This is a module designed for students of the life sciences and chemistry to equip them with the mathematical skills necessary for their core subjects and the ability to understand the mathematical language used in research papers in these areas.

[Complex Numbers:] necessity and definition; algebra including multiplication, conjugate, division, absolute value; Argand diagram representation; polar form, argument; exponential form; de Moivre's theorem, powers and roots. [Modelling with Differential Equations:] Derivation of differential equations of exponential growth and decay. Application to population growth, radioactive decay and other problems from science. [First Order Ordinary Differential Equations:] First order equations of variables separable and linear types; applications including chemical reactions, mixing problems, Newton's Law of Cooling, radioactive decay. [Second Order Ordinary Differential Equations:] Second order homogeneous equations with constant coefficients. Application to damped harmonic oscillators. [Partial Derivatives:] Functions of several variables; partial derivatives, definition and examples (e.g. from thermodynamics); higher partial derivatives; optimisation and Second Derivative Test for functions of two variables. [Linear Algebra]: Review of matrices and determinants (3X3). Lines and planes in three dimensions. Systems of equations as intersections of lines and planes. Matrices as linear transformations: scale, shear, rotation. Eigenvalues and eigenvectors. Matrix diagonalisation. Powers of a matrix. Possible applications include crystallography, forest management (sustainable yield); age-specific population growth; genetics.

1. Perform algebraic calculations with complex numbers. Write complex numbers in polar and exponential forms. Find roots of complex numbers and solve simple polynomial equations with complex roots. 2. Model growth and decay problems with differential equations and find their solutions. 3. Recognise and solve first order ordinary differential equations, including linear and variables separable equations. Apply these equations to various problems arising in science. 4. Recognise and solve second order constant coefficient ordinary differential equations. Apply these equations to damped harmonic oscillator (e.g. mass spring) problem. 5. Compute partial derivatives of functions of several variables. Optimise a function of two variables (unconstrained). 6. Find intersections of lines and planes in three dimensions. Compute eigenvalues and eigenvectors of a 3X3 matrix. Diagonalise a 3X3 matrix and calculate powers of the matrix. Be able to apply linear algebra to problems in chemistry and the life sciences.

Students should appreciate the uses of mathematics in solving problems arising in the chemical and life sciences and be able to bring to bear acquired mathematical skills in formulating and solving certain problems.

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Normal weekly lectures. Mid-term exam and final exam.