An Illustrative Guide to Multivariable and Vector Calculus
暫譯: 多變量與向量微積分圖解指南

Miklavcic, Stanley J.

An Illustrative Guide to Multivariable and Vector Calculus
  • 出版商: Springer
  • 出版日期: 2026-11-03
  • 售價: $3,230
  • 貴賓價: 9.5 折 $3,068
  • 語言: 英文
  • 頁數: 415
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 3032126177
  • ISBN-13: 9783032126177
  • 相關分類: 微積分 Calculus

    • 海外代購書籍(需單獨結帳)

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商品描述

This textbook focuses on one of the most valuable skills in multivariable and vector calculus: visualization. With nearly 200 carefully drawn color images, students who have long struggled picturing, for example, level sets or vector fields will find these abstract concepts rendered with clarity and ingenuity. This illustrative approach to the material covered in standard multivariable and vector calculus textbooks will serve as a much-needed and highly useful companion. The text will appeal to multivariable and vector calculus students and instructors around the world who seek an accessible, visual approach to this subject. Higher-level students, called upon to apply these concepts across science and engineering, will also find this a valuable and concise resource.

The second edition has been extensively revised. Several sections in the chapters on vectors and functions, differentiation of multivariable functions, and vector calculus have been completely rewritten. Other portions of the first edition have been reorganized, with some material relocated to more suitable sections. Many discussions have been expanded, and explanatory passages have been refined for greater clarity. A significant amount of new material has been added, primarily to provide a more comprehensive treatment of specific topics. Some original exercises have been replaced with fully worked examples, offering a more balanced guide for the reader. In addition, seventy new supplementary problems have been included, and asterisks now identify the more challenging ones.

Emphasizing portability, this book is an ideal complement to other references in the area. It begins by exploring preliminary ideas such as vector algebra, sets, and coordinate systems, before moving into the core areas of multivariable differentiation and integration, and vector calculus. Sections on the chain rule for second derivatives, implicit functions, PDEs, and the method of least squares offer additional depth; ample illustrations are woven throughout. Mastery Checks engage students in material on the spot, while longer exercise sets at the end of each chapter reinforce techniques.

商品描述(中文翻譯)

本教材著重於多變數微積分與向量微積分中最具價值的技能之一：視覺化。全書附有近 200 幅精心繪製的彩色圖像，長期難以想像等位集（level sets）或向量場（vector fields）等概念的學生，將能透過清晰且富創意的呈現方式理解這些抽象概念。本書以插圖輔助說明標準多變數與向量微積分教科書所涵蓋的內容，將成為一份深受期待且極具實用價值的補充教材。對於世界各地希望以易於理解、視覺化方式學習這門學科的多變數與向量微積分學生及教師而言，本書都相當適合。需要在科學與工程領域中應用這些概念的高階學生，也會發現本書是一本實用且精簡的參考資源。

第二版已進行大幅修訂。向量與函數、多變數函數微分，以及向量微積分等章節中的數個小節均已完全改寫。第一版的其他內容也重新編排，其中部分教材移至更合適的小節。許多討論內容有所擴充，說明文字也經過潤飾，以提升清晰度。此外，本版加入了大量新內容，主要是為了更完整地處理特定主題。部分原有習題已替換為完整解答的範例，為讀者提供更均衡的學習指引。除此之外，本版新增 70 道補充問題，並以星號標示較具挑戰性的題目。

本書強調便於攜帶與獨立使用，是其他相關參考資料的理想補充。內容首先探討向量代數、集合與座標系統等預備概念，接著進入多變數微分與積分，以及向量微積分的核心領域。書中另闢專節深入介紹二階導數的鏈鎖律（chain rule）、隱函數、偏微分方程（PDEs）與最小平方法（method of least squares），並穿插大量圖解。「掌握度檢核」（Mastery Checks）讓學生能即時檢驗對教材內容的理解；每章末尾較長的習題組則可幫助讀者鞏固相關技巧。

作者簡介

Stanley J. Miklavcic is Emeritus Professor of Mathematics at the University of South Australia. He was awarded a BSc Hons in Applied Mathematics and the University Medal by the University of New South Wales and holds a PhD from the Australian National University. His research interests include the application of mathematics and modelling in biology, physics and chemistry. A one-time recipient of a Queen Elizabeth Research Fellowship, Stanley has held academic positions in both Sweden and Australia and has published over 150 papers. Stanley is a Fellow of the Australian Mathematical Society and Member of both the Australasian Colloid and Interface Society and the Australian Society of Plant Scientists.

作者簡介(中文翻譯)

Stanley J. Miklavcic 是 University of South Australia 的數學榮譽教授。他於 University of New South Wales 取得應用數學理學士榮譽學位及 University Medal，並取得 Australian National University 的博士學位。他的研究興趣包括數學與建模在生物學、物理學及化學領域的應用。Stanley 曾獲 Queen Elizabeth Research Fellowship，並曾於瑞典及澳洲擔任學術職務，發表論文超過 150 篇。Stanley 是 Australian Mathematical Society 的 Fellow，亦是 Australasian Colloid and Interface Society 及 Australian Society of Plant Scientists 的會員。

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