GEOL1006: Foundations of Physical Geoscience

Outline of Lectures

Lecture 1: Geometry

Angular measure in degrees and radians. What is π? Radius, Circumference, Area of Circle, Why use radians? What is a tangent.

Extension to 3-dimensions. Surface area and Volume of a Sphere.

Area of a triangle. Right angled triangles.

Area of square, rectangle and parallelogram. Extension to 3-D. Volume of a parallelepiped.

Pythagoras theorem.

Lecture 2: Coordinates and Trigonometry

Similar triangles

Sines, cosines and tangents of angles

Formulae for general triangles.

Angles and half-angles.

Cartesian coordinates, maps and graphs.

Calculation of distances between two points in 2-d and 3-d.

Triangulation.

Cylindrical and Spherical Polar Coordinates

Lecture 3: Graphs

Why do we need graphs - presentation of data.

Types of graph.

Simple equations, e.g. straight line, polynomials, sinusoidal, exponential decay curve.

Continuous and discontinuous functions.

Sketching simple functions, e.g. sin(A), 1/r, Vol. of sphere v. radius etc..

Slope of a curve.

Area under a curve.

Solving quadratic equations

Lecture 4: Exponents

Squares, cubes etc. Expressing numbers as powers of 10.

What do non-integer exponents mean?

Logarithms and antilogarithms.

Powers of other numbers. Natural logarithms.

Lecture 5: Dimensional Analysis

Dimensional analysis.

SI Units (mass, time, length).

Significant figures.

Prefixes (M,m,μ, etc..)

Vectors and scalars.

Adding vectors, components of vectors, scalar product, vector product.

Lecture 6: Mechanics I

Mass, density, gravity, weight.

Acceleration - equations of linear motion.

Newton's laws of motion; force and momentum - F=ma

Resolution of forces and velocities.

Projectile motion.

Lecture 7: Mechanics II

Energy.

Work, energy (kinetic and potential) and power.

Circular motion.

Kepler's Laws

Newton's Law of Gravity - force of attraction of two objects.

Gravity as applied to planetary motions and "weighing the Earth".

Archimedes principle.

Lecture 8: Elasticity

Pressure and volume

Stress and strain

Hydrostatic and non-hydrostatic pressure

Bulk Modulus, shear modulus

Elasticity and seismic velocity

Poisson's ratio

Stress and strain tensors

Elastic constants

Lecture 9: Waves and Light I

What is a wave. Longitudinal and transverse waves.

Electromagnetic radiation.

Polarisation.

Wavelength, frequency, velocity, phase and amplitude

Reflection and refraction; Snells law - ray diagrams.

Refractive index.

Critical angle and Total Internal Reflection

Wave-front diagram - Huygens construction.

Lecture 10: Waves and light II

Electromagnetic spectrum.

Why do light and sound travel at different speeds in different media.

Colours and dispersion.

Constructive and destructive interference.

Interference colours.

Young’s double slit experiment

Diffraction gratings

The Wave Equation.

Adding Waves together

Real, imaginary and complex numbers

Amplitude phase diagrams

Proof of Snells Law

Seismic Waves

P-S wave conversion at boundaries.

Seismic tomography

Lecture 11: Thermal and Transport Processes I

What is heat. What is temperature. Thermometers. How cold and hot can you get?

Heat capacity. Specific heat. Thermal expansion

Thermal conduction. Thermal convection. Radiative heat transport.

Diffusion, viscosity and creep

Lecture 12: Thermal and Transport Processes II

Laws of Thermodynamics

Latent heat

Phase transformations

Melting

Viscosity

Lecture 13: Electricity & Magnetism I

What is electricity.

Electrical charges.

Force between charged bodies.

Electric field. Electric potential (voltage).

Electric Current.

Resistance and Ohm's law.

Resistivity and conductivity.

Mechanisms of electrical conduction.

Electrical Heating.

Lecture 14: Electricity & Magnetism II

Permanent magnets and electromagnets.

Dynamos and motors.

Forces on charged particles.

Principles of mass spectrometers.

Types of magnetic field.

Lecture 15: Errors and Statistics I

Basic terminology

Idea of a distribution of measurements.

Mean and mode.

Variance and standard deviation.

Standard error in the mean.

Lecture 16: Errors and Statistics II

Probability distribution.

Finding the best straight line on a graph.

Adding errors.

Accuracy and precision.

Lecture 17: Differentiation

Slope of a curve.

Straight line graphs and derivatives.

Graphs which aren’t straight lines - differentiation from first principles

Differentiation of simple functions – some standard results

Combining functions – more standard results and recipes.

Functions within functions – the Chain Rule.

Lecture 18: More Differentiation

Higher derivatives.

Partial Differentiation

Differential Equations

Lecture 19: Integration

Integration as the reverse of differentiation (indefinite integration)

Some standard results - integration of simple functions.

Using indefinite integration to solve differential equations.

Integrating more complicated functions.

Lecture 20: More Integration and Numerical Methods

Definite integration – finding areas and volumes

Trapezium Rule for integration

Simpsons Rule for integration

Newton’s method for solving algebraic equations