Mathematical Modelling for Earth Sciences

Mathematical modelling and computer simulations are an essential part of the analytical toolset used by earth scientists. Computer simulations based on mathematical models are routinely used to study geophysical, environmental and geological processes in many areas of work and research from geophysics to petroleum engineering and from hydrology to environmental fluid dynamics. Dr Yang has carefully selected topics which will be of most value to students and has recognised the need to be careful in his examples whilst being comprehensive enough to include important topics and popular algorithms. The book is designed to be theorem-free and yet to balance formality and practicality. Using worked examples and tackling each problem in a step-by-step manner the text is especially suitable for non-mathematicians approaching this aspect of earth sciences for the first time, The coverage and level, for instance in the calculus of variation and pattern formation, that even mathematicians will find the examples interesting. Topics covered include: vector and matrix analysis ordinary differential equations partial differential equations calculus of variations integral equations probability geostatistics numerical integration optimisation finite difference methods finite volume methods finite element methods reaction-diffusion system elasticity fracture mechanics poroelasticity, and flows in porous media. Mathematical Modelling for Earth Sciences introduces a wide range of mathematical modelling and numerical techniques, and is written for undergraduates and graduate students.