# Maths course for Year in Industry participants

MEI is pleased to offer Year in Industry students a course covering selected topics from A level Mathematics and Further Mathematics relevant to maths and maths-related courses in higher education. The course is designed to enable participants to consolidate and develop maths skills while they spend a year in industry prior to university entry.

Course participants are supported in their independent study via a forum which is moderated by a tutor. To successfully complete the course, participants must complete on-screen tests taken by the middle of each month throughout the course. Certificates will be provided to those who complete the course. Extensive notes and exercises with worked solutions are provided to prepare for the on-screen tests.

The course will run from November 13th 2019 to June 21st 2020.

Course fees are £90 per participant.

E-mail course organiser with any queries about the course.

The following topics are covered

1. Matrices (on screen test to be completed by 15th December 2019)
• Introduction to Matrices
• Matrices and transformations
• 2x2 determinants and inverse matrices
• 2x2 matrices and simultaneous equations
• Determinant of a 3x3 matrix
• Inverse of a 3x3 matrix
• Using 3x3 matrices to solve simultaneous equations
• Eigenvalues and eigenvectors
2. Vectors (on screen test to be completed by 19th January 2020)
• Introduction to vectors in 2D
• Introduction to vectors in 3D
• The scalar Product
• Planes
• The vector product
• Intersecting planes and lines
• Calculating distances
• Scalar triple product
3. Complex numbers (on screen test to be completed by 16th February 2020)
• Complex arithmetics
• The Argand diagram
• Modulus and argument
• Loci in the complex plane
• De Moivre's theorem and complex exponents
• Complex roots and geometrical applications
4. Differentiation (on screen test to be completed by 15th March 2020)
• Introduction to differentiation
• Maximum and minimum points
• Extending to negative and fractional powers
• Higher derivatives
• Differentiation of exponentials and logarithms
• Differentiation of trigonometric functions
• Differentiating products and quotients
• The chain rule
• Implicit differentiation
• Parametric differentiation
• Inverse trigonometric functions
5. Integration (on screen test to be completed by 19th April 2020)
• Introduction to integration
• The area bounded by a curve
• Further integration
• Integration by substitution
• Further techniques
• Integration by parts
• Reduction formulae
6. Functions of several variables (on screen test to be completed by 17th May 2020)
• Functions of two variables
• Partial differentiation
• Maxima and minima
7. Ordinary differential equations (on screen test to be completed by 21st June 2020)
• First order differential equations
• Second order differential equations with constant coefficients

Sample materials from the Introduction to matrices part of the course are given below.

Course fees are £90 per participant.