A first course in calculus:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Reading, Mass. [u.a.]
Addison-Wesley
1973
|
| Edition: | 3. ed. |
| Series: | World student series
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | Getr. Seitenzählung |
Staff View
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| 245 | 1 | 0 | |a A first course in calculus |
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Record in the Search Index
| _version_ | 1804135809026097152 |
|---|---|
| adam_text | Contents
Part One
Review of Basic Material
Chapter I
Numbers and Functions
1. Integers, rational numbers, and real numbers 5
2. Inequalities 8
3. Functions 14
4. Powers 16
Chapter II
Graphs and Curves
1. Coordinates 19
2. Graphs 22
3. The straight line 26
4. Distance between two points . . . . 31
5. Curves and equations 33
6. The circle 34
7. The parabola. Changes of coordinates 36
8. The hyperbola 39
Part Two
Differentiation and Elementary Functions
Chapter III
The Derivative
1. The slope of a curve 45
2. The derivative 49
3. Limits 54
4. Powers 59 ,
CONTENTS ix
5. Sums, products, and quotients 61
6. The chain rule 68
7. Higher derivatives 74
8. Rate of change 75
Chapter IV
Sine and Cosine
1. The sine and cosine functions 83
2. The graphs 87
3. Addition formula 90
4. The derivatives 93
5. Two basic limits 98
Chapter V
The Mean Value Theorem
1. The maximum and minimum theorem 103
2. The mean value theorem 109
3. Increasing and decreasing functions Ill
Chapter VI
Sketching Curves
1. Behavior as x becomes very large 125
2. Curve sketching 128
3. Convexity 133
4. Polar coordinates 140
5. Parametric curves 146
Chapter VII
Inverse Functions
1. Definition of inverse functions 153
2. Derivative of inverse functions 158
3. The arcsine 160
4. The arctangent 164
Chapter VIII
Exponents and Logarithms
1. The logarithm : 175
2. The exponential function 182
3. The general exponential function 188
4. Order of magnitude 192
5. Some applications 198
X CONTENTS
Part Three
Integration
Chapter IX
Integration
1. The indefinite integral 205
2. Continuous functions 208
3. Area 209
4. Fundamental theorem 213
5. Upper and lower sums 215
6. The basic properties 223
7. Integrable functions 226
Chapter X
Properties of the Integral
1. Further connection with the derivative 229
2. Sums 230
3. Inequalities 236
4. Improper integrals 239
Chapter XI
Techniques of Integration
1. Substitution 247
2. Integration by parts 251
3. Trigonometric integrals 253
4. Partial fractions 258
Chapter XII
Some Substantial Exercises
1. An estimate for (/;!) 269
2. Stirling s formula 270
3. Wallis product 272
Chapter XIII
Applications of Integration
1. Length of curves 275
2. Area in polar coordinates 281
3. Volumes of revolution 283
4. Work 287
CONTENTS xi
5. Density and mass 289
6. Probability 290
7. Moments 294
Part Four
Series
Chapter XIV
Taylor s Formula
1. Taylor s formula 303
2. Estimate for the remainder 307
3. Trigonometric functions 309
4. Exponential function 312
5. Logarithm 314
6. The arctangent 316
7. The binomial expansion 317
8. Uniqueness theorem 320
Chapter XV
Series
1. Convergent series 327
2. Series with positive terms 330
3. The ratio test 333
4. The integral test 335
5. Absolute and alternating convergence 338
6. Power series 241
7. Differentiation and integration of power series 345
Par I Five
Miscellaneous
Chapter XVI
Complex Numbers
1. Definition 353
2. Polar form 357
3. Complex valued functions 359
Appendix 1. e and a 363
1. Least upper bound 363
2. Limits 366
xii CONTENTS
3. Points of accumulation 374
4. Continuous functions 377
Appendix 2. Induction 381
Appendix 3. Sine and Cosine 385
Appendix 4. Physics and Mathematics 391
Part Six
Functions of Several Variables
Chapter XVII
Vectors
1. Definition of points in n space 397
2. Located vectors 403
3. Scalar product 405
4. The norm of a vector 408
5. Lines and planes 419
Chapter XVIII
Differentiation of Vectors
1. Derivative 429
2. Length of curves 437
Chapter XIX
Functions of Several Variables
1. Graphs and level curves 439
2. Partial derivatives 443
3. Differentiability and gradient 448
Chapter XX
The Chain Rule and the Gradient
1. The chain rule 455
2. Tangent plane 463
3. Directional derivative 465
4. Conservation law 468
Answers Al
Index II
|
| adam_txt |
Contents
Part One
Review of Basic Material
Chapter I
Numbers and Functions
1. Integers, rational numbers, and real numbers 5
2. Inequalities 8
3. Functions 14
4. Powers 16
Chapter II
Graphs and Curves
1. Coordinates 19
2. Graphs 22
3. The straight line 26
4. Distance between two points . . . . 31
5. Curves and equations 33
6. The circle 34
7. The parabola. Changes of coordinates 36
8. The hyperbola 39
Part Two
Differentiation and Elementary Functions
Chapter III
The Derivative
1. The slope of a curve 45
2. The derivative 49
3. Limits 54
4. Powers 59 ,
CONTENTS ix
5. Sums, products, and quotients 61
6. The chain rule 68
7. Higher derivatives 74
8. Rate of change 75
Chapter IV
Sine and Cosine
1. The sine and cosine functions 83
2. The graphs 87
3. Addition formula 90
4. The derivatives 93
5. Two basic limits 98
Chapter V
The Mean Value Theorem
1. The maximum and minimum theorem 103
2. The mean value theorem 109
3. Increasing and decreasing functions Ill
Chapter VI
Sketching Curves
1. Behavior as x becomes very large 125
2. Curve sketching 128
3. Convexity 133
4. Polar coordinates 140
5. Parametric curves 146
Chapter VII
Inverse Functions
1. Definition of inverse functions 153
2. Derivative of inverse functions 158
3. The arcsine 160
4. The arctangent 164
Chapter VIII
Exponents and Logarithms
1. The logarithm : 175
2. The exponential function 182
3. The general exponential function 188
4. Order of magnitude 192
5. Some applications 198
X CONTENTS
Part Three
Integration
Chapter IX
Integration
1. The indefinite integral 205
2. Continuous functions 208
3. Area 209
4. Fundamental theorem 213
5. Upper and lower sums 215
6. The basic properties 223
7. Integrable functions 226
Chapter X
Properties of the Integral
1. Further connection with the derivative 229
2. Sums 230
3. Inequalities 236
4. Improper integrals 239
Chapter XI
Techniques of Integration
1. Substitution 247
2. Integration by parts 251
3. Trigonometric integrals 253
4. Partial fractions 258
Chapter XII
Some Substantial Exercises
1. An estimate for (/;!)"" 269
2. Stirling's formula 270
3. Wallis' product 272
Chapter XIII
Applications of Integration
1. Length of curves 275
2. Area in polar coordinates 281
3. Volumes of revolution 283
4. Work 287
CONTENTS xi
5. Density and mass 289
6. Probability 290
7. Moments 294
Part Four
Series
Chapter XIV
Taylor's Formula
1. Taylor's formula 303
2. Estimate for the remainder 307
3. Trigonometric functions 309
4. Exponential function 312
5. Logarithm 314
6. The arctangent 316
7. The binomial expansion 317
8. Uniqueness theorem 320
Chapter XV
Series
1. Convergent series 327
2. Series with positive terms 330
3. The ratio test 333
4. The integral test 335
5. Absolute and alternating convergence 338
6. Power series 241
7. Differentiation and integration of power series 345
Par I Five
Miscellaneous
Chapter XVI
Complex Numbers
1. Definition 353
2. Polar form 357
3. Complex valued functions 359
Appendix 1. e and a 363
1. Least upper bound 363
2. Limits 366
xii CONTENTS
3. Points of accumulation 374
4. Continuous functions 377
Appendix 2. Induction 381
Appendix 3. Sine and Cosine 385
Appendix 4. Physics and Mathematics 391
Part Six
Functions of Several Variables
Chapter XVII
Vectors
1. Definition of points in n space 397
2. Located vectors 403
3. Scalar product 405
4. The norm of a vector 408
5. Lines and planes 419
Chapter XVIII
Differentiation of Vectors
1. Derivative 429
2. Length of curves 437
Chapter XIX
Functions of Several Variables
1. Graphs and level curves 439
2. Partial derivatives 443
3. Differentiability and gradient 448
Chapter XX
The Chain Rule and the Gradient
1. The chain rule 455
2. Tangent plane 463
3. Directional derivative 465
4. Conservation law 468
Answers Al
Index II |
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| spelling | Lang, Serge Verfasser aut A first course in calculus 3. ed. Reading, Mass. [u.a.] Addison-Wesley 1973 Getr. Seitenzählung txt rdacontent n rdamedia nc rdacarrier World student series Calculus Analysis (DE-588)4001865-9 gnd rswk-swf Infinitesimalrechnung (DE-588)4072798-1 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Infinitesimalrechnung (DE-588)4072798-1 s DE-604 Analysis (DE-588)4001865-9 s 2\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015086622&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Lang, Serge A first course in calculus Calculus Analysis (DE-588)4001865-9 gnd Infinitesimalrechnung (DE-588)4072798-1 gnd |
| subject_GND | (DE-588)4001865-9 (DE-588)4072798-1 (DE-588)4151278-9 |
| title | A first course in calculus |
| title_auth | A first course in calculus |
| title_exact_search | A first course in calculus |
| title_exact_search_txtP | A first course in calculus |
| title_full | A first course in calculus |
| title_fullStr | A first course in calculus |
| title_full_unstemmed | A first course in calculus |
| title_short | A first course in calculus |
| title_sort | a first course in calculus |
| topic | Calculus Analysis (DE-588)4001865-9 gnd Infinitesimalrechnung (DE-588)4072798-1 gnd |
| topic_facet | Calculus Analysis Infinitesimalrechnung Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015086622&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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