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. Author Xin-She Yang has carefully selected the topics which will be of most value to students. Dr. Yang has recognized the need to be careful in his examples while being comprehensive enough to include important topics and popular algorithms. The book is designed to be 'theorem-free' while balancing formality and practicality. Using worked examples and tackling each problem in a step-by-step manner, the text is especially suitable for more advanced students of this aspect of earth sciences. The coverage and level, for instance in the calculus of variation and pattern formation, will be of interest to mathematicians. Topics covered include: vector and matrix analysis . ordinary differential equations . partial differential equations . calculus of variations . integral equations . probability . geostatistics . numerical integration . optimization . finite difference methods . finite volume methods . finite element methods . reaction-diffusion system . elasticity . fracture mechanics . poroelasticity . flows in porous media.