Introduction
Chapter 1 Theoretical Basis of Calculus
1.1 Sets and Functions
1.1.1 Sets and their operations
1.1.2 Concepts of mappings and functions
1.1.3 Composition of mappings and composition of functions
1.1.4 Inverse mappings and inverse functions
1.1.5 Elementary functions and hyperbolic functions
1.1.6 Some examples for modelling of functions in practical problems
Exercises 1.1
1.2 Limit of Sequence
1.2.1 Concept of limit of a sequence
1.2.2 Conditions for convergence of a sequence
1.2.3 Rules of operations on convergent sequences
Exercises 1.2
1.3 Limit of Function
1.3.1 The concept of limit of a function
1.3.2 The properties and operation rules of functional limits
1.3.3 Two important limits
Exercises 1.3
1.4 Infinitesimal and Infinite Quantities
1.4.1 Infinitesimal quantities and their order
1.4.2 Equivalence transformations of infinitesimals
1.4.3 Infinite quantities
Exercises 1.4
1.5 Continuous Functions
1.5.1 The concept of continuous function and classification of discontinuous points
1.5.2 Operations on continuous functions and the continuity of elementary functions
1.5.3 Properties of continuous functions on a closed interval
Exercises 1.5
Chapter 2 The Differential Calculus and Its Applications
2.1 Concept of Derivatives
2.1.1 Definition of derivatives
2.1.2 Relationship between derivability and continuity
2.1.3 Some examples of derivative problems in science and technology
Exercises 2.1
2.2 Fundamental Derivation Rules
2.2.1 Derivation rules for sum, difference, product and quotient of functions
2.2.2 Derivation rule for composite functions
2.2.3 The derivative of an inverse function
2.2.4 Higher-order derivatives
Exercises 2.2
2.3 Derivation of Implicit Functions and Functions Defined by Parametric Equations
2.3.1 Method of derivation of implicit functions
2.3.2 Method of derivation of a function defined by parametric equations
2.3.3 Related rates of change
Exercises 2.3
2.4 The Differential
2.4.1 Concept of the differential
2.4.2 Geometric meaning of the differential
2.4.3 Rules of operations on differentials
……
Chapter 3 The Integral Calculus and Its Applications
Chpater 4 Infinite Series
Appendix:Answers and Hints for Exercises
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