Calculus : a complete course
著者
書誌事項
Calculus : a complete course
Addison-Wesley, c2000
2nd. ed, international ed
大学図書館所蔵 全3件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
注記
Includes index
内容説明・目次
内容説明
Written by an experienced author team with expertise in the use of technology and NCTM guidelines, this text provides an emphasis on multiple representations of concepts and an abundance of worked examples. Calculus is explored through the interpretation of graphs and tables as well as through the application of analytical methods. Rich exercises include graphical and data-based problems, and interesting real-life applications in biology, business, chemistry, economics, engineering, finance, physics, the social sciences and statistics. Stepped Explorations throughout the text provide guided investigations of key concepts and help students build problem-solving skills. A grapher is required.
目次
(All chapters end with Key Terms and Review Exercises.)
1. Prerequisites for Calculus.
Lines.
Functions and Graphs.
Exponential Functions.
Parametric Equations.
Functions and Logarithms.
Trigonometric Functions.
2. Limits and Continuity.
Rates of Change and Limits.
Limits Involving Infinity.
Continuity.
Rates of Change and Tangent Lines.
3. Derivatives.
Derivative of a Function.
Differentiability.
Rules for Differentiation.
Velocity and Other Rates of Change.
Derivatives of Trigonometric Functions.
Chain Rule.
Implicit Differentiation.
Derivatives of Inverse Trigonometric Functions.
Derivatives of Exponential and Logarithmic Functions.
Calculus At Work.
4. Applications of Derivatives.
Extreme Values of Functions.
Mean Value Theorem.
Connecting fe and f" with the Graph of f.
Modeling and Optimization.
Linearization and Newton's Method.
Related Rates.
5. The Definite Integral.
Estimating with Finite Sums.
Definite Integrals.
Definite Integrals and Antiderivatives.
Fundamental Theorem of Calculus.
Trapezoidal Rule.
Calculus At Work.
6. Differential Equations and Mathematical Modeling.
Antiderivatives and Slope Fields.
Integration by Substitution.
Integration by Parts.
Exponential Growth and Decay.
Population Growth.
Numerical Methods.
Calculus At Work.
7. Applications of Definite Integrals.
Integral as Net Change.
Areas in the Plane.
Volumes.
Lengths of Curves.
Applications from Science and Statistics.
Calculus At Work.
8. L'Hopital's Rule, Improper Integrals, and Partial Fractions.
L'Hopital's Rule.
Relative Rates of Growth.
Improper Integrals.
Partial Fractions and Integral Tables.
9. Infinite Series.
Power Series.
Taylor Series.
Taylor's Theorem.
Radius of Convergence.
Testing Convergence at Endpoints.
Calculus At Work.
10. Parametric, Vector, and Polar Functions.
Parametric Functions.
Vectors in the Plane.
Vector-Valued Functions.
Modeling Projectile Motion.
Polar Coordinates and Polar Graphs.
Calculus of Polar Curves.
11. Vectors and Analytic Geometry in Space.
Cartesian (Rectangular) Coordinates and Vectors in Space.
Dot Products.
Cross Products.
Lines and Planes in Space.
Cylinders and Cylindrical Coordinates.
Quadratic Surfaces.
12. Vector-Valued Functions and Motion in Space.
Vector-valued Functions and Space Curves.
Arc Length and the Unit Tangent Vector T.
Curvature, Torsion, and the TNB Frame.
Planetary Motion and Satellites.
13. Multivariable Functions and Their Derivatives.
Functions of Several Variables.
Limits and Continuity in Higher Dimensions.
Partial Derivatives.
Differentiability, Linearizations, and Differentials.
The Chain Rule.
Directional Derivatives, Gradient Vectors, and Tangent Planes.
Extreme Values and Saddle Points.
Lagrange Multipliers.
14. Multiple Integrals.
Double Integrals.
Area, Moments, and Centers of Mass.
Double Integrals in Polar Form.
Triple Integrals in Rectangular Coordinates.
Masses and Moments in Three Dimensions.
Triple Integrals in Cylindrical and Spherical Coordinates.
Substitutions in Multiple Integrals.
15. Integration in Vector Fields.
Line Integrals.
Vector Fields, Work, Circulation, and Flux.
Path Independence, Potential Functions, and Conservative Fields.
Green's Theorem in the Plane.
Surface Area and Surface Integrals.
Parametrized Surfaces.
Stokes's Theorem.
The Divergence Theorem and a Unified Theory.
Cumulative Review Exercises.
Appendices.
Formulas from Precalculus Mathematics.
Mathematical Induction.
Using the Limit Definition.
Proof of the Chain Rule.
Conic Sections.
Hyperbolic Functions.
A Brief Table of Integrals.
Determinants and Cramer's Rule.
Glossary.
Selected Answers.
Applications Index.
Index.
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