This is a package of modules to help people revise
and learn some of the mathematics they need to enter (British)
university courses in Science and Engineering. Each module originally
consisted of a text part - the Study Guide - and a companion Mathematica
Notebook of computer-based activities. The Study Guide has been
replaced by a book: Experiments
in Undergraduate Mathematics: A Mathematica-Based Approach.
The materials need Mathematica: they were written using version
2.2, and should work in version 2.1, but earlier versions may
be a problem.
At the original writing of this abstract (July
5, 1994) there were twelve notebooks:
These notebooks have been compressed into ten notebooks.
- Start Here - an introductory Notebook;
- Complex numbers 1 - introduces complex numbers and how they
arise in finding the roots of polynomial.
- Complex numbers 2 - complex arithmetic, complex conjugates,
Argand diagram, modulus and argument, polar form.
- Complex numbers 3 - De Moivre's Theorem, extracting roots,
curves and areas in the complex plane, circles, disks, rings,
perpendicular bisectors, complex exponential function.
- Differentiation 1 - tangent lines, limits, derivatives of
power functions, sine, cosine exponential and log functions.
- Differentiation 2 - Derivatives of sums, products, quotients,
and compositions of functions; maxima and minima; implicitly
- Integration 1 - Indefinite integration; important functions;
- Integration 2 - Definite integration; approximate methods.
- Integration 3 - Change of variable; integration by parts;
areas and volumes.
- Matrices 1 - Transformations in the plane, composition of
linear maps, matrix multiplication.
- Sequences - arithmetic, geometric, recurrence, and chaotic
sequences, arithmetic and geometric series.
- Series - binomial series, factorials, and MacLaurin series.
- Trigonometry 1 - radians and degrees, trigonometric functions,
amplitude, frequency and period, trig identities.
- Trigonometry 2 - trig formulae, double angle, half angle,
inverse trig functions, solving trig equations.
- Vectors 1 - directed line segments, vectors, scalar multiplication,
addition, components, basis, and magnitude.
- Vectors 2 - Scalar product; equation of a line.
(modified from the documentation)