Mathematics for Natural Scientists II

Advanced Methods

Lev Kantorovich (Autor)

Buch | Softcover

XXVII, 922 Seiten

2024 | 2nd ed. 2024
Springer International Publishing (Verlag)
978-3-031-46319-8 (ISBN)

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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.

lt;p>Prof. Kantorovich is a member of the Physics Faculty at King's College London. He has published three books and over 230 peer-reviewed papers. Prof. Kantorovich has taught mathematical methods in physics at King's College for more than 20 years, receiving two Excellence in Teaching Awards. He is a recipient of the Institute of Physics David Tabor Medal and Prize for 2023.

Elements of linear algebra.- Complex numbers and functions.- Fourier series.- Special Functions.- Fourier Transform.- Laplace Transform.- Curvilinear coordinates.- Partial differential equations of mathematical physics.- Calculus of variations.

Erscheinungsdatum	27.03.2024
Reihe/Serie	Undergraduate Lecture Notes in Physics
Zusatzinfo	XXVII, 922 p. 127 illus., 121 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Naturwissenschaften ► Chemie ► Physikalische Chemie
	Naturwissenschaften ► Physik / Astronomie ► Allgemeines / Lexika
	Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
Schlagworte	Engineering Mathematics textbook • Mathematical Methods in Physics textbook • Mathematics for engineering students • Mathematics for physics students • Mathematics of physical sciences • Math for engineering students • Math for physics students • Math for the physical sciences • Math used in physics and engineering
ISBN-10	3-031-46319-6 / 3031463196
ISBN-13	978-3-031-46319-8 / 9783031463198
Zustand	Neuware