercises - Day 2: Linear functions

Solutions to selected exercises

Straight line graphs - Day 3: Factorisation

Solutions to selected exercises - Day 4: The derivative of a function

Solutions to selected exercises

Stationary points and their nature - Day 5: The derivative of a polynomial

Solutions to selected exercises

Graphs of polynomials

Introduction to the rules of calculus up to page 4

Optimisation using calculus

Curve sketching using calculus - Day 6: Second derivatives

Solutions to selected exercises

The second derivative, concavity and points of inflection - Day 7: Index laws

Solutions to selected exercises

Indices - Day 8: The exponential function

Solutions to selected exercises

Exponential functions - Day 9: The derivative of a composite function

Solutions to selected exercises

Composite functions and their derivatives

Differentiation of the exp and log functions

Introduction to the rules of calculus from page 5 - Day 10: The circular functions

Solutions to selected exercises

Differentiation of trig functions - Day 11: Inverse functions

Solutions to selected exercises

Logarithmic functions and the log laws - Day 12: Absolute value

Solutions to selected exercises

Absolute values

## Additional resources: Extension 1 Mathematics Bridging Course

- Chapter 1: Functions I

Functions: The domain and range

The rules of calculus - Chapter 2: Functions II

Composite function (chain) rule

The math video on the chain rule is particularly useful. - Chapter 3: Trigonometric identities

Introduction to Trigonometric Functions

Trigonometric Identities - Chapter 4: Mathematical induction

Mathematical Induction - Chapter 5: Polynomials

Polynomials - Chapter 6: Solving equations

Absolute values

Solving inequalities - Chapter 7: Integration techniques

Introduction to Integration: Part 1 The Antiderivative

Introduction to Integration: Part 2 The Definite Integral - Chapter 8: Inverse functions

no material available - Chapter 9: Applications of calculus

no material available - Chapter 10: Counting and permutations

Counting techniques up to page 6 - Chapter 11: Combinations and the Binomial Theorem

Counting techniques from page 6