Mathematics

本書特色1. 全面表格化整理、論述圖像化。2. 習題區分基礎、進階題，有效掌握學習情況。3. 每章附範例解題影音。4. 新增線上教學頻道，包含作者已出版教科書之現場教學錄影，幫助讀者建立行動教室自我學習。內容簡介本教材內容相當豐富，在建立為工程與電資領域所用之數學為基礎的前提下分成「常微分方程式」、「線性代數」、「向量函數分析」、「傅立葉分析與偏微分方程式」及「複變分析」等五大部分，適合四年制大學部學生一學年上下兩學期各三學分，共六學分之工程數學課程，其重點分別簡介如下。第一部分：常微分方程式(第一到四章)幾乎所有大學中工程與電資領域相關系所在工程數學第一學期的教材內容都是以「常微分方程式」為主要內容，其內容包含有「一階常微分方程式」、「高階線性常微分方程式」、「拉氏轉換」與「常微分方程式之冪級數解」等四大主題重點。第二部分：線性代數(第五到七章)此部分教材內容包含了「向量運算與向量空間」、「矩陣分析」及「線性微分方程式系統」等三大重點。第三部分：向量函數分析(第八章)此部分內容包含向量微分、Del運算、線積分、面積分與積分三大定理(格林定理、高斯散度定理與史托克定理)，其觀念與計算被大量應用在電磁學(電資領域)與流體力學(工程領域)，是非常重要的單元。第四部分：傅立葉分析與偏微分方程式(第九到十章)本書中第九章介紹了正交函數集合與傅立葉分析，此單元在工程領域會用來求解第十章的偏微分方程式，除此之外，電資領域更大量應用到訊號分析與處理上。第五部分：複變分析(第十一章)本章共包含複數運算、複變函數與微分、複變函數積分、泰勒與洛朗展開式、留數定理及實變函數定積分等單元，本章節在工程與電資領域會用在一般物理學、熱力學、流體力學、自動控制、電路(子)學、訊號與系統與電機機械與控制等專業課程中。

This Element discusses the problem of mathematical knowledge, and its broader philosophical ramifications. It argues that the challenge to explain the (defeasible) justification of our mathematical beliefs ('the justificatory challenge'), arises insofar as disagreement over axioms bottoms out in disagreement over intuitions. And it argues that the challenge to explain their reliability ('the reliability challenge'), arises to the extent that we could have easily had different beliefs. The Element shows that mathematical facts are not, in general, empirically accessible, contra Quine, and that they cannot be dispensed with, contra Field. However, it argues that they might be so plentiful that our knowledge of them is unmysterious. The Element concludes with a complementary 'pluralism' about modality, logic and normative theory, highlighting its surprising implications. Metaphysically, pluralism engenders a kind of perspectivalism and indeterminacy. Methodologically, it vindicates Carnap

Mathematical logic grew out of philosophical questions regarding the foundations of mathematics, but logic has now outgrown its philosophical roots, and has become an integral part of mathematics in general. This book is designed for students who plan to specialize in logic, as well as for those who are interested in the applications of logic to other areas of mathematics. Used as a text, it could form the basis of a beginning graduate-level course. There are three main chapters: Set Theory, Model Theory, and Recursion Theory. The Set Theory chapter describes the set-theoretic foundations of all of mathematics, based on the ZFC axioms. It also covers technical results about the Axiom of Choice, well-orderings, and the theory of uncountable cardinals. The Model Theory chapter discusses predicate logic and formal proofs, and covers the Completeness, Compactness, and Löwenheim-Skolem Theorems, elementary submodels, model completeness, and applications to algebra. This chapter also continu

A lively, accessible history of mathematics throughout the ages and across the globe Mathematics is fundamental to our daily lives. Science, computing, economics—all aspects of modern life rely on some kind of maths. But how did our ancestors think about numbers? How did they use mathematics to explain and understand the world around them? Where do numbers even come from? In this Little History, Snezana Lawrence traces the fascinating history of mathematics, from the Egyptians and Babylonians to Renaissance masters and enigma codebreakers.Like literature, music, or philosophy, mathematics has a rich history of breakthroughs, creativity and experimentation. And its story is a global one. We see Chinese Mathematical Art from 200 BCE, the invention of algebra in Baghdad’s House of Wisdom, and sangaku geometrical theorems at Japanese shrines.Lawrence goes beyond the familiar names of Newton and Pascal, exploring the prominent role women have played in the history of maths, including Emmy N

《數學小史》用親切易懂的語言，帶領讀者走進數學的歷史長河，從古埃及與巴比倫時期，一路走到現代密碼學與數學理論的發展。書中不只介紹牛頓、帕斯卡等熟悉的名字，也細細描寫中國、阿拉伯、日本等地的數學成就，更特別介紹女性數學家的貢獻。這是一本融合人文與科學的溫暖數學故事書，適合對數字與知識充滿好奇的你。A lively, accessible history of mathematics throughout the ages and across the globeMathematics is fundamental to our daily lives. Science, computing, economics—all aspects of modern life rely on some kind of maths. But how did our ancestors think about numbers? How did they use mathematics to explain and understand the world around them? Where do numbers even come from?In this Little History, Snezana Lawrence traces the fascinating history of mathematics, from the Egyptians and Babylonians to Renaissance masters and enigma codebreakers. Like literature, music, or philosophy, mathematics has a rich history of breakthroughs, creativity and experimentation. And its story is a global one. We see Chinese Mathematical Art from 200 BCE, the invention of algebra in Baghdad’s House of Wisdom, and sangaku geometrical theorems at Japanese shrines. La

改變對數學的不了解 100個故事帶你暢遊數學的廣闊世界！ 在遠古時代就誕生的數學，做為人類文明的結晶，數學和歷史一樣不斷發展，成為人類認識和改造世界的最有力工具之一，數學的發展和研究不但存在在日常生活裡，更擴大到一般人較難以理解的深奧範疇中，因此大多數人無法理解數學的宏大和瑰麗，進而感到害怕排斥。 數學在我們的生活中無所不在，無論是簡單購買商品的算術；理財投資的財務觀念；與物理息息相關的自然現象，

The book provides the reader with a multifaceted picture of mathematics education in Israel, put into an international perspective where relevant. It is intended to give an overview of a wide range of

O’Neil所著《高等工程數學》第八版包括下列幾個特點，旨在使學生更容易接近數學以及對數學產生興趣： 一、新增「數往知來」（Math in Context），是由工程師為工程學生編寫的短文，從他們的角度提供洞察力，了解數學如何在各種現實世界的工程項目和設置中出現。 二、本書的組織已重新設計，以便更有效地關注特定主題。例如，增加了史特姆―李奧維里問題、波動和熱方程式的解法包括處理驅動函數的技術，以及

突破文理之限，老少咸宜。 只要你是地球人，看過本書，就能輕鬆讀懂上帝用來書寫宇宙的文字。宇宙之大，粒子之微，火箭之速，化工之巧，地球之變，生物之謎，日用之繁，無處不用數學。 生活中的數學問題，故事裡的數學知識，專業上的數學猜想，一本書全講透。 如果你認為數字、符號和公式很枯燥；如果你認為數學太難了，總是學不好；如果你認為除了加減乘除，數學沒什麼用處；如果…… 翻開這本書，你會有一個完全不一樣的答案

The only series for MYP 4 and 5 developed in cooperation with the International Baccalaureate (IB)Develop your skills to become an inquiring learner; ensure you navigate the MYP framework with confi

Enhance students' critical-thinking skills in grades K-12 using high-interest mathematics content. This classroom resource provides leveled text-dependent questions to support students as they examine

The IBMYP Mathematics Study Guide Level 3 is tailor-made for students in their third year of IBMYP studies and aims to build a solid foundation for further studies in Mathematics. Written by our highl

IGCSE Mathematics Study Guide id designed for students taking the Ed-excel/ CIE IGCSE Mathematics examination. Following the latest IGCSE topic areas, including number properties, algebra, geometry, t

IBMYP Mathematics Study Guide Level 4 is tailor-made for students in their fourth year of IBMYP studies and aims to build a solid foundation for further studies in Mathematics. Written by our highly e

?This book is the result of a joint venture between Professor Akio Kawauchi, Osaka City University, well-known for his research in knot theory, and the Osaka study group of mathematics education, foun

IBMYP Mathematics Level 5 Study Guide is tailor-made for students in their final year of IBMYP studies and provides a solid foundation for further studies in the IB program. Written by our highly expe

Mathews (California State U.-Fullerton) and Howell (Westmont College) present a textbook for students in mathematics, physics, and engineering at the junior or senior undergraduate level who have comp

Suitable for students from any educational background. Sample Tests with detailed and multiple solutions. Useful test taking strategies: tips for plugging-in and using graphing calculator. Over 100han

People who learn to solve problems 'on the job' often have to do it differently from people who learn in theory. Practical knowledge and theoretical knowledge is different in some ways but similar in other ways - or else one would end up with wrong solutions to the problems. Mathematics is also like this. People who learn to calculate, for example, because they are involved in commerce frequently have a more practical way of doing mathematics than the way we are taught at school. This book is about the differences between what we call practical knowledge of mathematics - that is street mathematics - and mathematics learned in school, which is not learned in practice. The authors look at the differences between these two ways of solving mathematical problems and discuss their advantages and disadvantages. They also discuss ways of trying to put theory and practice together in mathematics teaching.

The Mathematics: Modeling Our World curriculum is founded on the principle that mathematics is a necessary tool for understanding the physical and social worlds in which we live. This is not the same

The first paper was the outcome of joint research by Mr. Harvey and the author and was first published in the Bulletin of the Institute of Ethnology, No.23 (1967). The second paper was the first publi