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 Refresher is 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. They also have resource materials by topic and maths videos. For these follow the links from the Mathcentre homepage.

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 go here. For a list of the maths videos available follow the links from the Mathcentre student page. 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 go here. For a list of the maths videos available follow the links from the Mathcentre student page.
• 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