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KingStone

【繁體】基礎微積分

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KingStone

【繁體】基礎微積分

Name: 【繁體】基礎微積分
Brand: KingStone
SKU: 3136022401
Price: 32.64 USD
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内容簡介

微積分向來被視為深奧難學的科目，然而微積分對於許多理工科學生來說，
卻是必登之大殿，尤其在打紮根的基礎階段最為重要。

為使讀者免除初學微積分的心理障礙，本書在內容上沒有繁瑣的計算與艱澀難懂的理論，配合圖表敘述的輔助說明使讀者能輕易掌握微積分的學習要領，打破微積分艱澀難學的心理迷思，是初學微積分者的最佳入門書籍，同時亦適用於課堂教學使用。

第１章函數、圖形與極限
1.1函數
1.2函數圖形
1.3一次函數
1.4反函數
1.5極限
1.6極限定理
1.7連續
1.8無窮極限

第２章微分學
2.1導函數之定義
2.2基本微分公式
2.3鏈鎖律
2.4三角函數微分法
2.5反三角函數微分法
2.6指數與對數函數微分法
2.7高階導函數
2.8隱函數微分法

第３章微分學之應用
3.1均值定理
3.2洛比達法則
3.3增減函數與函數圖形之凹性
3.4極值
3.5繪圖

第４章積分及其應用
4.1反導函數
4.2定積分
4.3變數變換法在積分方法上之應用
4.4定積分之變數變換
4.5分部積分法
4.6三角代換積分法
4.7理分式積分法
4.8瑕積分
4.9定積分在求面積上之應用
4.10 定積分在其它幾何上之應用

第５章無窮級數
5.1無窮級數
5.2正項級數
5.3交錯級數
5.4冪級數

第６章多變數函數之微分與積分
6.1二變數函數
6.2二變數函數之基本微分法
6.3鏈鎖法則
6.4隱函數與全微分
6.5二變數函數之極值問題
6.6多重積分
6.7重積分在平面面積上之應用
6.8重積分之一些技巧

內容試閱

自序

這本書專攻微積分或基礎數學課程教學之用，因此在寫作上保持精簡、易讀二大原則：

1.所有例題、習題均經篩選，在難度上均不脫離基本問題之框架；同時有許多例題是以題組或一題多解方式出現，讀者可比較它們解決上之異同，同時亦可啟發讀者學習上之靈感。

2.本書在寫作上不特別強調嚴謹性，許多定理除非在導證過程中具有啟發性或可提升讀者解題技巧外，均只列結果而不予導證。

3.在每節重要或關鍵處均設有隨堂演練，教師可在課堂上先令同學練習然後請幾位同學在黑板演算，教師可從旁對其解題過程、表達方式予以評論，同時也可驗收教學成效。如果成效不理想，教師可再提供訓練教材，並施以隨堂演練。以我的教學經驗，這種教學方式可收最佳學習效果之利。

本書之適應範圍很廣，不同之讀者群各有其特殊之研究領域，學習生命科學的讀者或對環境污染或生態方面之數學模式感到興趣，但對經濟之需求彈性、生產函數等興趣缺缺，反之亦然，因此本書將這些專業應用排除在外，以便讀者能焦注於奠定微積分基礎，為了彌補這方面之不足，教師得令同學蒐集微積分在自己專業領域應用之有關報告，應更有意義且更能提高同學學習之動機。

五南編輯部在本書寫作過程中，給我許多寶貴意見，在此特與致謝，此外作者在這方面經驗仍嫌不足，謬誤之處在所難免，尙祈海內外方眾不吝賜正，不勝感荷。

黃學亮敬識

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