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#### Calculate this: learning CALCULUS just got a whole lot easier!

Stumped trying to understand calculus? *Calculus Demystified*, Second Edition, will help you master this essential mathematical subject.

Written in a step-by-step format, this practical guide begins by covering the basics--number systems, coordinates, sets, and functions. You'll move on to limits, derivatives, integrals, and indeterminate forms. Transcendental functions, methods of integration, and applications of the integral are also covered. Clear examples, concise explanations, and worked problems make it easy to understand the material, and end-of-chapter quizzes and a final exam help reinforce key concepts.

*It's a no-brainer! You'll get:*

- Applications of the derivative and the integral
- Rules of integration
- Coverage of improper integrals
- An explanation of calculus with logarithmic and exponential functions
- Details on calculation of work, averages, arc length, and surface area

*Simple enough for a beginner, but challenging enough for an advanced student, Calculus Demystified, Second Edition, is one book you won't want to function without!*

**MULTIPLY your chances of understanding DISCRETE MATHEMATICS**

If you're interested in learning the fundamentals of discrete mathematics but can't seem to get your brain to function, then here's your solution. Add this easy-to-follow guide to the equation and calculate how quickly you learn the essential concepts.

Written by award-winning math professor Steven Krantz, *Discrete Mathematics Demystified* explains this challenging topic in an effective and enlightening way. You will learn about logic, proofs, functions, matrices, sequences, series, and much more. Concise explanations, real-world examples, and worked equations make it easy to understand the material, and end-of-chapter exercises and a final exam help reinforce learning.

This fast and easy guide offers:

- Numerous figures to illustrate key concepts
- Sample problems with worked solutions
- Coverage of set theory, graph theory, and number theory
- Chapters on cryptography and Boolean algebra
- A time-saving approach to performing better on an exam or at work

Simple enough for a beginner, but challenging enough for an advanced student, *Discrete Mathematics Demystified* is your integral tool for mastering this complex subject.

Here's the perfect self-teaching guide to help anyone master differential equations--a common stumbling block for students looking to progress to advanced topics in both science and math. Covers First Order Equations, Second Order Equations and Higher, Properties, Solutions, Series Solutions, Fourier Series and Orthogonal Systems, Partial Differential Equations and Boundary Value Problems, Numerical Techniques, and more.

For many years, this classroom-tested, best-selling text has guided mathematics students to more advanced studies in topology, abstract algebra, and real analysis. **Elements of Advanced Mathematics, Third Edition** retains the content and character of previous editions while making the material more up-to-date and significant.

This third edition adds four new chapters on point-set topology, theoretical computer science, the P/NP problem, and zero-knowledge proofs and RSA encryption. The topology chapter builds on the existing real analysis material. The computer science chapters connect basic set theory and logic with current hot topics in the technology sector. Presenting ideas at the cutting edge of modern cryptography and security analysis, the cryptography chapter shows students how mathematics is used in the real world and gives them the impetus for further exploration. This edition also includes more exercises sets in each chapter, expanded treatment of proofs, and new proof techniques.

Continuing to bridge computationally oriented mathematics with more theoretically based mathematics, this text provides a path for students to understand the rigor, axiomatics, set theory, and proofs of mathematics. It gives them the background, tools, and skills needed in more advanced courses.

Mathematics is a poem. It is a lucid, sensual, precise exposition of beautiful ideas directed to specific goals. It is worthwhile to have as broad a cross-section of mankind as possible be conversant with what goes on in mathematics. Just as everyone knows that the Internet is a powerful and important tool for communication, so everyone should know that the Poincaré conjecture gives us important information about the shape of our universe. Just as every responsible citizen realizes that the mass-production automobile was pioneered by Henry Ford, so everyone should know that the P/NP problem has implications for security and data manipulation that will affect everyone.

This book endeavors to tell the story of the modern impact of mathematics, of its trials and triumphs and insights, in language that can be appreciated by a broad audience. It endeavors to show what mathematics means for our lives, how it impacts all of us, and what new thoughts it should cause us to entertain. It introduces new vistas of mathematical ideas and shares the excitement of new ideas freshly minted. It discusses the significance and impact of these ideas, and gives them meaning that will travel well and cause people to reconsider their place in the universe.

Mathematics is one of mankind's oldest disciplines. Along with philosophy, it has shaped the very modus of human thought. And it continues to do so. To be unaware of modern mathematics is to miss out on a large slice of life. It is to be left out of essential modern developments. We want to address this point, and do something about it. This is a book to make mathematics exciting for people of all interests and all walks of life. Mathematics is exhilarating, it is ennobling, it is uplifting, and it is fascinating. We want to show people this part of our world, and to get them to travel new paths.

The first three editions of this popular textbook attracted

a loyal readership and widespread use. Students find the book to be concise, accessible, and

complete. Instructors find the book to be clear, authoritative, and dependable.

The goal of this new edition is to make real analysis relevant and accessible

to a broad audience of students with diverse backgrounds. Real analysis

is a basic tool for all mathematical scientists, ranging from mathematicians to physicists to

engineers to researchers in the medical profession. This text aims to be the

generational touchstone for the subject and the go-to text for developing young

scientists.

In this new edition we endeavor to make the book accessible to a broader

audience. This edition includes more explanation, more elementary examples,

and the author stepladders the exercises. Figures are updated and clarified. We make

the sections more concise, and omit overly technical details.

We have updated and augmented the multivariable material in order to bring out

the geometric nature of the topic. The figures are thus enhanced and fleshed out.

Features

- A renewed enthusiasm for the topic comes through in a revised presentation
- A new organization removes some advanced topics and retains related ones
- Exercises are more tiered, offering a more accessible course
- Key sections are revised for more brevity

"Krantz is a very prolific writer. He … creates excellent examples and problem sets."

—Albert Boggess, Professor and Director of the School of Mathematics and Statistical Sciences, Arizona State University, Tempe, USA

Designed for a one- or two-semester undergraduate course,** Differential Equations: Theory, Technique and Practice, Second Edition** educates a new generation of mathematical scientists and engineers on differential equations. This edition continues to emphasize examples and mathematical modeling as well as promote analytical thinking to help students in future studies.

**New to the Second Edition**

- Improved exercise sets and examples
- Reorganized material on numerical techniques
- Enriched presentation of predator-prey problems
- Updated material on nonlinear differential equations and dynamical systems
- A new appendix that reviews linear algebra

In each chapter, lively historical notes and mathematical nuggets enhance students’ reading experience by offering perspectives on the lives of significant contributors to the discipline. "Anatomy of an Application" sections highlight rich applications from engineering, physics, and applied science. Problems for review and discovery also give students some open-ended material for exploration and further learning.

The book is an excellent introduction to a variety of topics and presents many of the basic elements of linear partial differential equations in the context of how they are applied to the study of complex analysis. The author treats the Dirichlet and Neumann problems for elliptic equations and the related Schauder regularity theory, and examines how those results apply to the boundary regularity of biholomorphic mappings. He studies the ?-Neumann problem, then considers applications to the complex function theory of several variables and to the Bergman projection.

*Essentials of Mathematical Thinking* addresses the growing need to better comprehend mathematics today. Increasingly, our world is driven by mathematics in all aspects of life. The book is an excellent introduction to the world of mathematics for students not majoring in mathematical studies.

The author has written this book in an enticing, rich manner that will engage students and introduce new paradigms of thought. Careful readers will develop critical thinking skills which will help them compete in today’s world.

The book explains:

- What goes behind a Google search algorithm
- How to calculate the odds in a lottery
- The value of Big Data
- How the nefarious Ponzi scheme operates

Instructors will treasure the book for its ability to make the field of mathematics more accessible and alluring with relevant topics and helpful graphics. The author also encourages readers to see the beauty of mathematics and how it relates to their lives in meaningful ways.

Authored by a ranking authority in harmonic analysis of several complex variables, this book embodies a state-of-the-art entrée at the intersection of two important fields of research: complex analysis and harmonic analysis. Written with the graduate student in mind, it is assumed that the reader has familiarity with the basics of complex analysis of one and several complex variables as well as with real and functional analysis. The monograph is largely self-contained and develops the harmonic analysis of several complex variables from the first principles. The text includes copious examples, explanations, an exhaustive bibliography for further reading, and figures that illustrate the geometric nature of the subject. Each chapter ends with an exercise set. Additionally, each chapter begins with a prologue, introducing the reader to the subject matter that follows; capsules presented in each section give perspective and a spirited launch to the segment; preludes help put ideas into context. Mathematicians and researchers in several applied disciplines will find the breadth and depth of the treatment of the subject highly useful.

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