Calculus of A Single Variable

Calculus of A Single Variable pdf epub mobi txt 电子书 下载 2026

出版者:Houghton Mifflin College Div
作者:Larson, Ron
出品人:
页数:760
译者:
出版时间:2005
价格:$144.36
装帧:HRD
isbn号码:9780618503032
丛书系列:
图书标签:
  • 数学
  • 教科书
  • 藏书
  • 美国
  • 教材
  • 微积分
  • 单变量微积分
  • 高等数学
  • 数学分析
  • 极限
  • 导数
  • 积分
  • 函数
  • 数学
  • 教材
想要找书就要到 小美书屋
立刻按 ctrl+D收藏本页
你会得到大惊喜!!

具体描述

Ideal for the single-variable, one-, or two-semester calculus course, Calculus of a Single Variable, 8/e, contains the first 9 chapters of Calculus, 8/e. The text continues to offer instructors and students new and innovative teaching and learning resources. The Calculus series was the first to use computer-generated graphics, to include exercises involving the use of computers and graphing calculators, to be available in an interactive CD-ROM format, to be offered as a complete, online calculus course, and to offer a two-semester Calculus I with Precalculus text. Every edition of the series 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 Eighth Edition is the first calculus program to offer algorithmic homework and testing created in Maple so that answers can be evaluated with complete mathematical accuracy.

Two primary objectives guided the authors in writing 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 saves the instructor time. The Eighth Edition continues to provide an evolving range of conceptual, technological, and creative tools that enable instructors to teach the way they want to teach and students to learn they way they learn best.

The explanations, theorems, and definitions have been thoroughly and critically reviewed. Additionally, the exercise sets have been carefully and extensively examined to ensure they cover all calculus topics appropriately.

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.

The Eduspace online resources have been integrated into a comprehensive learning system that combines numerous dynamic calculus resources with online homework and testing materials. Eduspace with eSolutions combines all the features of Eduspace with an electronic version of the textbook exercises and the complete solutions to the odd-numbered text exercises, providing students with a convenient and comprehensive way to do homework and view the course materials.

The Integrated Learning System addresses the changing needs of today's instructors and students. Recognizing that the calculus course is presented in a variety of teaching and learning environments, the program resources are available in print, CD-ROM, and online formats.

SMARTHINKING online tutoring brings students real-time, online tutorial support when they need it most.

书名:《多元微积分基础与应用》 作者:[请在此处填写作者姓名] 出版社:[请在此处填写出版社名称] --- 图书简介 《多元微积分基础与应用》是一本旨在为读者提供扎实的多变量微积分理论基础,并深入探讨其在物理学、工程学、经济学以及计算机科学等多个领域中实际应用的高级教材。本书的编写严格遵循从基础概念到复杂理论的逻辑递进路线,力求在保持数学严谨性的同时,确保内容的直观性和可理解性,特别适合作为大学本科高年级或研究生初级阶段的专业参考书。 第一部分:向量代数与空间几何(Vector Algebra and Spatial Geometry) 本书的第一部分为后续的多变量微积分学习奠定必要的线性代数和几何基础。我们首先从三维欧几里得空间($mathbb{R}^3$)的结构入手,详细阐述向量的定义、加法、标量乘法、点积(内积)和叉积(外积)的几何意义及其代数计算方法。重点分析点积在投影和功的计算中的应用,以及叉积在确定平面法向量和力矩方面的关键作用。 随后,我们过渡到空间曲线的参数化表示。这部分内容不仅包括空间曲线的几何描述,还引入了曲线的弧长计算,为后续的线积分做好了铺垫。平面和空间中曲线的曲率(Curvature)和挠率(Torsion)的概念将被详细推导,揭示曲线在三维空间中弯曲和扭转的内在度量。 空间曲面的描述是本部分的高潮。我们介绍曲面的参数方程表示法,并详细讨论法向量、第一、第二基本形式。特别地,对曲面的高斯曲率(Gaussian Curvature)和平均曲率(Mean Curvature)的分析,将为读者理解曲面几何特性提供深刻的洞察力。这些几何工具是理解微分几何和物理学中曲面张力问题的基石。 第二部分:偏导数与多元函数微分学(Partial Differentiation and Multivariable Differential Calculus) 本部分是多元微积分的核心。我们从单变量函数的极限和连续性概念出发,自然地推广到定义在 $mathbb{R}^n$ 上的函数。偏导数(Partial Derivatives)的定义及其物理意义被清晰地阐述。我们着重讨论方向导数(Directional Derivatives)和梯度向量(Gradient Vector),强调梯度不仅指示函数增长最快的方向,而且垂直于函数的等值面(Level Surfaces)。 链式法则(The Chain Rule)在多元函数中的复杂形式将通过清晰的树状图和矩阵表示法进行系统梳理,确保读者能够熟练处理复合函数的微分。 为了进行最优化问题的分析,我们引入了二阶偏导数,并详细推导了泰勒定理(Taylor's Theorem)在更高维度上的形式。 Hessian 矩阵的引入至关重要,我们将利用其正定性、负定性或不定性来判别多元函数在临界点(Critical Points)处的局部极值(Local Extrema)。对于无约束优化问题,牛顿法及其在多元空间中的迭代过程将被详细介绍。 第三部分:积分学在多维空间中的扩展(Extension of Integration to Higher Dimensions) 本部分将读者从一维的定积分世界带入多维积分的广阔领域。我们首先引入二重积分(Double Integrals)和三重积分(Triple Integrals),重点阐述积分的物理意义,如质量、质心和转动惯量。Fubini 定理的严格表述和实际应用,特别是如何处理积分次序的改变,将是本节的重点。 极坐标、柱坐标和球坐标系下的坐标变换技术被系统地讲解,特别是雅可比行列式(Jacobian Determinant)在面积和体积元素转换中的核心作用。 线积分(Line Integrals)和面积分(Surface Integrals)的引入,使得积分的概念从简单的区域扩展到了曲线和曲面。我们详细区分了第一类和第二类线积分,并讨论了它们在计算物理量,如电磁场中的功、流体中的质量等方面的应用。 第四部分:矢量微积分与场论基础(Vector Calculus and Foundations of Field Theory) 这是本书最具挑战性也最富应用价值的部分。我们正式引入标量场(Scalar Fields)和矢量场(Vector Fields)。矢量场的散度(Divergence)和旋度(Curl)的定义及其物理直观被深入剖析:散度衡量场的源汇强度,而旋度描述场的旋转趋势。这些概念是理解流体力学、电磁学(麦克斯韦方程组的微分形式)的基础。 随后,我们将微积分的基本定理扩展到高维空间: 1. 格林公式(Green's Theorem): 将平面区域上的二重积分与边界曲线上的线积分联系起来。 2. 斯托克斯公式(Stokes' Theorem): 揭示了曲面上旋度通量与边界曲线上线积分之间的深刻关系。 3. 高斯散度定理(Gauss' Divergence Theorem): 将闭合体积上的散度通量与通过该体积边界的通量联系起来。 本书对这些核心定理的推导将采用清晰的几何论证和严格的数学步骤相结合的方式,旨在帮助读者不仅“会用”,更能“理解”它们背后的深刻原理。 第五部分:应用与专题探讨(Applications and Special Topics) 在最后一部分,我们将所学的理论知识应用于解决复杂的实际问题: 变分法引言: 初步介绍泛函的概念以及欧拉-拉格朗日方程的推导,为理解经典力学中的最小作用量原理打下基础。 参数曲面的优化: 讨论在约束条件下的极值问题,即拉格朗日乘数法(Lagrange Multipliers)的几何解释和实用技巧。 场论在工程中的应用: 详细分析热传导方程、流体连续性方程等偏微分方程的建立过程,展示多元微积分如何成为描述自然界动态系统的数学语言。 通过系统的学习,读者将能够熟练地运用多元微积分工具来分析、建模和解决涉及空间变化率和多变量相互作用的复杂问题。本书的习题设计兼顾了计算技巧的训练和概念理解的深化,确保读者能够完全掌握从二维平面到高维空间的数学思维飞跃。

作者简介

Ron Larson received his PhD. in mathematics from the University of Colorado and has been a professor of mathematics at The Pennsylvania State University since 1970. He has pioneered the use of multimedia to enhance the learning of mathematics, having authored over 30 software titles since 1990. Dr. Larson has also conducted numerous seminars and in-service workshops for math teachers around the country about using computer technology as a teaching tool and motivational aid. His Interactive Calculus (a complete text on CD-ROM) received the 1996 Texty Award for the most innovative mathematics instructional material at the college level, and it was the first mainstream college textbook to be offered on the Internet.

Bob Hostetler received his PhD. in Mathematics from The Pennsylvania State University in 1970. He has taught at Penn State for many years and has authored several calculus, precalculus, and intermediate algebra textbooks. His teaching specialties include remedial algebra, calculus, and math education, and his research interests include mathematics education and textbooks.

Bruce Edwards has been a mathematics professor at the University of Florida since 1976. Dr. Edwards majored in mathematics at Stanford University, graduating in 1968. He then joined the Peace Corps and spent four years teaching math in Colombia, South America. He returned to the United States and Dartmouth in 1972, and he received his PhD. in mathematics in 1976. Dr. Edwards' research interests include the area of numerical analysis, with a particular interest in the so-called CORDIC algorithms used by computers and graphing calculators to compute function values. His hobbies include jogging, reading, chess, simulation baseball games, and travel.

目录信息

读后感

评分

评分

评分

评分

评分

用户评价

评分

以前都学过,其实就没怎么看

评分

以前都学过,其实就没怎么看

评分

以前都学过,其实就没怎么看

评分

以前都学过,其实就没怎么看

评分

以前都学过,其实就没怎么看

本站所有内容均为互联网搜索引擎提供的公开搜索信息,本站不存储任何数据与内容,任何内容与数据均与本站无关,如有需要请联系相关搜索引擎包括但不限于百度google,bing,sogou

© 2026 book.quotespace.org All Rights Reserved. 小美书屋 版权所有