Introduction to calculus with analytic geometry:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
McGraw-Hill
1962
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 360 S. |
Internformat
MARC
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| 100 | 1 | |a Andree, Richard V. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Introduction to calculus with analytic geometry |c Richard V. Andree |
| 264 | 1 | |a New York [u.a.] |b McGraw-Hill |c 1962 | |
| 300 | |a XI, 360 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Calculus | |
| 650 | 4 | |a Geometry, Analytic | |
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Datensatz im Suchindex
| _version_ | 1804129090143256576 |
|---|---|
| adam_text | Contents
Preface v
Chapter 1. Basic Algebraic Theory 1
1 1 Introduction 1
1 2 Functions and Relations 1
1 3 More General Functions 4
1 4 The Function Notation 5
1 5 Inequalities 8
1 6 Absolute Value 8
1 7 Two Basic Properties 10
1 8 The Structure of the Number System 10
1 9 Two Unusual Real Numbers 12
1 10 The Meaning of Division 12
1 11 Solution Set of an Equation 11
1 12 Auxiliary Equations 22
1 13 A/ = /(* + Ax) f(x) 27
1 14 Self Test 30
Chapter 2. Basic Geometric Theory 31
2 1 Analytic (Coordinate) Geometry 31
2 2 The Distance between Two Points 38
2 3 Loci 43
2 4 Solution of Inequalities of First Degree 49
2 5 Slope of a Line 53
2 6 The Equation of a Line 57
2 7 Self Test 65
Chapter 3. Tangents and Limits 66
3 1 The Line Tangent to a Curve at a Point 66
3 2 Limit of a Function 69
3 3 Continuous Function 72
ix
Contents
3 4 Slope of a Tangent Line 80
3 5 Increments 86
3 6 Self Test 90
Chapter 4. Differential Calculus 91
4 1 The Derivative 91
4 2 The Delta Process 92
4 3 Generalization 97
4 4 Preliminary Theorems on Differentiation 97
4 5 The Derivative of a Polynomial 100
4 6 Maximum and Minimum Values of a Function 105
4 7 Applications Involving Maxima and Minima 118
4 8 Differentiation of a Product 123
4 9 Differentiation of a Power of a Function 126
4 10 Derivative of a Composite Function 129
4 11 Some Additional Applications 132
4 12 Self Test 136
Chapter 5. Extended Theorems of Differentiation 138
5 1 Negative, Fractional, and Zero Exponents 138
5 2 Scientific Notation 142
d(kx )
5 3 An Extension of the Theorem ^— = knx 1 147
dx
5 4 A Further Extension of the Theorem f = fcr™ 1 149
ax
5 5 Self Test 154
Chapter 6. Rates of Change 156
6 1 Kate of Change 156
6 2 Average Rate of Change I56
6 3 Velocity 158
6 4 General Rate of Change I62
6 5 Self Test 166
Chapter 7. Integral Calculus I67
7 1 S Notation 167
7 2 lim f(x) I72
7 3 Area 173
7 4 The Spring Problem 180
¦n
7 5 Some Remarks on lim /(£ ) Ax; 184
7 6 The Definite Integral 184
7 7 Some Preliminary Theorems on Integrals 188
7 8 Fundamental Theorem of Integral Calculus 191
7 9 Integration Continued 198
7 10 Summary 206
7 11 Techniques of Integration 2
7 12 Self Test 213
Contents ^j
Chapter 8. Applications of the Integral 214
8 1 Motion 224
8 2 On Setting Up Problems 219
8 3 Further Applications of Integration 227
8 4 Self Test 237
Chapter 9. Logarithmic and Exponential Functions 238
9 1 / — In x, and e 238
J x
9 2 Use of Tables of In x 247
9 3 The Inverse Function of y = In x, Namely, y = e* 250
9 4 Self Test 253
Chapter 10. Trigonometric Functions 255
10 1 Trigonometric Definitions 255
10 2 Limits of Trigonometric Functions 260
10 3 Derivatives of cos u and sin v 262
10 4 Derivatives of Other Trigonometric Functions 268
10 5 Integration of Trigonometric Functions 268
10 6 Self Test 274
Chapter 11. Techniques of Integration 276
11 1 Techniques 276
11 2 Integration by Parts 276
11 3 Trigonometric Substitution 280
11 4 Self Test 287
Chapter 12. Epilogue 288
Reading List 291
Answers and Hints 303
List of Symbols 355
Index 357
Table of Integrals Inside Front Cover
|
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| indexdate | 2024-07-09T18:59:36Z |
| institution | BVB |
| language | English |
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| physical | XI, 360 S. |
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| spelling | Andree, Richard V. Verfasser aut Introduction to calculus with analytic geometry Richard V. Andree New York [u.a.] McGraw-Hill 1962 XI, 360 S. txt rdacontent n rdamedia nc rdacarrier Calculus Geometry, Analytic HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009740264&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Andree, Richard V. Introduction to calculus with analytic geometry Calculus Geometry, Analytic |
| title | Introduction to calculus with analytic geometry |
| title_auth | Introduction to calculus with analytic geometry |
| title_exact_search | Introduction to calculus with analytic geometry |
| title_full | Introduction to calculus with analytic geometry Richard V. Andree |
| title_fullStr | Introduction to calculus with analytic geometry Richard V. Andree |
| title_full_unstemmed | Introduction to calculus with analytic geometry Richard V. Andree |
| title_short | Introduction to calculus with analytic geometry |
| title_sort | introduction to calculus with analytic geometry |
| topic | Calculus Geometry, Analytic |
| topic_facet | Calculus Geometry, Analytic |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009740264&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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