內容大鋼
With the international development of universities and the open running strategies,many universities and majors require higher-level education on teaching. Bilingualteaching and full English teaching have become widespread educational modes. Manyforeign original Calculus textbooks have been introduced in recent years, but comparedto domestic Calculus textbooks, there exist a number of differences in system, contentand styles. For example, domestic textbooks focus on profound concepts and theoreticalderivation, while foreign original textbooks emphasize the application and numericalmethods, leading to the inconvenience for readers to learn. Thus, with extensive anddeep investigation, we organized a team of teachers who have overseas study experienceand long-term teaching experience to compile this Calculus textbook, which absorbs theadvantages of both domestic and foreign textbooks, mainly reflected in the followingaspects.
1. The introduction of mathematical concepts is focused on understanding, withexplicit language and detailed depiction. Most examples contain a geometric picture toaid understanding.
2. We try to retain the rigorous derivation as domestic calculus textbooks, andmost theorems are proved.
3. The application is emphasized, embodied from examples and exercises. Wesuggest students do the exercises as much as possible to hone the ability of applyingmathematics.
目錄
Chapter 1 Functions and Limits
1.1 Functions
1.1.1 Sets
1.1.2 Intervals and Neighborhood
1.1.3 Function
1.1.4 Properties of Function
1.1.5 Inverse Function
1.1.6 Composite Function
1.1.7 Elementary Functions
Problem Set 1.1
1.2 The Limit of a Function
1.2.1 Intuitive Meaning of Limit
1.2.2 The Precise Definition of a Limit
1.2.3 One-Sided Limits
1.2.4 The Limit at Infinity
1.2.5 The Properties of Limits
Problem Set 1.2
1.3 Limit of a Sequence
Problem Set 1.3
1.4 Infinitesimals and Infinity
1.4.1 Infinitesimal
1.4.2 Infinite Limit
1.4.3 The Relationship between Infinitesimal and Infinite Limit
Problem Set 1.4
1.5 The Limit Theorems
Problem Set 1.5
1.6 Two Remarkable Limits
1.6.1 The Squeeze Theorem
1.6.2 Remarkable Limit □（數學公式）
1.6.3 Monotonic Sequence Theorem
1.6.4 Remarkable Limit Limit □（數學公式）
Problem Set 1.6
1.7 Comparison of Infinitesimals
Problem Set 1.7
1.8 Continuity
1.8.1 Continuity at a Point
1.8.2 Continuity on an Interval
1.8.3 Discontinuous Points
1.8.4 Operations on Continuous Functions
Problem Set 1.8
1.9 Properties of Continuous Functions on Closed Intervals
Problem Set 1.9
Chapter Exercise 1
Chapter 2 Derivatives and Differentials
2.1 Concept of Derivatives
2.1.1 Two Examples with the Same Theme
2.1.2 Definition of Derivatives
2.1.3 Left-hand Derivatives and Right-hand Derivatives
2.1.4 The Relationship between Differentiability and Continuity
Problem Set 2.1
2.2 Rules of Finding Derivatives
2.2.1 Four Arithmetic Operation Rules of Derivatives
2.2.2 The Derivative Rule for Inverse Functions
2.2.3 The Derivative Rule for Composite Functions
2.2.4 The Summary of Derivative Formulas and Rules
Problem Set 2.2
2.3 Higher-Order Derivatives
Problem Set 2.3
2.4 Implicit Differentiation and Parametric Equations
2.4.1 Implicit Differentiation
2.4.2 Parametric Equations
……
Chapter 3 The Mean Value Theorems and the Applications of Derivatives
Chapter 4 Indefinite Integrals
Chapter 5 Definite Integrals
Chapter 6 Applications of Definite Integral
Chapter 7 Differential Equations
Chapter 8 Space Analytic Geometry
Chapter 9 Derivatives of Multi-variable Functions
Chapter 10 Integrals in Space
Chapter 11 Line Integrals and Surface Integrals
Chapter 12 Infinite Series
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