Calculus (Book): Difference between revisions

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{{Stub}}
{{Stub}}
{{InfoboxBook
{{InfoboxBook
|title=Basic Mathematics
|title=Calculus
|image=[[File:Lang Basic Mathematics Cover.jpg]]
|image=[[File:Apostol Calculus V1 Cover.jpg]]
|author=[https://en.wikipedia.org/wiki/Serge_Lang Serge Lang]
|author=[https://en.wikipedia.org/wiki/Tom_M._Apostol Tom Apostol]
|language=English
|language=English
|series=
|series=
|genre=
|genre=
|publisher=Springer
|publisher=Wiley
|publicationdate=1 July 1988
|publicationdate=16 January 1991
|pages=496
|pages=666
|isbn10=0387967877
|isbn10=0471000051
|isbn13=978-0387967875
|isbn13=978-0471000051
}}
}}
The textbook '''''Basic Mathematics''''' by [https://en.wikipedia.org/wiki/Serge_Lang Serge Lang] provides an overview of mathematical topics usually encountered through the end of high school/secondary school, specifically arithmetic, algebra, trigonometry, logic, and geometry. It serves as a solid review no matter how far along one may be in their studies, be it just beginning or returning to strengthen one's foundations.
The textbook '''''Calculus''''' by [https://en.wikipedia.org/wiki/Tom_M._Apostol Tom Apostol] introduces calculus.  
 
Reading the Foreword and the Interlude is recommended for those unfamiliar with reading math texts.


== Table of Contents ==
== Table of Contents ==
Line 23: Line 21:
! Chapter/Section # !! Title !! Page #
! Chapter/Section # !! Title !! Page #
|-  
|-  
! colspan="3" | PART I: ALGEBRA
! colspan="3" | I. INTRODUCTION
|-
|-
! colspan="3" | Chapter 1: Numbers
! colspan="3" | Part 1: Historical Introduction
|-
|-
| 1 || The integers || 5
| I 1.1 || The two basic concepts of calculus || 1
|-
|-
| 2 || Rules for addition || 8
| I 1.2 || Historical background || 2
|-
|-
| 3 || Rules for multiplication || 14
| I 1.3 || The method of exhaustion for the area of a parabolic segment || 3
|-
|-
| 4 || Even and odd integers; divisibility || 22
| <nowiki>*</nowiki>I 1.4 || Exercises || 8
|-
|-
| 5 || Rational numbers || 26
| I 1.5 || Rational numbers || 8
|-
|-
| 6 || Multiplicative inverses || 42
| I 1.6 || Multiplicative inverses || 10
|-  
|-  
! colspan="3" | Chapter 2: Linear Equations
! colspan="3" | Chapter 2: Linear Equations

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Calculus
Apostol Calculus V1 Cover.jpg
Information
Author Tom Apostol
Language English
Publisher Wiley
Publication Date 16 January 1991
Pages 666
ISBN-10 0471000051
ISBN-13 978-0471000051

The textbook Calculus by Tom Apostol introduces calculus.

Table of Contents

Chapter/Section # Title Page #
I. INTRODUCTION
Part 1: Historical Introduction
I 1.1 The two basic concepts of calculus 1
I 1.2 Historical background 2
I 1.3 The method of exhaustion for the area of a parabolic segment 3
*I 1.4 Exercises 8
I 1.5 Rational numbers 8
I 1.6 Multiplicative inverses 10
Chapter 2: Linear Equations
1 Equations in two unknowns 53
2 Equations in three unknowns 57
Chapter 3: Real Numbers
1 Addition and multiplication 61
2 Real numbers: positivity 64
3 Powers and roots 70
4 Inequalities 75
Chapter 4: Quadratic Equations
Interlude: On Logic and Mathematical Expressions
1 On reading books 93
2 Logic 94
3 Sets and elements 99
4 Notation 100
PART II: INTUITIVE GEOMETRY
Chapter 5: Distance and Angles
1 Distance 107
2 Angles 110
3 The Pythagoras theorem 120
Chapter 6: Isometries
1 Some standard mappings of the plane 133
2 Isometries 143
3 Composition of isometries 150
4 Inverse of isometries 155
5 Characterization of isometries 163
6 Congruences 166
Chapter 7: Area and Applications
1 Area of a disc of radius r 173
2 Circumference of a circle of radius r 180
PART III: COORDINATE GEOMETRY
Chapter 8: Coordinates and Geometry
1 Coordinate systems 191
2 Distance between points 197
3 Equation of a circle 203
4 Rational points on a circle 206
Chapter 9: Operations on Points
1 Dilations and reflections 213
2 Addition, subtraction, and the parallelogram law 218
Chapter 10: Segments, Rays, and Lines
1 Segments 229
2 Rays 231
3 Lines 236
4 Ordinary equation for a line 246
Chapter 11: Trigonometry
1 Radian measure 249
2 Sine and cosine 252
3 The graphs 264
4 The tangent 266
5 Addition formulas 272
6 Rotations 277
Chapter 12: Some Analytic Geometry
1 The straight line again 281
2 The parabola 291
3 The ellipse 297
4 The hyperbola 300
5 Rotation of hyperbolas 305
PART IV: MISCELLANEOUS
Chapter 13: Functions
1 Definition of a function 313
2 Polynomial functions 318
3 Graphs of functions 330
4 Exponential function 333
5 Logarithms 338
Chapter 14: Mappings
1 Definition 345
2 Formalism of mappings 351
3 Permutations 359
Chapter 15: Complex Numbers
1 The complex plane 375
2 Polar form 380
Chapter 16: Induction and Summations
1 Induction 383
2 Summations 388
3 Geometric series 396
Chapter 17: Determinants
1 Matrices 401
2 Determinants of order 2 406
3 Properties of 2 x 2 determinants 409
4 Determinants of order 3 414
5 Properties of 3 x 3 determinants 418
6 Cramer's Rule 424
Index 429
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