• Search for extraterrestrial life from a human perspective
• Evolution of stars and planetary systems
• Formation of our solar system
• Comets & asteroids and their relevance to life on Earth
• Evolution of life on Earth
• Extremophiles: life forms in extreme environments
• Panspermia, i.e. the spreading of life through space
• Molecules in space: the observations of complex hydrocarbons and other sophisticated molecules
• Circumstellar habitable zone: will life only be found in the traditional "comfort zones" of solar systems?
• Hazards to life from the Galaxy
• Progress over the last century in our knowledge and expectations about potential life on Mars, and on the Jovian moons: Titan & Europa
• Exoplanets, detection techniques and results
• SETI: searching for signals from extra-terrestrials and the Drake equation

Learning & teaching methods

Assessment methods

There is not final exam during the exam week. The multi-choice test will be held during the last lecture slot and will last for 1 hour.

Referral Method: By examination

Functions of two or more variables:

Evaluate partial derivatives, find critical points, and, for functions of two variables,  classify them. 

Multiple Integrals of a scalar function in (2 and 3 dimensions):
Evaluate integrals of simple functions over regions in plane bounded by graphs of simple functions, either directly or by change of coordinate system.

Evaluate integrals over volumes bounded by planes, spheres and cylinders, using cylindrical and polar coordinates.

Vector Calculus:
Gradients, divergences and curls.  

Curves and line integrals:
Express, in simple cases, curves given parametrically. Evaluate lengths of curves in 2 and 3 dimensions. Evaluate integrals of scalar functions along curves with respect to arc-length. Evaluate the integral of the tangential component of a vector field along a curve.  Conservative fields.

Surfaces:
Integration of normal components of a vector field or of a scalar field over surfaces described parametrically.

The divergence theorem and  and Stokes' theorem and their application. 

Differential equations
Types of ordinary differential equation. Solving simple differential equations, separation of variables, integrating factors and first order linear ordinary differential equations. Exact differential equations. Second order differential equations. Homogeneous linear ordinary differential equations with constant coefficients. Free and forced damped harmonic oscillator.

Learning & teaching methods

Lectures, small group tutorials, private study. The method of delivery in lectures will be “chalk and talk”, using skelatal lecture notes.

Assessment methods

Referral Method: By examination

• calculate the scalar and vector product of two vectors;
• algebraically manipulate 3 by 3 matrices, and solve eigenvalue problems in 2 dimensions;
• solve simple polynomial equations, including complex solutions
• sketch and manipulate exponential, trigonometric and hyperbolic functions;
• differentiate functions of one variable and use this to classify critical points;
• understand the concept of a limit and be able to determine its value if it exists;
• construct a Taylor series of a function and understand its relevance to local behaviour;
• understand the nature of simple complex valued functions;
• differentiate functions and manipulate them when changing variables;
• integrate various functions of one variable. 

Basic vector algebra, cross and dot product, geometrical and physical applications.

Matrices and determinants, inverse of a matrix, using matrices to solve simultaneous equations.
Eigenvalue problems.

Solving quadratic equations, factorising higher order polynomials.

Complex numbers, powers of i, Argand diagrams, modulus and argument of a complex number, complex conjugates. The algebra of complex numbers: addition, subtraction, multiplication and division in both Cartesian and polar form.

Specifying a function, its domain and range. Composition of functions. Graphs of functions. One-to-one functions, inverse functions and their graphs. Even and odd functions, periodic functions, trigonometric functions, inverse trigonometric functions.

Informal definition of a limit, rules for evaluating limits, infinite limits.

Rules for differentiation, higher derivatives, critical points and applications to graph sketching. Exponential and natural logarithm functions, power functions, hyperbolic functions, inverse hyperbolic functions and their derivatives. Derivatives of vectors.

L'Hôpital's Rule, Taylor series expansions and remainder terms.

Complex exponentials and trigonometric functions. De Moivre's Theorem, calculating powers and roots, and solving equations.

Integration, the Fundamental Theorem of Calculus, indefinite integrals, methods of integration, partial fractions, integration by parts.

Learning & teaching methods

Lectures, small group tutorials, private study. The method of delivery in lectures will be “chalk and talk”, however the students will be provided with printed skeletal notes, highlighting all the key results and saving them from excessive note taking. Hard copies of the skeletal notes and all the assignments will be provided, and the material will also be provided in the module Blackboard site.

Assessment methods

Referral Method: By examination