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Mathematics for Natural Scientists II

Advanced Methods

  • Textbook
  • © 2024
  • Latest edition

Overview

Authors:
  1. Lev Kantorovich

    1. Department of Physics, School of Natural and Mathematical Sciences, King’s College London, London, UK

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  • Provides an exceptionally concise and clear treatment of essential mathematical methods
  • Contains practice problems and solutions in each chapter
  • Serves as the basis for a one-semester undergraduate mathematics course for physics and engineering majors

Part of the book series: Undergraduate Lecture Notes in Physics (ULNP)

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About this book

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. 



Keywords

Table of contents (9 chapters)

  1. Front Matter

    Pages i-xxvii
    Download chapter PDF

  2. Elements of Linear Algebra

    • Lev Kantorovich
    Pages 1-255

  3. Complex Numbers and Functions

    • Lev Kantorovich
    Pages 257-410

  4. Fourier Series

    • Lev Kantorovich
    Pages 411-486

  5. Special Functions

    • Lev Kantorovich
    Pages 487-604

  6. Fourier Transform

    • Lev Kantorovich
    Pages 605-654

  7. Laplace Transform

    • Lev Kantorovich
    Pages 655-717

  8. Curvilinear Coordinates

    • Lev Kantorovich
    Pages 719-779

  9. Partial Differential Equations of Mathematical Physics

    • Lev Kantorovich
    Pages 781-848

  10. Calculus of Variations

    • Lev Kantorovich
    Pages 849-914

  11. Back Matter

    Pages 915-922
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Authors and Affiliations

  • Department of Physics, School of Natural and Mathematical Sciences, King’s College London, London, UK

    Lev Kantorovich

About the author

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. 

 


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