《海外优秀数学类教材系列丛书：微积分上（第7版 影印版）》详细介绍了微积分的概念、理论和方法，语言朴实、流畅、通俗易懂，书中的例题、习题贴近生活实际，能充分调动学生学习的兴趣。全书分上、下两册，上册内容包括：函数和模型、极限和变化率、微分法则、微分的应用、积分、积分的应用、积分法、积分的进一步应用、微分方程、参数方程和极坐标。下册内容包括：无穷序列和级数、向量和解析几何、向量函数、偏导数、多重积分、向量微积分、二阶微分方程。
本书可作为高等学校非数学类专业微积分、高等数学课程双语教学的教材，也可供广大师生教学参考之用。
- Preface
- To the Student
- Diagnostic Tests
- 1 A PREVIEW OF CALCULUS Functions and Models
- 1.1 Four Ways to Represent a Function
- 1.2 Mathematical Models： A Catalog of Essential Functions
- 1.3 New Functions from Old Functions
- 1.4 Graphing Calculators and Computers
- 1.5 Exponential Functions
- 1.6 Inverse Functions and Logarithms Review
- 2 Principles of Problem Solving Limits and Derivatives
- 2.1 The Tangent and Velocity Problems
- 2.2 The Limit of a Function
- 2.3 Calculating Limits Using the Limit Laws
- 2.4 The Precise Definition of a Limit
- 2.5 Continuity
- 2.6 Limits at Infinity
- 2.7 Derivatives and Rates of Change 143
- 2.8 The Derivative as a Function
- Review
- Problems Plus
- 3 Differentiation Rules
- 4 Applications of Differentiation
- 5 Integrals
- 6 Applications of Integration
- 7 Techniques of Integration
- 8 Further Applications of Integration
- 9 Differential Equations
- 10 Parametric Equations and Polar Coordinates
- 11 Infinite Sequences and Series
- 12 Vectors and the Geometry of Space
- 13 Vector Functions
- 14 Partial Derivatives
- 15 Multiple Integrals
- 16 Vector Calculus
- 17 Second-Order Differential Equations
- Appendixes
- Index
