Mathematical Methods in the Earth and Environmental Sciences

The Earth and environmental sciences are becoming progressively more quantitative due to the increased use of mathematical models and new data analysis techniques. This accessible introduction presents an overview of the mathematical methods essential for understanding Earth processes, providing an invaluable resource for students and early career researchers who may have missed (or forgotten) the mathematics they need to succeed as scientists. Topics build gently from basic methods such as calculus to more advanced techniques including linear algebra and differential equations. The practical applications of the mathematical methods to a variety of topics are discussed, ranging from atmospheric science and oceanography to biogeochemistry and geophysics. Including over 530 exercises and end-of-chapter problems, as well as additional computer codes in Python and MATLAB®, this book supports readers in applying appropriate analytical or computational methods to solving real research questions.

Preface; 1. Estimation and dimensional analysis; 2. Derivatives and integrals; 3. Series and summations; 4. Scalars, vectors, and matrices; 5. Probability; 6. Ordinary differential equations; 7. Vectors and calculus; 8. Special functions; 9. Fourier series and integral transforms; 10. Partial differential equations; 11. Tensors; Appendix A. Units and dimensions; Appendix B. Tables of useful formulae; Appendix C. Complex numbers; Notes; References; Index.

Adrian Burd is an associate professor at the Department of Marine Sciences at the University of Georgia. As a marine scientist, he applies mathematical tools to understand marine systems, including the carbon cycle in the oceans, the health of seagrass and salt marshes, and the fate of oil spills. His work has taken him around the globe, from the heat of Laguna Madre and Florida Bay to the cold climes of Antarctica.