“…PREFACEPRELIMINARIES Sets FunctionsREAL NUMBERSField AxiomsOrder Axioms Natural Numbers, Integers, Rational NumbersCompleteness Axiom Decimal Representation of Real Numbers Countable SetsSEQUENCESSequences and ConvergenceProperties of Convergent Sequences Monotonic SequencesThe Cauchy Criterion Subsequences Upper and Lower Limits Open and Closed Sets INFINITE SERIESBasic Properties Convergence TestsLIMIT OF A FUNCTIONLimit of a Function Basic Theorems Some Extensions of the LimitMonotonic Functions CONTINUITY Continuous Functions Combinations of Continuous Functions Continuity on an IntervalUniformContinuityCompact Sets and ContinuityDIFFERENTIATION The DerivativeTheMean Value TheoremL'Hôpital's RuleTaylor's TheoremTHE RIEMANN INTEGRALRiemann Integrability Darboux's Theorem and Riemann SumsProperties of the Integral The Fundamental Theorem of Calculus Improper IntegralsSEQUENCES AND SERIES OF FUNCTIONSSequences of FunctionsProperties of Uniform ConvergenceSeries of FunctionsPower Series LEBESGUE MEASURE Classes of Subsets of R Lebesgue Outer Measure Lebesgue Measure Measurable Functions LEBESGUE INTEGRATIONDefinition of the Lebesgue IntegralProperties of the Lebesgue Integral Lebesgue Integral and Pointwise ConvergenceLebesgue and Riemann IntegralsREFERENCESNOTATIONINDEX.…”
Enlace del recurso

“…While an elementary physics course of some kind would be helpful to the reader, no specific background in physics is assumed, making this book accessible to students with a grounding in multivariable calculus and linear algebra. Many exercises are provided to develop the reader's understanding of and facility in quantum-theoretical concepts and calculations.…”
Enlace del recurso
Enlace del recurso

“…The first volume begins with length measurement as dominated by the Pythagorean Theorem (three proofs) with application to number theory; areas measured by slicing and scaling, where Archimedes uses the physical weights and balances to calculate spherical volume and is led to the invention of calculus; areas by cut and paste, leading to the Bolyai-Gerwien theorem on squaring polygons; areas by counting, leading to the theory of continued fractions, the efficient rational approximation of real numbers, and Minkowski's theorem on convex bodies; straight-edge and compass constructions, giving complete proofs, including the transcendence of e and \pi, of the impossibility of squaring the circle, duplicating the cube, and trisecting the angle; and finally to a construction of the Hausdorff-Banach-Tarski paradox that shows some spherical sets are too complicated and cloudy to admit a well-defined notion of area.…”
Enlace del recurso

“…The book is well-suited for theorists, pure and applied mathematicians, solid-state physicists, chemists, and others working with the Schrödinger equation, the path integral technique and applications of fractional calculus in various research areas. It is useful to skilled researchers as well as to graduate students looking for new ideas and advanced approaches. …”
Enlace del recurso

“…Only basic secondary school mathematics is required, including an understanding of numbers and elementary geometry, but no calculus. Including numerous exercises, with hints provided, this textbook is suitable for self-study and use alongside lecture courses.…”
Enlace del recurso
Enlace del recurso

“…Various chapters of the book can be used for graduate courses; the main prerequisite is a basic knowledge of calculus, linear algebra, and probability theory.…”
Enlace del recurso

“…The chapter written by Jon Wolfson introduces the emerging field of Lagrangian variational problems, which blends in novel ways the structures of symplectic geometry and the techniques of the modern calculus of variations. The lectures provide an up-do-date overview and an introduction to the research literature in each of their areas. …”
Enlace del recurso

“…Thanks to the accessible style used, readers only need a basic command of Calculus. This book will appeal to scientists, teachers, and graduate students in Mathematics, in particular Mathematical Analysis, Probability and Statistics, Numerical Analysis and Mathematical Physics.…”
Enlace del recurso
Enlace del recurso

“…An interactive tutorial on Schubert Calculus emphasizes the geometric and topological aspects of the topic and is suitable for combinatorialists as well as geometrically minded researchers seeking to gain familiarity with relevant combinatorial tools. …”
Enlace del recurso
Enlace del recurso

“…Readers should be conversant with multivariate calculus and linear algebra. They are also expected to have taken an introductory level course in analysis. …”
Enlace del recurso

“…The applications of linear algebra are extensive and substantial--several of those recur throughout the text in different contexts, including many that elucidate concepts from multivariable calculus. Unusual features of the text include a pervasive emphasis on the geometric interpretation and viewpoint as well as a very complete treatment of the singular value decomposition. …”
Enlace del recurso

“…Mathematicians interested in the calculus of variations, optimal control and in applied functional analysis will find this book a useful guide to the turnpike phenomenon in infinite dimensional spaces. …”
Enlace del recurso
Enlace del recurso

“…This book is an introduction to real analysis for a one-semester course aimed at students who have completed the calculus sequence and preferably one other course, such as linear algebra. …”
Enlace del recurso

“…As the study reveals, this question was central in the early days of calculus, when transcendental quantities and operations entered the stage. …”
Enlace del recurso
Enlace del recurso

“…Mathematics in Everyday Life supports beginning university students in science and engineering by offering extra practice in calculus, linear algebra, geometry, trigonometry, elementary number theory, and probability. …”
Enlace del recurso
Enlace del recurso

“…The text requires only a first-year course in mathematics (calculus and linear algebra) and is also accessible to computer scientists and engineers. …”
Enlace del recurso

“…This textbook is specifically designed to meet the needs of students taking the two-semester calculus-based introductory physics courses now favored in many countries around the world. …”
Enlace del recurso
Enlace del recurso

“…The discussion of limit theorems serves as a gateway to extensive coverage of the theory of stochastic processes, including, for example, stationarity and ergodicity, Poisson and Wiener processes and their trajectories, other Markov processes, jump-diffusion processes, stochastic calculus, and stochastic differential equations. All these conceptual tools then converge in a dynamical theory of Brownian motion that compares the Einstein–Smoluchowski and Ornstein–Uhlenbeck approaches, highlighting the most important ideas that finally led to a connection between the Schrödinger equation and diffusion processes along the lines of Nelson’s stochastic mechanics. …”
Enlace del recurso
Enlace del recurso

“…These lay the groundwork for differential and integral calculus, which are carefully covered in the following chapters. …”
Enlace del recurso
Enlace del recurso

“…George Boole (1815-1864) is well known to mathematicians for his research and textbooks on the calculus, but his name has spread world-wide for his innovations in symbolic logic and the development and applications made since his day. …”
Enlace del recurso
Enlace del recurso