Synopses & Reviews
This set features:
Foundations of Differential Geometry, Volume 1 by Shoshichi Kobayashi and Katsumi Nomizu (978-0-471-15733-5)
Foundations of Differential Geometry, Volume 2 by Shoshichi Kobayashi and Katsumi Nomizu (978-0-471-15732-8)
Differential and Integral Calculus, Volume 1 by Richard Courant (978-0-471-60842-4)
Differential and Integral Calculus, Volume 2 by Richard Courant (978-0-471-60840-0)
Linear Operators, Part 1: General Theory by Neilson Dunford and Jacob T. Schwartz (978-0-471-60848-6)
Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert Space Theory by Neilson Dunford and Jacob T. Schwartz (978-0-471-60847-9)
Linear Operators, Part 3: Spectral Operators by Neilson Dunford and Jacob T. Schwartz (978-0-471-60846-2)
Applied and Computational Complex Analysis, Volume 1, Power Series Integration Conformal Mapping Location of Zero by Peter Henrici (978-0-471-60841-7)
Applied and Computational Complex Analysis, Volume 2, Special Functions-Integral Transforms- Asymptotics-Continued Fractions by Peter Henrici (978-0-471-54289-6)
Applied and Computational Complex Analysis, Volume 3, Discrete Fourier Analysis, Cauchy Integrals, Construction of Conformal Maps, Univalent Functions by Peter Henrici (978-0-471-58986-0)
Synopsis
Volume 2 of the classic advanced calculus text
Richard Courant's Differential and Integral Calculus is considered an essential text for those working toward a career in physics or other applied math. Volume 2 covers the more advanced concepts of analytical geometry and vector analysis, including multivariable functions, multiple integrals, integration over regions, and much more, with extensive appendices featuring additional instruction and author annotations. The included supplement contains formula and theorem lists, examples, and answers to in-text problems for quick reference.
Synopsis
Differential and Integral Calculus, Volume 2:
“Unlike modern mathematicians who pursue their research apart from engineering or physical applications, Richard Courant was adverse to abstract theories and vague theorems. The topics covered in this set will provide the reader with a solid background to understanding the mathematics of heat conduction, electricity and magnetism, fluid dynamics and elasticity.” –Amazon Review
This book includes not only calculational techniques, but also an introduction to real analysis, good mathematical reasoning, and proof techniques. Courant leads the way straight to useful knowledge, and aims at making the subject easier to grasp, not only by giving proofs step by step, but also by throwing light on the interconnexions and purposes of the whole.
Table of Contents
Partial table of contents:
Preliminary Remarks on Analytical Geometry and Vector Analysis: Rectangular Coordinates and Vectors, Affine Transformations and the Multiplication of Determinants.
Functions of Several Variables and Their Derivatives: Continuity, The Total Differential of a Function and Its Geometrical Meaning.
Developments and Applications of the Differential Calculus: Implicit Functions, Maxima and Minima.
Multiple Integrals: Transformation of Multiple Integrals, Improper Integrals.
Integration over Regions in Several Dimensions: Surface Integrals, Stokes's Theorem in Space.
Differential Equations: Examples on the Mechanics of a Particle, Linear Differential Equations.
Calculus of Variations: Euler's Differential Equation in the Simplest Case, Generalizations.
Functions of a Complex Variable: The Integration of Analytic Functions, Cauchy's Formula and Its Applications.
Appendixes.
Index.