內容大鋼
This textbook is aimed at undergraduate foreign students ofmedicine and pharmacy in China.The book makes an effort to guidestudents, particularly of medicine and pharmacy, through the coreconcepts of calculus and to help them understand how those conceptsapply to their lives and the world around them.It emphasizes theimportant role of calculus in the medicine and pharmacy sciences.Most of the contents have been practiced at Jiangsu University.Thematerial is well-suited for self-study, as we know from experience.
The book is intended for the first semester of study.It coversthe traditional single variable calculus course as well as probabilityand statistics.Emphasis is put on calculus since it serves as the baseof probability theory.There are eight chapters in the textbook.Thevery first chapter talks about function, about which students havebeen familiar with.Topics that follow are traditional contents ofdifferential calculus and the basic concepts of integral, as well asprobability and statistics: limits, derivatives, additional derivativetopics, graphing and optimization, integration, applications ofintegration, probability and statistics.
目錄
Chapter 1 Functions
1.1 Lines in the Plane
1.1.1 Coordinates on the Line
1.1.2 Cartesian Coordinates in the Plane
1.1.3 Linear Equations
1.1.4 Equations of Lines
Exercise 1.1
1,2 Concept of Function
1.2.1 Basic Conception
1.2.2 Function Notation
1.2.3 Even and Odd Functions
1.2.4 Increasing and Decreasing Functions
Exercise 1.2
1.3 Polynomial and Rational Functions
1.3.1 Linear Functions and Straight Lines
1.3.2 Quadratic Functions
1.3.3 Polynomial Functions and Rational Functions
Exercise 1.3
Summary and Review
Chapter 2 Limits
2.1 Concept of Limit
2.1.1 Intuitive Definition of Limits
2.1.2 Properties of Limits
Exercise 2.1
2.2 Infinite Limits
2.2.1 Infinite Limits
2.2.2 Vertical Asymptote
Exercise 2.2
2.3 Continuity
2.3.1 Concept of Continuity
2.3.2 Continuity Properties
2.3.3 The Extreme Value Theorem
2.3.4 The Intermediate Value Theorem
2.3.5 Solving Inequalities Using Continuity Properties
Exercise 2.3
2.4 Limits at Infinity
2.4.1 Horizontal Asymptotes
2.4.2 Exponential Functions
Exercise 2.4
2.5 Precise Definition of Limits
2.5.1 Limits at Finite Points that Have Finite Values
2.5.2 Infinite Limits
2.5.3 Definition of Limits at Infinity
Exercise 2.5
Summary and Review
Chapter 3 Derivatives
3.1 Definition of the Derivative
3.1.1 Instantaneous Rates of Change
3.1.2 Geometric Interpretation
3.1.3 Differentiability and Continuity
Exercise 3.1
3.2 Basic Differentiation Properties
3.2.1 Constant Function Rule
3.2.2 The Power Rule
3.2.3 Sum and Difference Rule
3.2.4 Derivative of Polynomials
Exercise 3.2
3.3 Differentials
3.3.1 Differentials
3.3.2 Linear Approximation
Exercise 3.3
Summary and Review
Chapter 4 Additional Derivative Topics
4.1 Derivatives of Products and Quotients
4.1.1 Derivatives of Products
4.1.2 Derivatives of Quotients
Exercise 4.1
4.2 The Chain Rule
4.2.1 Composite Functions
4.2.2 Proof of the Chain Rule
4.2.3 The General Power Rule
Exercise 4.2
4.3 Logarithmic Function
4.3.1 Inverse Function
4.3.2 Differentiability of Inverses
4.3.3 Logarithmic Functions
Exercise 4.3
4.4 Derivative of e" and In x
4.4.1 Derivative of the Natural Exponential Functions
4.4.2 Derivative of Exponential Functions
4.4.3 Exponential Growth and Decay
4.4.4 Derivative of Logarithmic Functions
Exercise 4.4
4.5 Implicit Differentiation
Exercise 4.5
4.6 Related Rates
Exercise 4.6
Summary and Review
Chapter 5 Graphing and Optimization
5.1 Local Extrema and the Mean Value Theorem
5.1.1 Local Extrema
5.1.2 Critical Numbers
5.1.3 The Mean Value Theorem
Exercise 5.1
5.2 The First Derivatives and Graphs
5.2.1 The First Derivatives and Monotonicity
5.2.2 The First Derivative Test
Exercise 5.2
5.3 The Second Derivatives and Graphs
5.3.1 Higher Derivatives
5.3.2 Concavity
Exercise 5.3
5.4 Optimization
5.4.1 Locating Absolute Extrema
5.4.2 The Second Derivative and Extrema
5.4.3 The Second Derivative Test for Absolute Extrema
5.4.4 Optimization Problems
Exercise 5.4
5.5 L'Hospital's Rule
5.5.1 Indeterminate Forms
5.5.2 L'Hospital's Rule in Other Cases
5.5.3 Other Indeterminate Forms
Exercise 5.5
5.6 Periodicity and Trigonometric Functions
5.6.1 Definition of Periodic Function
5.6.2 Trigonometric Functions
Exercise 5.6
5.7 Graphing of Functions
Exercise 5.7
Summary and Review
Chapter 6 Integration
6.1 Antiderivatives and Indefinite Integrals
6.1.1 Antiderivatives
6.1.2 Indefinite Integrals
6.1.3 Indefinite Integrals List
6.1.4 Properties of the Indefinite Integral
6.1.5 Differential Equation
Exercise 6.1
6.2 The Definite Integral
6.2.1 Area Problem
6.2.2 Distance Problem
6.2.3 The Definite Integral
Exercise 6.2
6.3 Properties of the Definite Integral
Exercise 6.3
6.4 Fundamental Theorem of Calculus
Exercise 6.4
6.5 The Substitution Rule
6.5.1 Substitution with Indefinite Integrals
6.5.2 Substitution for Definite Integrals
Exercise 6.5
6.6 Integration by Parts
Exercise 6.6
Summary and Review
Chapter 7 Applications of Integration
7.1 Area between Curves
Exercise 7.1
7.2 Average Values
7.2.1 Cumulative Change
7.2.2 Definition of Average Value
Exercise 7,2
7.3 Improper Integrals
7.3.1 Integrating over an Infinite Interval
7.3.2 Discontinuous Integrand
Exercise 7.3
Summary and Review
Chapter 8 Probability and Statistics
8.1 The Probability of Events
8.1.1 Counting Techniques
8.1.2 Sample Space and Events
8.1.3 The Definition of Probability
8.1.4 Equally Likely Outcomes Model
Exercise 8.1
8.2 The Conditional Probability and Independent Events
8.2.1 The Conditional Probability
8.2.2 The Law of Total Probability and the Bayes Formula
8.2.3 Independent Events
Exercise 8.2
8.3 Random Variables and Distributions
8.3.1 Random Variables
8.3.2 The Probability Distribution of a Discrete Random Variable
8.3.3 The Cumulative Distribution Function of a Random Variable
8.3.4 Continuous Random Variables
Exercise 8.3
8.4 Means and Variances
8.4.1 Means
8.4.2 Variances
Exercise 8.4
8.5 Statistics Tools
8.5.1 Random Samples and Statistics
8.5.2 Estimating Means and Proportions
8.5.3 Linear Regression
Exercise 8.5
Summary and Review
Bibliography
Appendix A Differentiation and Integration Formulas
Appendix B Table of the cdf of the Standard Normal Distribution
Answers to Even-numbered Problems
Index
[