Recommended texts:

• Paul Monk 'Maths for Chemists' (Oxford).

• L. Bostock & S. Chandler 'Core Maths for A-level' (2nd ed.) (Stanley Thomas).

• Peter Tebutt 'Basic Mathematics for Chemists' (Wiley).

• Robert Lambourne and Michael Tinker 'Basic Mathematics for the Physical Sciences' (Wiley)

Aim: The lectures will provide you with an introduction to calculus at a level appropriate to students without A-level training in the subject. The emphasis is on using the mathematics rather than on formal proofs. Chemical examples will be used in illustration where possible. The lectures will be supplemented by tutorials. This course is meant to give you the basic knowledge of the core maths that is necessary to understand the Chemistry courses you will meet over the next few years.

The following topics will be covered:

1) What is Calculus?

Graphs, slopes and areas

2) Functions

What is a function? Definition plus examples

3) Simple Functions - graph plotting

Linear Equations; Quadratic Equations; Higher Polynomials; Rational Functions; Trignometrical Functions; Exponential & Logarithmic Functions.

4) Basic Differentiation

Linear Equations - graphically; gradient of a general function; Analytical Differentiation; Differentiation 'magic' formula; Addition Rule; Negative Powers of x; Roots - fractional powers of x; Using Differentiation to calculate slopes; Maxima & Minima; Types of stationary point; Product Rule; Quotient Rule; Function of a Function; Chain Rule; Sequential Step Method.

5) Exponential Functions

General expression; numerical examples; The exponential function; Variants of the exponential function.

6) Logarithmic Functions

Common & Natural Logs; Laws of Logs; Differential of ln x.

7) Trignometrical Functions

Sin, Cos, Tan; Inverse Trig Functions; Differentials of Trig functions.

8) Integration - Calculating Areas

Calculating Areas - counting squares; Notation; Integration as the Reverse of Differentiation; Indefinite Integrals; Integration 'magic' formula; Definite Integrals; Negative Integrals; Integrals of Common Functions.

Objectives

After completing this course you should be able to demonstrate that you can:

• Sketch simple functions (polynomials, etc) and label the interesting points of the curve.

• Differentiate:

Simple functions (linears, quadratics, polynomials)

inverse functions ()

root functions

exponential functions

log functions

trig functions (sin, cos, tan)

• You should also be able to use, (and know when to use) the Product rule, Quotient rule, and the Function of a Function rules (Chain rule or Sequential step method) to differentiate compound functions.

• Find the stationary points of a simple function, and determine their type (max, min or point of inflection).

• Integrate

All of the above types of simple functions

• Calculate areas under simple functions