vbid/9783031463204

Description

This textbook, the second in a series (the first covered fundamentals and basics), seeks to make its material accessible to physics students. Physics/engineering can be greatly enhanced by knowledge of advanced mathematical techniques, but the math-specific jargon and laborious proofs can be off-putting to students not well versed in�abstract�math. This book uses examples and proofs designed to be clear and convincing from the context of physics, as well as providing�a large number of�both solved and unsolved problems in each chapter. This is the second edition, and it has been�significantly�revised and enlarged, with Chapters 1 (on linear algebra) and 2 (on the calculus of complex numbers and functions) having been particularly expanded. The enhanced topics throughout the book include: vector spaces,�general (non-Hermitian, including normal and defective) matrices and their right/left eigenvectors/values,�Jordan form, pseudoinverse,�linearsystems�of differential�equations, Gaussian elimination, fundamental theorem of algebra,�convergence of a Fourie series and�Gibbs-Wilbraham phenomenon, careful�derivation of�the Fourier integral�and of �the inverse Laplace transform. New material has been added�on many physics topics meant to illustrate the maths,�such�as 3D rotation, properties of the free electron gas,�van Hove singularities,�and methods for both solving PDEs with a Fourier transform and calculating the width of a domain wall in a ferromagnet,�to mention just a few. This textbook should prove invaluable to all of those with an interest in physics/engineering who have previously experienced difficulty processing the math involved.�Typham this is the title: Mathematics for Natural Scientists II Advanced Methods 2nd Edition