Calculus early transcendentals（metric edition） (9版)

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【簡介】 Calculus：Early Transcendentals, Metric Edition ISBN13：9780357113516 出版社：Cengage Learning; Inc 作者：James Stewart (McMaster University);Saleem (California State University Watson Long Beach);Daniel K. Clegg (Palomar College) 【目錄】 Preface. To the Student. Diagnostic Tests. A Preview of Calculus. 1. FUNCTIONS AND MODELS. Four Ways to Represent a Function. Mathematical Models: A Catalog of Essential Functions. New Functions from Old Functions. Exponential Functions. Inverse Functions and Logarithms. Review. Principles of Problem Solving. 2. LIMITS AND DERIVATIVES. The Tangent and Velocity Problems. The Limit of a Function. Calculating Limits Using the Limit Laws. The Precise Definition of a Limit. Continuity. Limits at Infinity; Horizontal Asymptotes. Derivatives and Rates of Change. Writing Project: Early Methods for Finding Tangents. The Derivative as a Function. Review. Problems Plus. 3. DIFFERENTIATION RULES. Derivatives of Polynomials and Exponential Functions. Applied Project: Building a Better Roller Coaster. The Product and Quotient Rules. Derivatives of Trigonometric Functions. The Chain Rule. Applied Project: Where Should a Pilot Start Descent? Implicit Differentiation. Discovery Project: Families of Implicit Curves. Derivatives of Logarithmic Functions and Inverse Trigonometric Functions. Rates of Change in the Natural and Social Sciences. Exponential Growth and Decay. Applied Project: Controlling Red Blood Cell Loss During Surgery. Related Rates. Approximations and Differentials. Discovery Project: Taylor Polynomials. Hyperbolic Functions. Review. Problems Plus. 4. APPLICATIONS OF DIFFERENTIATION. Maximum and Minimum Values. Applied Project: The Calculus of Rainbows. The Mean Value Theorem. What Derivatives Tell Us about the Shape of a Graph. Indeterminate Forms and l'Hospital's Rule. Writing Project: The Origins of l'Hospital's Rule. Summary of Curve Sketching. Graphing with Calculus and Technology. Optimization Problems. Applied Project: The Shape of a Can. Applied Project: Planes and Birds: Minimizing Energy. Newton's Method. Antiderivatives. Review. Problems Plus. 5. INTEGRALS. The Area and Distance Problems. The Definite Integral. Discovery Project: Area Functions. The Fundamental Theorem of Calculus. Indefinite Integrals and the Net Change Theorem. Writing Project: Newton, Leibniz, and the Invention of Calculus. The Substitution Rule. Review. Problems Plus. 6. APPLICATIONS OF INTEGRATION. Areas Between Curves. Applied Project: The Gini Index. Volumes. Volumes by Cylindrical Shells. Work. Average Value of a Function. Applied Project: Calculus and Baseball. Applied Project: Where to Sit at the Movies. Review. Problems Plus. 7. TECHNIQUES OF INTEGRATION. Integration by Parts. Trigonometric Integrals. Trigonometric Substitution. Integration of Rational Functions by Partial Fractions. Strategy for Integration. Integration Using Tables and Technology. Discovery Project: Patterns in Integrals. Approxi

Probability and Statistical Inference (10版)

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【簡介】 Advances in computing technology, particularly in science and business, have increased the need for more statistical scientists to examine the huge amount of data being collected. Written by veteran statisticians, Probability and Statistical Inference, 10th Edition is an authoritative introduction to an in-demand field. It emphasizes the existence of variation in almost every process, and how the study of probability and statistics helps us understand this variation. This applied overview of probability and statistics reinforces basic mathematical concepts with numerous real-world examples and applications to illustrate the relevance of key concepts. A good calculus background is needed, but no previous study of probability or statistics is required. It is designed for a 2-semester course, but also can be adapted for a 1-semester course.  【目錄】 Ch 1 Probability Ch 2 Discrete Distributions Ch 3 Continuous Distributions Ch 4 Bivariate Distributions Ch 5 Distributions of Functions of Random Variables Ch 6 Point Estimation Ch 7 Interval Estimation Ch 8 Tests of Statistical Hypotheses Ch 9 More Tests

Mathematics for Economics and Business 6/E 2009 <PH> 0-273-72228-X (6版)

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書名：Mathematics for Economics and Business 6/E 2009 <PH> 0-273-72228-X 作者：Ian Jacques 出版社：PEARSON 出版日期：2009-12 ISBN：9780273722281

Introductory Course on Financial Mathematics (1版)

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This book is an elementary introduction to the basic concepts of financial mathematics with a central focus on discrete models and an aim to demonstrate simple, but widely used, financial derivatives for managing market risks. Only a basic knowledge of probability, real analysis, ordinary differential equations, linear algebra and some common sense are required to understand the concepts considered in this book. Financial mathematics is an application of advanced mathematical and statistical methods to financial management and markets, with a main objective of quantifying and hedging risks. Since the book aims to present the basics of financial mathematics to the reader, only essential elements of probability and stochastic analysis are given to explain ideas concerning derivative pricing and hedging. To keep the reader intrigued and motivated, the book has a ‘sandwich’ structure: probability and stochastics are given in situ where mathematics can be readily illustrated by application to finance. The first part of the book introduces one of the main principles in finance — ‘no arbitrage pricing’. It also introduces main financial instruments such as forward and futures contracts, bonds and swaps, and options. The second part deals with pricing and hedging of European- and American-type options in the discrete-time setting. In addition, the concept of complete and incomplete markets is discussed. Elementary probability is briefly revised and discrete-time discrete-space stochastic processes used in financial modelling are considered. The third part introduces the Wiener process, Ito integrals and stochastic differential equations, but its main focus is the famous Black–Scholes formula for pricing European options. Some guidance for further study within this exciting and rapidly changing field is given in the concluding chapter. There are approximately 100 exercises interspersed throughout the book, and solutions for most problems are provided in the appendices. Sample Chapter(s) Historical Remarks (180 KB) Bonds and Swaps (490 KB) Binary Model of Price Evolution (394 KB) Connection to 'Reality' (289 KB) Request Inspection Copy Contents: Historical Remarks Financial Instruments and Arbitrage: Preliminary Examples Forwards, Futures and Arbitrage Bonds and Swaps European Options Problems for Part I Discrete-Time Stochastic Modelling and Option Pricing: Binary Model of Price Evolution Elements of Probability Theory Discrete-Time Stochastic Processes Multiperiod Binary Tree Model Complete and Incomplete Markets American Options Problems for Part II Continuous-Time Stochastic Modelling and the Black—Scholes Formula: Connection to 'Reality' Probabilistic Model for an Experiment with Infinitely Many Outcomes Limit of the Discrete-Price Model and Price of a European Option in the Continuous-Time Case Brownian Motion (Wiener Process) Simplistic Introduction to Ito Calculus Problems for Part III Further Study Appendix: Solutions Readership: Undergraduate and postgraduate students taking a course in financial mathematics.

Theory of Stochastic Processes: with Applications to Financial Mathematics and Risk Theory

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Providing the necessary materials within a theoretical framework, this volume presents stochastic principles and processes, and related areas. Over 1000 exercises illustrate the concepts discussed, including modern approaches to sample paths and optimal stopping.