How To Derive A Formula Volume 1 Basic Analytical Skills And Methods For Physical Scientists

Will artificial intelligence solve all problems, making scientific formulae redundant? The authors of this book would argue that there is still a vital role in formulating them to make sense of the laws of nature. To derive a formula one needs to follow a series of steps; last of all, check that the result is correct, primarily through the analysis of limiting cases. The book is about unravelling this machinery.Mathematics is the 'queen of all sciences', but students encounter many obstacles in learning the subject — familiarization with the proofs of hundreds of theorems, mysterious symbols, and technical routines for which the usefulness is not obvious upfront. Those interested in the physical sciences could lose motivation, not seeing the wood for the trees.How to Derive a Formula is an attempt to engage these learners, presenting mathematical methods in simple terms, with more of an emphasis on skills as opposed to technical knowledge. Based on intuition and common sense rather than mathematical rigor, it teaches students from scratch using pertinent examples, many taken across the physical sciences.This book provides an interesting new perspective of what a mathematics textbook could be, including historical facts and humour to complement the material.

V. 1. Basic analytical skills and methods for physical scientists -- v. 2. Further analytical skills and methods for physical scientists.

V. 1. Basic analytical skills and methods for physical scientists -- v. 2. Further analytical skills and methods for physical scientists.

Will artificial intelligence make scientific formulae redundant by eventually solving all current and future physical problems? The authors of this book would argue that there is still a vital role for humans to play in making sense of the laws of nature. To derive a formula one follows a series of steps, only the last of which is to check that the result is correct. The book is about unravelling this machinery.Mathematics is the 'queen of all sciences', but students encounter many obstacles in learning the subject: familiarization with the proofs of hundreds of theorems, mysterious symbols, and technical routines for which the usefulness is not obvious upfront. Learners could lose motivation, not seeing the wood for the trees.This two-volume book How to Derive a Formula is an attempt to engage learners by presenting mathematical methods in as simple terms as possible, with more of an emphasis on skills as opposed to technical knowledge. Based on intuition and common sense rather than mathematical rigour, it teaches students from scratch using pertinent examples, many taken from across the physical sciences to demonstrate the application of the methods taught.This book draws on humour and historical facts to provide an interesting new perspective on what a mathematics textbook could be. The two volumes are presented as an ascent to Everest. Volume 1 covered the necessary basics, taking readers from Base Camp to Camps 1 and 2. This volume moves readers from Camp 2 up to Camps 3 and 4, tackling more advanced methods for deriving formulae. Inevitably, Volume 2 requires readers to tackle more challenging terrain than was experienced in Volume 1 and so is targeted at more advanced students.

Will artificial intelligence make scientific formulae redundant by eventually solving all current and future physical problems? The authors of this book would argue that there is still a vital role for humans to play in making sense of the laws of nature. To derive a formula one follows a series of steps, only the last of which is to check that the result is correct. The book is about unravelling this machinery.Mathematics is the 'queen of all sciences', but students encounter many obstacles in learning the subject: familiarization with the proofs of hundreds of theorems, mysterious symbols, and technical routines for which the usefulness is not obvious upfront. Learners could lose motivation, not seeing the wood for the trees.This two-volume book How to Derive a Formula is an attempt to engage learners by presenting mathematical methods in as simple terms as possible, with more of an emphasis on skills as opposed to technical knowledge. Based on intuition and common sense rather than mathematical rigour, it teaches students from scratch using pertinent examples, many taken from across the physical sciences to demonstrate the application of the methods taught.This book draws on humour and historical facts to provide an interesting new perspective on what a mathematics textbook could be. The two volumes are presented as an ascent to Everest. Volume 1 covered the necessary basics, taking readers from Base Camp to Camps 1 and 2. This volume moves readers from Camp 2 up to Camps 3 and 4, tackling more advanced methods for deriving formulae. Inevitably, Volume 2 requires readers to tackle more challenging terrain than was experienced in Volume 1 and so is targeted at more advanced students.

Bridging the gap between traditional books on quantum and statistical physics, this series is an ideal introductory course for students who are looking for an alternative approach to the traditional academic treatment.This pedagogical approach relies heavily on scientific or technological applications from a wide range of fields. For every new concept introduced, an application is given to connect the theoretical results to a real-life situation. Each volume features in-text exercises and detailed solutions, with easy-to-understand applications.This third volume covers several basic and more advanced subjects about transitions in quantum and statistical physics. Part I describes how the quantum statistics of fermions and bosons differ and under what condition they can merge into the classical-particle-statistics framework seen in Volume 2. This section also describes the fundamentals of conductors, semiconductors, superconductors, superfluids and Bose-Einstein condensates. Part II introduces time-dependent transitions between quantum states. The time evolution of a simple two-level model gives the minimum background necessary to understand the principles behind lasers and their numerous applications. Time-dependent perturbation theory is also covered, as well as standard approaches to the scattering of massive particles. A semi-classical treatment of electromagnetic field-matter interaction is described with illustrations taken from a variety of processes such as phonon scattering, charge distribution or spin densities. The third and last part of the book gives a brief overview of quantum electrodynamics with applications to photon absorption or emission spectroscopies and a range of scattering regimes. There follows a short introduction to the role of multiphoton processes in quantum entanglement based experiments.

Electromagnetism is one of the four fundamental forces in nature, and underlies almost everything we experience in our daily lives, whether we realise it or not. The complete theory was first written down in the late 19th century, and remains an essential part of a scientific education. The mathematics behind the theory, however, can be intimidatingly complex. Furthermore, it is not always clear to beginners why the theory is either useful or interesting, nor how it relates to modern research in theoretical physics.The aim of this book is to guide students towards a detailed understanding of the full theory of electromagnetism, including its practical applications. Later chapters introduce more modern formulations of the theory than are found in traditional undergraduate courses, thus bridging the gap between a first course in electromagnetism, and the advanced concepts needed for further study in physics. The final chapter reviews exciting current research stating that possible theories of (quantum) gravity may be much more closely related to electromagnetism than previously thought.Throughout the book, an informal conversational style is used to demystify intimidating concepts. Relevant mathematical ideas are introduced in a self-contained manner, and exercises are provided with full solutions to aid understanding. This book is essential reading for anyone undertaking a physics degree, but will also be of interest to engineers and chemists.

The Cambridge Handbook of Physics Formulas is a quick-reference aid for students and professionals in the physical sciences and engineering. It contains more than 2000 of the most useful formulas and equations found in undergraduate physics courses, covering mathematics, dynamics and mechanics, quantum physics, thermodynamics, solid state physics, electromagnetism, optics and astrophysics. An exhaustive index allows the required formulas to be located swiftly and simply, and the unique tabular format crisply identifies all the variables involved. The Cambridge Handbook of Physics Formulas comprehensively covers the major topics explored in undergraduate physics courses. It is designed to be a compact, portable, reference book suitable for everyday work, problem solving or exam revision. All students and professionals in physics, applied mathematics, engineering and other physical sciences will want to have this essential reference book within easy reach.