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This book is designed as per NEP 2020 guidelines and is meant for undergraduate physics students. The text begins with a coverage of kinetic theory and dynamics of ideal gases and then proceeds to discuss real gases. Thereafter the basic formalism, zeroth law, first and second laws of thermodynamics are introduced. It concludes with chapters on thermodynamic potentials and Maxwell's relations as well as classical and quantum theory of black body radiation. Written in a lucid manner, students will require only a prior knowledge of mathematical concepts such as differentiation and integration to understand these topics. Each chapter is divided into sections and subsections for ease of comprehension. Special attention has been paid to the simplification of concepts by providing intermediate steps for difficult derivations. Chapters are supported by a rich pool of practice questions like multiple choice questions, short answer type questions, long answer type questions, and numerical problems.
Adopting a unified mathematical framework, this textbook gives a comprehensive derivation of the rules of continuum physics, describing how the macroscopic response of matter emerges from the underlying discrete molecular dynamics. Covered topics include elasticity and elastodynamics, electromagnetics, fluid dynamics, diffusive transport in fluids, capillary physics and thermodynamics. By also presenting mathematical methods for solving boundary-value problems across this breadth of topics, readers develop understanding and intuition that can be applied to many important real-world problems within the physical sciences and engineering. A wide range of guided exercises are included, with accompanying answers, allowing readers to develop confidence in using the tools they have learned. This book requires an understanding of linear algebra and vector calculus and will be a valuable resource for undergraduate and graduate students in physics, chemistry, engineering and geoscience.
How do mathematicians approach a problem, explore the possibilities, and develop an understanding of a whole area around it? The issue is not simply about obtaining 'the answer'; rather, Beardon explains that a mathematical problem is just one of many related ones that should be simultaneously investigated and discussed at various levels, and that understanding this is a crucial step in becoming a creative mathematician. The book begins with some good advice about procedure, presentation, and organisation that will benefit every mathematician, budding, teaching or practised. In the rest of the book, Beardon presents a series of simple problems, then, through discussion, consideration of special cases, computer experiments, and so on, the reader is taken through these same problems, but at an increasing level of sophistication and generality. Mathematics is rarely a closed book, and seemingly innocent problems, when examined and explored, can lead to results of significance.
Understanding Fluid Flow takes a fresh approach to introducing fluid dynamics, with physical reasoning and mathematical developments inextricably intertwined. The 'dry' fluid dynamics described by potential theory is set within the context of real viscous flows to give fundamental insight into how fluids behave. The book gives a flavour of theoretical, experimental and numerical approaches to analysing fluid flow, and implicitly develops skills in applied mathematical modelling of physical systems. It is supplemented by movies that are freely downloadable.
The primary task of electrostatics is to find the electric field of a given stationary charge distribution. In principle, this purpose is accomplished by Coulomb’s law, in the form of Eq. 2.8:
The fundamental problem electrodynamics hopes to solve is this (Fig. 2.1): We have some electric charges, (call them source charges); what force do they exert on another charge, (call it the test charge)? The positions of the source charges are given (as functions of time); the trajectory of the test particle is to be calculated.
Remember the basic problem of classical electrodynamics: we have a collection of charges (the “source” charges), and we want to calculate the force they exert on some other charge (the “test” charge – Fig. 2.1). According to the principle of superposition, it is sufficient to find the force of a single source charge – the total is then the vector sum of all the individual forces.
If you ask the average person what “magnetism” is, you will probably be told about refrigerator decorations, compass needles, and the North Pole – none of which has any obvious connection with moving charges or current-carrying wires. And yet, in classical electrodynamics all magnetic phenomena are due to electric charges in motion; if you could examine a piece of magnetic material on an atomic scale you would find tiny currents: electrons orbiting around nuclei and spinning about their axes.
In this chapter we study conservation of energy, momentum, and angular momentum, in electrodynamics. But I want to begin by reviewing the conservation of charge, because it is the paradigm for all conservation laws. What precisely does conservation of charge tell us? That the total charge in the Universe is constant? Well, sure – that’s global conservation of charge. But local conservation of charge is a much stronger statement: if the charge in some region changes, then exactly that amount of charge must have passed in or out through the surface. The tiger can’t simply rematerialize outside the cage; if it got from inside to outside it must have slipped through a hole in the fence.