高等數學引論（第1捲 英文版） 下載 mobi epub pdf 電子書 2024

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　　《高等數學引論（第1捲 英文版）》是我國名數學傢華羅庚在上世紀60年代編寫的教學用書，曾在中國科學技術大學講授。全書包含瞭微積分、高等代數、常微分方程、復變函數論等內容。全書反映瞭作者的“數學是一門有緊密內在聯係的學問，應將大學數學係的基礎課放在一起來講”的教學思想，還包括瞭作者的“要埋有伏筆”、“生書熟講，熟書生溫”等教學技巧，書中還介紹瞭數學理論的不少應用。

目錄

Preface
Translator's note
Introduction
1 Real and complex numbers
1．1 Rational numbers
1．2 The existence of irrational numbers
1．3 A description of real numbers
1．4 Limit
1．5 The Bolzano-Weierstrass theorem
1．6 Definitions for complex numbers and vectors
1．7 Polar coordinates and multiplication
1．8 De Moivre's theorem
1．9 Completeness of the complex numbers
1．10 Introduction to quaternions
Supplement
1．11 Binary arithmetics
1．12 Periodic decimals
1．13 Rational approximations to real numbers
1．14 Error terms
1．15 Solutions to cubic and quartic equations

2 Vector algebra
2．1 Space coordinates and vectors
2．2 Addition of vectors
2．3 The decomposition of a vector
2．4 Inner product （scalar product）
2．5 Vector product （outer product）
2．6 Multiple products
2．7 Change of coordinates
2．8 Planes
2．9 Equation for a line in space

2 Supplement
2．10 Main formulae in spherical trigonometry
2．11 Duality principle
2．12 Right-angled and right-sided triangles
2．13 Forces， systems and equivalent systems
2．14 Combination of parallel forces
2．15 Moments
2．16 Couples
2．17 Standard form for a system
2．18 Equilibrium and its applications

3 Functions and graphs
3．1 Variables
3．2 Functions
3．3 Implicit functions
3．4 Functions represented by graphs and tables
3．5 Several elementary functions
3．6 Functions with simple special properties
3．7 Periodic functions
3．8 Representations for a complex function
3．9 Line of regression
3．10 Lagrange's interpolation formula
3．11 Other interpolation formulae
3．12 Experimental formulae
3．13 Family of curves

4 Limits
4．1 Limits of sequences
4．2 Sequences without limits
4．3 Series
4．4 Conditionally convergent series
4．5 The method of Zu Chongzhi in calculating π
4．6 Archimedes' method for the area of a parabolic region
4．7 Calculating pressure on a boundary
4．8 The number e
4．9 Taking limit in the continuum
4．10 On several important limits
4．11 Some examples
4．12 Orders of infinity
4．13 The symbols ~， O and o
4．14 Continuous functions
……
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