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Calculus


1. 

Lambda Calculus with Types

Lambda Calculus with Types

By: Henk Barendregt; Wil Dekkers; Richard Statman

Publisher: Cambridge University Press

Publication Date: 30-JUN-2013

Insert Date: 05-NOV-2013

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This handbook with exercises reveals in formalisms, hitherto mainly used for hardware and software design and verification, unexpected mathematical beauty. The lambda calculus forms a prototype universal programming language, which in its untyped version is related to Lisp, and was treated in the first author's classic The Lambda Calculus (1984). The formalism has since been extended with types and used in functional programming (Haskell, Clean) and proof assistants (Coq, Isabelle, HOL), used in designing and verifying IT products and mathematical proofs. In this book, the authors focus...

2. 

Calculus: Concepts and Methods

Calculus: Concepts and Methods

By: Ken Binmore; Joan Davies

Publisher: Cambridge University Press

Publication Date: 07-FEB-2002

Insert Date: 05-SEP-2013

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The pebbles used in ancient abacuses gave their name to the calculus, which today is a fundamental tool in business, economics, engineering and the sciences. This introductory book takes readers gently from single to multivariate calculus and simple differential and difference equations. Unusually the book offers a wide range of applications in business and economics, as well as more conventional scientific examples. Ideas from univariate calculus and linear algebra are covered as needed, often from a new perspective. They are reinforced in the two-dimensional case, which is studied in...

3. 

Stochastic Calculus and Differential Equations for Physics and Finance

Stochastic Calculus and Differential Equations for Physics and Finance

By: Joseph McCauley

Publisher: Cambridge University Press

Publication Date: 28-FEB-2013

Insert Date: 05-SEP-2013

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Stochastic calculus provides a powerful description of a specific class of stochastic processes in physics and finance. However, many econophysicists struggle to understand it. This book presents the subject simply and systematically, giving graduate students and practitioners a better understanding and enabling them to apply the methods in practice. The book develops Ito calculus and Fokker–Planck equations as parallel approaches to stochastic processes, using those methods in a unified way. The focus is on nonstationary processes, and statistical ensembles are emphasized in time series...

4. 

The Integral

The Integral

By: Steven G. Krantz

Publisher: Morgan & Claypool Publishers

Publication Date: 02-JAN-2011

Insert Date: 03-SEP-2013

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This book treats all of the most commonly used theories of the integral. After motivating the idea of integral, we devote a full chapter to the Riemann integral and the next to the Lebesgue integral. Another chapter compares and contrasts the two theories. The concluding chapter offers brief introductions to the Henstock integral, the Daniell integral, the Stieltjes integral, and other commonly used integrals. The purpose of this book is to provide a quick but accurate (and detailed) introduction to all aspects of modern integration theory. It should be accessible to any student who has...

5. 

Financial Calculus

Financial Calculus

By: Martin Baxter; Andrew Rennie

Publisher: Cambridge University Press

Publication Date: 19-SEP-1996

Insert Date: 27-JUL-2013

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The rewards and dangers of speculating in the modern financial markets have come to the fore in recent times with the collapse of banks and bankruptcies of public corporations as a direct result of ill-judged investment. At the same time, individuals are paid huge sums to use their mathematical skills to make well-judged investment decisions. Here now is the first rigorous and accessible account of the mathematics behind the pricing, construction and hedging of derivative securities. Key concepts such as martingales, change of measure, and the Heath-Jarrow-Morton model are described with...

6. 

A First Course in Mathematical Analysis

A First Course in Mathematical Analysis

By: David Alexander Brannan

Publisher: Cambridge University Press

Publication Date: 17-AUG-2006

Insert Date: 09-JUL-2013

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Mathematical Analysis (often called Advanced Calculus) is generally found by students to be one of their hardest courses in Mathematics. This text uses the so-called sequential approach to continuity, differentiability and integration to make it easier to understand the subject.Topics that are generally glossed over in the standard Calculus courses are given careful study here. For example, what exactly is a 'continuous' function? And how exactly can one give a careful definition of 'integral'? The latter question is often one of the mysterious points in a Calculus course - and it is quite...

7. 

Precalculus: A Functional Approach to Graphing and Problem Solving, 6th Edition

Precalculus: A Functional Approach to Graphing and Problem Solving, 6th Edition

By: Karl J. Smith

Publisher: Jones & Bartlett Learning

Publication Date: 01-NOV-2011

Insert Date: 22-JUN-2013

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Every New Copy of Precalculus: A Functional Approach to Graphing and Problem Solving Includes Access to the Student Companion Website! Precalculus: A Functional Approach to Graphing and Problem Solving prepares students for the concepts and applications they will encounter in future calculus courses. In far too many texts, process is stressed over insight and understanding, and students move on to calculus ill equipped to think conceptually about its essential ideas. This text provides sound development of the important mathematical underpinnings of calculus, stimulating problems and...

8. 

Stochastic Calculus for Finance

Stochastic Calculus for Finance

By: Marek Capiski; Ekkehard Kopp; Janusz Traple

Publisher: Cambridge University Press

Publication Date: 23-AUG-2012

Insert Date: 05-DEC-2012

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This book focuses specifically on the key results in stochastic processes that have become essential for finance practitioners to understand. The authors study the Wiener process and Ito integrals in some detail, with a focus on results needed for the Black–Scholes option pricing model. After developing the required martingale properties of this process, the construction of the integral and the Ito formula (proved in detail) become the centrepiece, both for theory and applications, and to provide concrete examples of stochastic differential equations used in finance. Finally, proofs of...

9. 

The Gross-Zagier Formula on Shimura Curves

The Gross-Zagier Formula on Shimura Curves

By: Xinyi Yuan; Shou-wu Zhang; Wei Zhang

Publisher: Princeton University Press

Publication Date: 11-NOV-2012

Insert Date: 29-NOV-2012

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This comprehensive account of the Gross-Zagier formula on Shimura curves over totally real fields relates the heights of Heegner points on abelian varieties to the derivatives of L-series. The formula will have new applications for the Birch and Swinnerton-Dyer conjecture and Diophantine equations. The book begins with a conceptual formulation of the Gross-Zagier formula in terms of incoherent quaternion algebras and incoherent automorphic representations with rational coefficients attached naturally to abelian varieties parametrized by Shimura curves. This is followed by a complete...

10. 

Pre-Calculus For Dummies, 2nd Edition

Pre-Calculus For Dummies, 2nd Edition

By: 

Publisher: For Dummies

Publication Date: 26-JUN-2012

Insert Date: 14-JUL-2012

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The fun and easy way to learn pre-calculus Getting ready for calculus but still feel a bit confused? Have no fear. Pre-Calculus For Dummies is an un-intimidating, hands-on guide that walks you through all the essential topics, from absolute value and quadratic equations to logarithms and exponential functions to trig identities and matrix operations. With this guide's help you'll quickly and painlessly get a handle on all of the concepts — not just the number crunching — and understand how to perform all pre-calc tasks, from graphing to tackling proofs. You'll also get a new...

11. 

Precalculus with Calculus Previews, 5th Edition

Precalculus with Calculus Previews, 5th Edition

By: Dennis G. Zill; Jacqueline M. Dewar

Publisher: Jones & Bartlett Learning

Publication Date: 27-DEC-2012

Insert Date: 04-MAY-2012

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Building off the success of Zill and Dewar's popular Essentials of Precalculus with Calculus Previews, the new Fifth Edition continues to include all of the outstanding features and learning tools found in the original text while incorporating additional topics of coverage that some courses may require. With a continued effort to keep the text complete, yet concise, the authors have included four additional chapters making the text a clear choice for many mainstream courses. Additional chapters include a new chapter on Polar Coordinates, as well as Triangle Trigonometry, Systems of Equations...

12. 

Hypoelliptic Laplacian and Orbital Integrals (AM-177)

Hypoelliptic Laplacian and Orbital Integrals (AM-177)

By: Jean-Michel Bismut

Publisher: Princeton University Press

Publication Date: 08-AUG-2011

Insert Date: 03-OCT-2011

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This book uses the hypoelliptic Laplacian to evaluate semisimple orbital integrals in a formalism that unifies index theory and the trace formula. The hypoelliptic Laplacian is a family of operators that is supposed to interpolate between the ordinary Laplacian and the geodesic flow. It is essentially the weighted sum of a harmonic oscillator along the fiber of the tangent bundle, and of the generator of the geodesic flow. In this book, semisimple orbital integrals associated with the heat kernel of the Casimir operator are shown to be invariant under a suitable hypoelliptic deformation,...

13. 

The Calculus of Friendship

The Calculus of Friendship

By: Steven Strogatz

Publisher: Princeton University Press

Publication Date: 07-MAR-2011

Insert Date: 03-OCT-2011

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The Calculus of Friendship is the story of an extraordinary connection between a teacher and a student, as chronicled through more than thirty years of letters between them. What makes their relationship unique is that it is based almost entirely on a shared love of calculus. For them, calculus is more than a branch of mathematics; it is a game they love playing together, a constant when all else is in flux. The teacher goes from the prime of his career to retirement, competes in whitewater kayaking at the international level, and loses a son. The student matures from high school math...

14. 

Technical Mathematics with Calculus, 6th Edition

Technical Mathematics with Calculus, Sixth Edition

By: 

Publisher: John Wiley & Sons

Publication Date: 12-APR-2011

Insert Date: 16-APR-2011

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This textbook has been in constant use since 1980, and this edition represents the first major revision of this text since the second edition. It was time to select, make hard choices of material, polish, refine, and fill in where needed. Much has been rewritten to be even cleaner and clearer, new features have been introduced, and some peripheral topics have been removed. The authors continue to provide real-world, technical applications that promote intuitive?reader learning. Numerous fully worked examples and boxed and numbered formulas give students the essential practice they need...

15. 

Master Math: Calculus

Master Math: Calculus

By: Debra Anne Ross

Publisher: Course Technology PTR

Publication Date: 01-JUN-2009

Insert Date: 21-FEB-2010

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Get ready to master the principles and operations of calculus! Master Math: Calculus is a comprehensive reference guide that explains and clarifies the principles of calculus in a simple, easy-to-follow style and format. Beginning with the most basic fundamental topics and progressing through to the more advanced, the book helps clarify calculus using step-by-step procedures and solutions, along with examples and applications. A complete table of contents and a comprehensive index enable you to quickly find specific topics, and the approachable style and format facilitate an understanding of...

16. 

Master Math: Pre-Calculus

Master Math: Pre-Calculus

By: Debra Anne Ross

Publisher: Course Technology PTR

Publication Date: 01-MAY-2009

Insert Date: 05-JAN-2010

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Get ready to master the principles and formulas of pre-calculus! Master Math: Pre-Calculus is a comprehensive reference guide that explains and clarifies pre-calculus and introductory calculus principles in a simple, easy-to-follow style and format. Beginning with the most basic fundamental topics and progressing through to the more advanced topics that will help prepare you for introductory calculus, the book helps clarify pre-calculus using step-by-step procedures and solutions, along with examples and applications. A complete table of contents and a comprehensive index enable you to...

17. 

The Manga Guide to Calculus

The Manga Guide to Calculus

By: ; ;

Publisher: No Starch Press

Publication Date: 19-AUG-2009

Insert Date: 11-NOV-2009

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Noriko is just getting started as a junior reporter for the Asagake Times . She wants to cover the hard-hitting issues, like world affairs and politics, but does she have the smarts for it? Thankfully, her overbearing and math-minded boss, Mr. Seki, is here to teach her how to analyze her stories with a mathematical eye. In The Manga Guide to Calculus , you'll follow along with Noriko as she learns that calculus is more than just a class designed to weed out would-be science majors. You'll see that calculus is a useful way to understand the patterns in physics, economics, and...