The Visual Display of Quantitative Information, 2nd edition
by Edward R. Tufte
from Graphics Press
A timeless classic in how complex information should be presented graphically. The Strunk & White of visual design. Should occupy a place of honor--within arm's reach--of everyone attempting to understand or depict numerical data graphically. The design of the book is an exemplar of the principles it espouses: elegant typography and layout, and seamless integration of lucid text and perfectly chosen graphical examples. Very Highly Recommended.
Calculus Made Easy
by Silvanus P. Thompson
from St. Martin's Press
Schaum's Outline of Calculus (Fourth Edition)
by Elliott Mendelson
from McGraw-Hill
Students can gain a thorough understanding of differential and integral calculus with this powerful study tool. They'll also find the related analytic geometry much easier. The clear review of algebra and geometry in this edition will make calculus easier for students who wish to strengthen their knowledge in these areas. Updated to meet the emphasis in current courses, this new edition of a popular guideÂÂ--more than 104,000 copies were bought of the prior edition--ÂÂincludes problems and examples using graphing calculators.
Ordinary Differential Equations
by Morris Tenenbaum
from Dover Publications
Partial Differential Equations for Scientists and Engineers (Dover Books on Advanced Mathematics)
by Stanley J. Farlow
from Dover Publications
An Imaginary Tale: The Story of "i" [the square root of minus one]
![An Imaginary Tale: The Story of "i" [the square root of minus one]](http://ecx.images-amazon.com/images/I/51EdpS4WaIL._SL160_.jpg)
by Paul J. Nahin
from Princeton University Press
At the very beginning of his book on i, the square root of minus one, Paul Nahin warns his readers: "An Imaginary Tale has a very strong historical component to it, but that does not mean it is a mathematical lightweight. But don't read too much into that either. It is *not* a scholarly tome meant to be read only by some mythical, elite group.... Large chunks of this book can, in fact, be read and understood by a high school senior who has paid attention to his or her teachers in the standard fare of pre-college courses. Still, it will be most accessible to the million or so who each year complete a college course in freshman calculus.... But when I need to do an integral, let me assure you I have not fallen to my knees in dumbstruck horror. And neither should you."
Nahin is a professor of electrical engineering at the University of New Hampshire; he has also written a number of science fiction short stories. His style is far more lively and humane than a mathematics textbook while covering much of the same ground. Readers will end up with a good sense for the mathematics of i and for its applications in physics and engineering. --Mary Ellen Curtin
Today complex numbers have such widespread practical use--from electrical engineering to aeronautics--that few people would expect the story behind their derivation to be filled with adventure and enigma. In An Imaginary Tale, Paul Nahin tells the 2000-year-old history of one of mathematics' most elusive numbers, the square root of minus one, also known as i. He recreates the baffling mathematical problems that conjured it up, and the colorful characters who tried to solve them.
In 1878, when two brothers stole a mathematical papyrus from the ancient Egyptian burial site in the Valley of Kings, they led scholars to the earliest known occurrence of the square root of a negative number. The papyrus offered a specific numerical example of how to calculate the volume of a truncated square pyramid, which implied the need for i. In the first century, the mathematician-engineer Heron of Alexandria encountered I in a separate project, but fudged the arithmetic; medieval mathematicians stumbled upon the concept while grappling with the meaning of negative numbers, but dismissed their square roots as nonsense. By the time of Descartes, a theoretical use for these elusive square roots--now called "imaginary numbers"--was suspected, but efforts to solve them led to intense, bitter debates. The notorious i finally won acceptance and was put to use in complex analysis and theoretical physics in Napoleonic times.
Addressing readers with both a general and scholarly interest in mathematics, Nahin weaves into this narrative entertaining historical facts and mathematical discussions, including the application of complex numbers and functions to important problems, such as Kepler's laws of planetary motion and ac electrical circuits. This book can be read as an engaging history, almost a biography, of one of the most evasive and pervasive "numbers" in all of mathematics.
Calculus: Early Transcendental Functions
by Ron Larson
from Houghton Mifflin Company
Designed for the three-semester engineering calculus course, Calculus: Early Transcendental Functions, 4/e, continues to offer instructors and students innovative teaching and learning resources. Two primary objectives guided the authors in the revision of this book: to develop precise, readable materials for students that clearly define and demonstrate concepts and rules of calculus; and to design comprehensive teaching resources for instructors that employ proven pedagogical techniques and save time. The Larson/Hostetler/Edwards Calculus program offers a solution to address the needs of any calculus course and any level of calculus student.
Every edition from the first to the fourth of Calculus: Early Transcendental Functions, 4/e has made the mastery of traditional calculus skills a priority, while embracing the best features of new technology and, when appropriate, calculus reform ideas. Now, the Fourth Edition is part of the first calculus program to offer algorithmic homework and testing created in Maple so that answers can be evaluated with complete mathematical accuracy.
- Exercise sets have been carefully examined and revised to ensure they cover all calculus topics appropriately. Many new exercises have been added.
- A variety of exercise types are included in each exercise set. Questions involving skills, writing, critical thinking, problem-solving, applications, and real-data applications are included throughout the text. Exercises are presented in a variety of question formats, including matching, free response, true/false, modeling, and fill-in the blank.
- Putnam Exam Questions—taken from the William Lowell Putnam Mathematical Competition—offer challenging problems that often require students to look for creative solutions; Graphical Analysis exercises offer the opportunity to analyze graphs; Think About It exercises require students to use critical reasoning skills to explore the intricacies of calculus.
- Explanations, theorems, and definitions in the text have been thoroughly reviewed to ensure the text is mathematically precise and easily comprehensible.
- Clear, multi-step examples with worked-out solutions help students learn difficult mathematical concepts. Examples correspond to the exercises, serving as a supportive reference for students. This is the only text on the market where every example, proof, and explanation begins and ends on the same page.
- Explorations help students develop their intuitive understanding of calculus concepts. These optional activities are short enough to integrate into class, but they can also be omitted without loss of continuity.
- Theorem boxes clearly explain important mathematical concepts.
- The Integrated Learning System resources are available in print, CD-ROM, and online formats.
- Eduspace, powered by Blackboard, Houghton Mifflin's online learning tool, offers your students quality online homework, tutorials, multimedia, and testing that correspond to the Calculus: Early Transcendental Functions text. This content is paired with the course management tools of Blackboard. In addition, eSolutions, the complete solutions to the odd-numbered text exercises, provides students with a convenient and comprehensive way to do homework and view the course materials.
- SMARTHINKING online tutoring brings students real-time, online tutorial support when they need it most.
Calculus: Graphical, Numerical, and Algebraic
by Franklin Demana
from Pearson Scott Foresman
Advanced Calculus Demystified
by David Bachman
from McGraw-Hill Professional
Your INTEGRAL tool for mastering ADVANCED CALCULUS
Interested in going further in calculus but don't where to begin? No problem! With Advanced Calculus Demystified, there's no limit to how much you will learn.
Beginning with an overview of functions of multiple variables and their graphs, this book covers the fundamentals, without spending too much time on rigorous proofs. Then you will move through more complex topics including partial derivatives, multiple integrals, parameterizations, vectors, and gradients, so you'll be able to solve difficult problems with ease. And, you can test yourself at the end of every chapter for calculated proof that you're mastering this subject, which is the gateway to many exciting areas of mathematics, science, and engineering.
This fast and easy guide offers:
- Numerous detailed examples to illustrate basic concepts
- Geometric interpretations of vector operations such as div, grad, and curl
- Coverage of key integration theorems including Green's, Stokes', and Gauss'
- Quizzes at the end of each chapter to reinforce learning
- A time-saving approach to performing better on an exam or at work
Simple enough for a beginner, but challenging enough for a more advanced student, Advanced Calculus Demystified is one book you won't want to function without!
A New Kind of Science
by Stephen Wolfram
from Wolfram Media
Physics and computer science genius Stephen Wolfram, whose Mathematica computer language launched a multimillion-dollar company, now sets his sights on a more daunting goal: understanding the universe. Wolfram lets the world see his work in A New Kind of Science, a gorgeous, 1,280-page tome more than a decade in the making. With patience, insight, and self-confidence to spare, Wolfram outlines a fundamental new way of modeling complex systems.
On the frontier of complexity science since he was a boy, Wolfram is a champion of cellular automata--256 "programs" governed by simple nonmathematical rules. He points out that even the most complex equations fail to accurately model biological systems, but the simplest cellular automata can produce results straight out of nature--tree branches, stream eddies, and leopard spots, for instance. The graphics in A New Kind of Science show striking resemblance to the patterns we see in nature every day.
Wolfram wrote the book in a distinct style meant to make it easy to read, even for nontechies; a basic familiarity with logic is helpful but not essential. Readers will find themselves swept away by the elegant simplicity of Wolfram's ideas and the accidental artistry of the cellular automaton models. Whether or not Wolfram's revolution ultimately gives us the keys to the universe, his new science is absolutely awe-inspiring. --Therese Littleton
This long-awaited work from one of the world's most respected scientists presents a series of dramatic discoveries never before made public. Starting from a collection of simple computer experiments---illustrated in the book by striking computer graphics---Wolfram shows how their unexpected results force a whole new way of looking at the operation of our universe.
Wolfram uses his approach to tackle a remarkable array of fundamental problems in science: from the origin of the Second Law of thermodynamics, to the development of complexity in biology, the computational limitations of mathematics, the possibility of a truly fundamental theory of physics, and the interplay between free will and determinism.
Written with exceptional clarity, and illustrated by more than a thousand original pictures, this seminal book allows scientists and non-scientists alike to participate in what promises to be a major intellectual revolution.
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