Calculus of one and several variables:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Glenview, Ill.
Scott, Foresman
1973
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003627432&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | 903, 127 S.m.Abb. |
Internformat
MARC
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| 100 | 1 | |a Seeley, Robert Thomas |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Calculus of one and several variables |
| 264 | 1 | |a Glenview, Ill. |b Scott, Foresman |c 1973 | |
| 300 | |a 903, 127 S.m.Abb. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-003627432 | |
Datensatz im Suchindex
| _version_ | 1819247319075258368 |
|---|---|
| adam_text | Contents
Part One. Calculus of One Variable
Introduction
A Thumbnail Sketch of the History of Calculus 1
The Plan of This Book 6
Chapter 0 Prerequisites
0.1 The Real Numbers as Points on a Line 9
0.2 The Symbols =*¦ and =* 15
0.3 Points in the Plane 16
0.4 Functions and Graphs 32
Summary 48
Review Problems 50
Chapter I An Introduction to Derivatives
Forward 53
1.1 Limits 56
1.2 Derivatives 65
1.3 Reflection in a Parabolic Mirror 73
1.4 The Derivative as an Aid to Graphing 78
1.5 Maximum Problems 83
1.6 Newton s Method for Square Roots (optional) 87
Appendix: The Accuracy of Newton s Method for
Square Roots (optional) 89
1.7 Velocity and Other Applications 93
1.8 Leibniz Notation 106
Chapter II Computation of Derivatives
Forward 109
2.1 Derivatives of Sums and Products 111
2.2 The Derivative of a Quotient 120
2.3 Derivatives of the Trigonometric Functions 126
Appendix: The Trigonometric Functions 132
2.4 Composite Functions and the Chain Rule 142
2.5 Derivatives of Inverse Functions 152
2.6 The Natural Logarithm 159
2.7 Logs and Exponentials 170
2.8 Hyperbolic Functions (optional) 178
2.9 Summary of Derivative Formulas 181
2.10 Implicit Differentiation and Related Rates 185
2.11 Some Geometric Examples (optional) 191
Chapter III Applications of Derivatives
3.1 Increasing and Decreasing Functions 198
3.2 Parallel Graphs 206
3.3 Exponential Growth and Decay 211
3.4 Second Derivatives 216
3.5 Periodic Motion (optional) 225
Chapter IV Theory of Maxima
4.1 The Maximum Value Theorem 233
4.2 The Mean Value Theorem 249
Chapter V Introduction to Integrals
5.1 The Definite Integral 257
5.2 A Problem of Existence 268
5.3 The Fundamental Theorem of Calculus 271
5.4 Some Applications of Integrals 282
5.5 Unbounded Intervals and Discontinuous
Functions 301
Chapter VI Techniques of Integration
Forward 309
6.1 Linear Combinations 312
6.2 Substitution 317
Appendix: Completing the Square 327
6.3 Integration by Parts 329
6.4 Rational Functions 337
6.5 Special Trigonometric Integrals 354
6.6 Trigonometric Substitution 361
6.7 Separable Differential Equations 368
6.8 First Order Linear Differential Equations 372
6.9 Generalities on Differential Equations 379
Chapter VII Vectors and the Laws of Motion
7.1 Plane Vectors 383
7.2 Length and Inner Product 387
7.3 Vectors in Analytic Geometry 393
7.4 Paths in the Plane 400
7.5 Differentiation of Vector Functions; Velocity and
Acceleration 404
7.6 L Hopital s Rule 411
7.7 Geometry of Parametric Curves (optional) 416
7.8 Polar Coordinates 421
7.9 Area and Arc Length in Polar Coordinates 427
7.10 Vectors and Polar Coordinates 431
7.11 Planetary Motion 435
Chapter VIII Complex Numbers
Forward 441
8.1 Definition and Elementary Algebraic Properties of
the Complex Numbers 442
8.2 Geometry of the Complex Numbers 446
8.3 Multiplication of Complex Numbers 448
8.4 Complex Functions of a Real Variable 454
8.5 Linear Differential Equations with Constant Coeffi¬
cients; The Homogeneous Second Order Case 460
8.6 Linear Differential Equations with Constant Coeffi¬
cients; The General Case 466
8.7 The Fundamental Theorem of Algebra 474
Chapter IX Approximations
Forward 479
9.1 Approximation by the Tangent Line 481
9.2 The Taylor Expansion 484
9.3 Newton s Method 492
9.4 The Trapezoid Rule and Simpson s Rule 495
Chapter X Infinite Sequences
Forward 505
10.1 Limit of a Sequence 506
10.2 The Algebra of Limits 513
10.3 Bounded and Monotone Sequences 525
10.4 Sequence Limits and Function Limits 530
10.5 The Bolzano Weierstrass Theorem 536
Chapter XI Infinite Series
11.1 Some Uses and Abuses of Infinite Series 543
11.2 The Sum of an Infinite Series 552
11.3 Positive Series 561
Appendix: Error Estimates (optional) 572
11.4 Absolute Convergence; Alternating Series 575
11.5 Power Series 581
11.6 Analytic Definition of Trigonometric and Exponential
Functions 597
11.7 Grouping, Reordering, and Products of Series 602
Part Two. Calculus of Several Variables
Chapter I Vectors
Forward 611
1.1 The Vector Space R3 612
1.2 The Cross Product 623
1.3 Spheres, Planes, and Lines 634
1.4 The Vector Space Rn 647
1.5 Linear Dependence and Bases 652
Chapter II Curves in Rn
2.1 Definitions and Elementary Properties 669
2.2 Newton s Law of Motion 679
2.3 The Geometry of Curves in R3 687
Chapter III Differentiation of Functions of Two Variables
3.1 Definitions, Examples, and Elementary Theorems
699
3.2 Polynomials of Degree One 711
Appendix: Two Dimensional Linear Programming
717
3.3 Partial Derivatives, the Gradient, and the Chain
Rule 725
3.4 Computations with the Chain Rule 743
3.5 The Implicit Function Theorem 750
3.6 Derivatives of Higher Order 763
3.7 The Taylor Expansion 770
3.8 Maxima and Minima 775
Chapter IV Double Integrals, Vector Fields, and Line
Integrals
Forward 783
4.1 Double Integrals 784
4.2 Vector Fields 798
4.3 Line Integrals 805
4.4 Green s Theorem 818
4.5 Change of Variable 832
Chapter V Functions of n Variables
Forward 843
5.1 Continuity, Partial Derivatives, and Gradients 844
5.2 The Implicit Function Theorem 854
5.3 Taylor Expansions 860
5.4 Vector Fields and Line Integrals in Rs 863
5.5 Surface Integrals and Stokes Theorem 868
5.6 Triple Integrals 883
5.7 The Divergence Theorem 891
5.8 A Very Brief Introduction to Differential Forms 899
Appendix I Numbers
Forward A l
1.1 Summation A 2
1.2 Mathematical Induction and the Natural Numbers
A 6
1.3 Inequalities, and the Rational Numbers A 13
1.4 Ordered Fields A 18
1.5 The Least Upper Bound Axiom, and the Real Num¬
bers A 26
1.6 The Integers as Real Numbers: Archimedean
Property A 31
Appendix II How to Prove the Basic Propositions of Calculus
11.1 Limits A 35
11.2 More Limits A 44
11.3 Derivatives and Tangents A 49
11.4 Continuous Functions A 51
11.5 Functions Continuous on a Closed Finite Interval
A 54
11.6 Inverse Functions A 61
11.7 Uniform Continuity A 66
11.8 Integrals of Continuous Functions A 69
11.9 Arc Length A 83
11.10 L H6pital s Rule for the «/« Case A 90
Answers to Selected Problems
Calculus of One Variable A 93
Calculus of Several Variables A 115
Table of Natural Logarithms
Index
|
| any_adam_object | 1 |
| author | Seeley, Robert Thomas |
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| dewey-ones | 515 - Analysis |
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| dewey-sort | 3515 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| indexdate | 2024-12-20T08:38:23Z |
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| language | English |
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| spellingShingle | Seeley, Robert Thomas Calculus of one and several variables Calculo (Matematica) - Intermediario larpcal Calculus Analysis (DE-588)4001865-9 gnd |
| subject_GND | (DE-588)4001865-9 |
| title | Calculus of one and several variables |
| title_auth | Calculus of one and several variables |
| title_exact_search | Calculus of one and several variables |
| title_full | Calculus of one and several variables |
| title_fullStr | Calculus of one and several variables |
| title_full_unstemmed | Calculus of one and several variables |
| title_short | Calculus of one and several variables |
| title_sort | calculus of one and several variables |
| topic | Calculo (Matematica) - Intermediario larpcal Calculus Analysis (DE-588)4001865-9 gnd |
| topic_facet | Calculo (Matematica) - Intermediario Calculus Analysis |
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