Mathematics for Natural Scientists II

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 inabstractmath. This book uses examples and proofs designed to be clear and convincing from the context of physics, as well as providinga large number ofboth solved and unsolved problems in each chapter. This is the second edition, and it has beensignificantlyrevised 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,linearsystemsof differentialequations, Gaussian elimination, fundamental theorem of algebra,convergence of a Fourie series andGibbs-Wilbraham phenomenon, carefulderivation ofthe Fourier integraland of the inverse Laplace transform. New material has been addedon many physics topics meant to illustrate the maths,suchas 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.