Please note: This course will be taught online only. In person study is not available for this course.

Chris Saker is a Professor in the School of Mathematics Statistics and Actuarial Science at the University of Essex. In addition, for nearly 20 years he worked as part of a Government funded project who aims included increasing the uptake of level 3 mathematics and providing improvement in teaching of level 3 qualifications. In this role he was particularly interested in supporting students in their transition from school to university education. Chris has also taught on the maths course at the Essex Summer School for nearly 20 years.

Course Content
The course provides participants with an introduction to functions and differentiation, the areas of mathematics that allows us to calculate rates of change. This course is aimed at being accessible to those who have not studies differentiation before, or who have limited experience in the area and want to improve their understanding and confidence. The course offers participants a clear and accessible foundation to support the understanding of these topics when they are applied in other subject areas. Specifically, the course will explore the following topics:

  • Basic functions and function types (linear functions, polynomials, exponential and logarithmic functions)
  • Differentiation and interpretation of derivatives
  • Using differentiation to find finding maxima, minima, and critical points
  • Partial derivatives and multivariable functions

 
Course Objectives
Upon completion of this course, participants will have gained a conceptual and practical understanding of basic functions including polynomials, logarithms and exponentials, and how to calculate the derivative of such functions of one or two variable and use this this to locate stationary points.

Course Prerequisites
This is an introductory and highly accessible course. No specific mathematical background is required.

Representative Background Reading
Since this is an introductory course, participants are not required to complete any prior reading.

Required texts
All relevant materials will be provided within the course lecture notes.

Day 1:
We begin the course by covering the basics of linear equations, that is equations of the form y=mx+c. We will spend some time gaining an underrating of that the coefficients in the equation tell us about the equation, and will look at problems such as how to determine the equation of straight line that passes through two given points and how to calculate the inverse function of a linear equation. From there we move on to look at quadratic equation, how to sketch them, and how we find the root of such equations before moving on to briefly look at higher order polynomials.

Day 2:
We continue from yesterday by moving on to looking at logarithms and exponential function. We will gain an understanding of the behaviour of these functions, the algebraic laws that allow us to manipulate expressions involving them. We will spend some time practicing working with them and will finish by looking at how we can use applications to regression. We will also have a brief look at common trigonometric functions and the periodic behaviour of these functions.

Day 3:
Today we move to a new topic and start to look at calculus, specifically differentiation. We will begin with the basics, looking at the problem of calculating the gradient of a curve at a given graphically and work towards developing at limiting arguments allowing us to calculate the derivative, that is the function that tells us the gradient of our original function, at any given point. From here we move on to look at the basics rules that allow us to more easily calculate the derivative of polynomial functions.

Day 4:
We continue to build upon ideas from yesterday by looking at the derivate of a functions such as logarithms and exponentials and trigonometric functions. We will also look at develop techniques to allow us to evaluate more complicated integrals, namely the product rule, the quotient rule, and the chain rule. We will finish by looking at how we can use differentiation other than calculate points of interest of auctions such as maxima, minima, and points of inflection.

Day 5:
On our final day we will looking at applications of differentiation by calculating stationary points of functions before  move on to look at functions of more than one variable.  We look at how to visualise and understand the nature of these functions before finishing by looking at how we can use differentiation with functions of more than on variable and how to locate stationary points of surfaces when working functions of two variables.