Essential calculus with applications 微积分精要及应用

Calculus is an extremely powerful tool for solving a host of practical probleins in fields as diverse as physics, biology, and economics, to mention just a few. In this rigorous but accessible text, a noted mathematician introduces undergraduate-level students to the problem-solving techniques that make a working knowledge of calculus iudispep, sable for any mathematician.
The author first supplies the necessary mathematical background, including sets, inequalities,absohlte value, mathematical induction, and other "'precalculns" material. Chapter Two begins the actual study of differential calculus with a discussion of the key concept of function, and a thorough treatment of derivatives and limits, in Chapter Three differentiation is used as a tool;among the topics covered here are wqoeity, continuous and differentiable functions, the indefinite integrak local extrema, and concrete optimization problems. Chapter Four treats integral calculus, employing the standard definition of the Biemann integral, and deals with the mean value theorem for integrals, the main techniques of integration, and improper integrals.Chapter Five offers a brief introduction to differential equations and their applications, including problems of growth, decay, and motion. The final chapter is devoted to the differential calculus of functions of several variables.
Numerous problems and answers, and a newly added section of "'Supplementary Hints and Answers," enable the student to test his grasp of the material before going on. Concise and well written, Essential Calculus with Applications is ideal as a primary text or as a refresher for anyone wishing to review the fundamentals of this crucial discipline.

To the Instructor
To the Student
Chapter 1 MATHEMATICAL BACKGROUND
1.1. Introductory Remarks
1.2. Sets
1.3. Numbers
1.4. Inequalities
1.5. The Absolute Value
1.6. Intervals and Neighborhoods
1.7. Rectangular Coordinates
1.8. Straight Lines
1.9. More about Straight Lines
Chapter 2 DIFFERENTIAL CALCULUS
2.1. Functions
2.2. More about Functions
2.3. Graphs
2.4. Derivatives and Limits
2.5. More about Derivatives
2.6. More about Limits
2.7. Differentiation Technique
2.8. Further Differentiation Technique
2.9. Other Kinds of Limits
Chapter 3 DIFFERENTIATION AS A TOOL
3.1. Velocity and Acceleration
3.2. Related Rates and Business Applications
3.3. Properties of Continuous Functions
3.4. Properties of Differentiable Functions
3.5. Applications of the Mean Value Theorem
3.6. Local Extrema
3.7. Concavity and Inflection Points
3.8. Optimization Problems
Chapter 4 INTEGRAL CALCULUS
4.1. The Definite Integral
4.2. Properties of Definite Integrals
4.3. The Logarithm
4.4. The Exponential
4.5. More about the Logarithm and Exponential
4.6. Integration Technique
4.7. Improper Integrals
Chapter 5 INTEGRATION AS A TOOL
5.1. Elementary Differential Equations
5.2. Problems of Growth and Decay
5.3. Problems of Motion
Chapter 6 FUNCTIONS OF SEVERAL VARIABLES
6.1. From Two to n Dimensions
6.2. Limits and Differentiation
6.3. The Chain Rule
6.4. Extrema in n Dimensions
Tables
Selected Hints and Answers
Supplementary Hints and Answers
Index