This text in multivariable calculus fosters comprehension through
meaningful explanations. Written with students in mathematics,
the physical sciences, and engineering in mind, it extends
concepts from single variable calculus such as derivative,
integral, and important theorems to partial derivatives, multiple
integrals, Stokesâ€™ and divergence theorems. Students with a
background in single variable calculus are guided through a... more...

A renowned mathematician who considers himself both applied and
theoretical in his approach, Peter Lax has spent most of his
professional career at NYU, making significant contributions to
both mathematics and computing. He has written several important
published works and has received numerous honors including the
National Medal of Science, the Lester R. Ford Award, the
Chauvenet Prize, the Semmelweis Medal, the Wiener Prize, and the... more...

Includes sections on the spectral resolution and spectral
representation of self adjoint operators, invariant subspaces,
strongly continuous one-parameter semigroups, the index of
operators, the trace formula of Lidskii, the Fredholm determinant,
and more.
* Assumes prior knowledge of Naive set theory, linear algebra,
point set topology, basic complex variable, and real
variables.
* Includes an appendix on the Riesz representation theorem.

This revised edition of a classic book, which established
scattering theory as an important and fruitful area of research,
reflects the wealth of new results discovered in the intervening
years. This new, revised edition should continue to inspire
researchers to expand the application of the original ideas
proposed by the authors.

Complex Proofs of Real Theorems is an extended meditation on
Hadamard's famous dictum, "The shortest and best way between two
truths of the real domain often passes through the imaginary one."
Directed at an audience acquainted with analysis at the first year
graduate level, it aims at illustrating how complex variables can
be used to provide quick and efficient proofs of a wide variety of
important results in such areas of analysis as approximation... more...

The theory of hyperbolic equations is a large subject, and its applications are many: fluid dynamics and aerodynamics, the theory of elasticity, optics, electromagnetic waves, direct and inverse scattering, and the general theory of relativity. This book is an introduction to most facets of the theory and is an ideal text for a second-year graduate course on the subject. The first part deals with the basic theory: the relation of hyperbolicity to the... more...

These lecture notes of the courses presented at the first CIME session 1994 by leading scientists present the state of the art in recent mathematical methods in Nonlinear Wave Propagation.

This book deals with the mathematical side of the theory of shock waves. The author presents what is known about the existence and uniqueness of generalized solutions of the initial value problem subject to the entropy conditions. The subtle dissipation introduced by the entropy condition is investigated and the slow decay in signal strength it causes is shown.

Praise for the First Edition". . .recommended for the teacher and researcher as well as for graduate students. In fact, [it] has a place on every mathematician's bookshelf." -American Mathematical MonthlyLinear Algebra and Its Applications, Second Edition presents linear algebra as the theory and practice of linear spaces and linear maps with a unique focus on the analytical aspects as well as the numerous applications of the subject. In addition to... more...