Provides a comprehensive tour of the mathematical methods needed by physical science students.

This completely revised edition provides a tour of the mathematical knowledge and techniques needed by students across the physical sciences. There are new chapters on probability and statistics and on inverse problems. It serves as a stand-alone text or as a source of exercises and examples to complement other textbooks.

An engagingly-written account of mathematical tools and ideas, this book provides a graduate-level introduction to the mathematics used in research in physics. The first half of the book focuses on the traditional mathematical methods of physics – differential and integral equations, Fourier series and the calculus of variations. The second half contains an introduction to more advanced subjects, including differential geometry, topology and complex variables. The authors' exposition avoids excess rigor whilst explaining subtle but important points often glossed over in more elementary texts. The topics are illustrated at every stage by carefully chosen examples, exercises and problems drawn from realistic physics settings. These make it useful both as a textbook in advanced courses and for self-study. Password-protected solutions to the exercises are available to instructors at www.cambridge.org/9780521854030.

Market_Desc: · Physicists and Engineers· Students in Physics and Engineering Special Features: · Covers everything from Linear Algebra, Calculus, Analysis, Probability and Statistics, to ODE, PDE, Transforms and more· Emphasizes intuition and computational abilities· Expands the material on DE and multiple integrals· Focuses on the applied side, exploring material that is relevant to physics and engineering· Explains each concept in clear, easy-to-understand steps About The Book: The book provides a comprehensive introduction to the areas of mathematical physics. It combines all the essential math concepts into one compact, clearly written reference. This book helps readers gain a solid foundation in the many areas of mathematical methods in order to achieve a basic competence in advanced physics, chemistry, and engineering.

Table of Contents Mathematical Preliminaries Determinants and Matrices Vector Analysis Tensors and Differential Forms Vector Spaces Eigenvalue Problems Ordinary Differential Equations Partial Differential Equations Green's Functions Complex Variable Theory Further Topics in Analysis Gamma Function Bessel Functions Legendre Functions Angular Momentum Group Theory More Special Functions Fourier Series Integral Transforms Periodic Systems Integral Equations Mathieu Functions Calculus of Variations Probability and Statistics.

Designed for first and second year undergraduates at universities and polytechnics, as well as technical college students.

This Student Solution Manual provides complete solutions to all the odd-numbered problems in Essential Mathematical Methods for the Physical Sciences. It takes students through each problem step-by-step, so they can clearly see how the solution is reached, and understand any mistakes in their own working. Students will learn by example how to select an appropriate method, improving their problem-solving skills.

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.

We live in an age where working in science or engineering offers tremendous professional opportunities - the pace of scientific development is truly breathtaking. Yet many researchers struggle with the pressures of the fast-paced academic workplace, and struggle to harmonize their work and personal lives. The result can be burnout, exhaustion, and stress on a personal level, and difficulty in recruiting and retaining talented, diverse people to science and engineering. This book, written for graduate students and researchers at all stages of their careers, aims to help scientists by identifying and questioning the core beliefs that drive a culture of overwork, and provides real-world examples and exercises for those wishing to do things differently. Written in a lively narrative style, and including interview excerpts from practicing scientists, social scientists, and engineers, this book serves as a guide for those seeking to practice the seven traits of the joyful scientist.