Calculus: Applications and Technology, 3/e
暫譯: 微積分:應用與技術,第3版

Edmond C. Tomastik

  • 出版商: Thomson
  • 出版日期: 2004-04-27
  • 售價: $980
  • 語言: 英文
  • 頁數: 608
  • 裝訂: Hardcover
  • ISBN: 0534464963
  • ISBN-13: 9780534464967
  • 相關分類: 微積分 Calculus
  • 下單後立即進貨 (約5~7天)

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商品描述

Description:

CALCULUS: APPLICATIONS AND TECHNOLOGY is a modern text that is guided by four basic principles: The Rule of Four, technology, the Way of Archimedes, and an exploratory teaching method. Where appropriate, each topic is presented graphically, numerically, algebraically, and verbally, helping students gain a richer, deeper understanding of the material. A pronounced emphasis in the text on technology, whether graphing calculators or computers, permits instructors to spend more time teaching concepts. Additionally, applications play a central role in the text and are woven into the development of the material. More than 500 referenced exercises and hundreds of data sets contained in the text make this text useful and practical for students. Most importantly, this text lets students investigate and explore calculus on their own, and discover concepts for themselves.

 

Table of Contents:

1. FUNCTIONS.
Graphers Versus Calculus. Functions. Mathematical Models. Exponential Models. Combinations of Functions. Logarithms.
2. MODELING WITH LEAST SQUARES.
Method of Least Squares. Quadratic Regression. Cubic, Quartic, and Power Regression. Exponential and Logarithmic Regression. Logistic Regression. Selecting the Best Model.
3. THE DERIVATIVE.
Introduction to Calculus. Limits. Rates of Change. The Derivative. Local Linearity.
4. RULES FOR THE DERIVATIVE.
Derivatives of Powers, Exponents, and Sums. Derivatives of Products and Quotients. The Chain Rule. Derivatives of Exponential and Logarithmic Functions. Elasticity of Demand. Management of Renewable Natural Resources.
5. CURVE SKETCHING AND OPTIMIZATION.
The First Derivative. The Second Derivative. Limits at Infinity. Additional Curve Sketching. Absolute Extrema. Optimization and Modeling. The Logistic Model. Implicit Differentiation and Related Rates.
6. INTEGRATION.
Antiderivatives. Substitution. Distance Traveled. The Definite Integral. The Fundamental Theorem of Calculus. Area Between Two Curves. Additional Applications of the Integral.
7. ADDITIONAL TOPICS IN INTEGRATION.
Integration by Parts. Integration Using Tables. Numerical Integration. Improper Integrals.
8. FUNCTIONS OF SEVERAL VARIABLES.
Functions of Several Variables. Partial Derivatives. Extrema of Functions of Two Variables. Lagrange Multipliers. Total Differentials and Approximations. Double Integrals.
OPTIONAL CD-ROM CHAPTERS.
9. THE TRIGONOMETRIC FUNCTIONS.
Angles. The Sine and Cosine. Differentiation of the Sine and Cosine Functions. Integrals of the Sine and Cosine Functions. Other Trigonometric Functions.
10. TAYLOR POLYNOMIALS AND INFINITE SERIES.
Taylor Polynomials. Errors in Taylor Polynomial Approximation. Infinite Sequences. Infinite Series. The Integral and Comparison Tests. The Ratio Test and Absolute Convergence. Taylor Series.
11. PROBABILITY AND CALCULUS.
Discrete Probability. Continuous Probability Density Functions. Expected Value and Variance. The Normal Distribution.
12. DIFFERENTIAL EQUATIONS.
Differential Equations. Separation of Variables. Approximate Solutions to Differential Equations. Qualitative Analysis. Harvesting a Renewable Resource.
Appendix A: Review.
Appendix B: Tables.

商品描述(中文翻譯)

**描述:**
《微積分:應用與技術》是一本現代化的教材,遵循四個基本原則:四種表達方式(The Rule of Four)、技術、阿基米德的方法(the Way of Archimedes)以及探索式教學法。在適當的情況下,每個主題都以圖形、數字、代數和口頭方式呈現,幫助學生更深入地理解材料。文本中對技術的強調,無論是圖形計算器還是電腦,讓教師能夠花更多時間教授概念。此外,應用在文本中扮演著核心角色,並融入材料的發展中。文本中包含超過500個參考練習和數百個數據集,使這本書對學生來說既有用又實用。最重要的是,這本書讓學生能夠自主探索微積分,並自行發現概念。

**目錄:**
1. 函數。
圖形計算器與微積分。函數。數學模型。指數模型。函數的組合。對數。
2. 最小二乘法建模。
最小二乘法。二次回歸。三次、四次及冪次回歸。指數和對數回歸。邏輯回歸。選擇最佳模型。
3. 導數。
微積分簡介。極限。變化率。導數。局部線性。
4. 導數的法則。
幂、指數和和的導數。乘積和商的導數。鏈式法則。指數和對數函數的導數。需求的彈性。可再生自然資源的管理。
5. 曲線描繪與優化。
一階導數。二階導數。無窮大處的極限。額外的曲線描繪。絕對極值。優化與建模。邏輯模型。隱式微分與相關速率。
6. 積分。
反導數。替換法。行駛距離。定積分。微積分基本定理。兩曲線之間的面積。積分的其他應用。
7. 積分中的附加主題。
分部積分。使用表格的積分。數值積分。不當積分。
8. 多變數函數。
多變數函數。偏導數。兩變數函數的極值。拉格朗日乘數。全微分與近似。重積分。
可選的CD-ROM章節。
9. 三角函數。
角度。正弦與餘弦。正弦與餘弦函數的微分。正弦與餘弦函數的積分。其他三角函數。
10. 泰勒多項式與無窮級數。
泰勒多項式。泰勒多項式近似的誤差。無窮序列。無窮級數。積分與比較測試。比率測試與絕對收斂。泰勒級數。
11. 機率與微積分。
離散機率。連續機率密度函數。期望值與方差。常態分佈。
12. 微分方程。
微分方程。變數分離。微分方程的近似解。定性分析。可再生資源的收穫。
附錄A:回顧。
附錄B:表格。