Calculus with Maple V:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Pacific Grove, Calif.
Brooks/Cole Publ. Co.
1993
|
| Schriftenreihe: | Brooks/Cole symbolic computation series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXII, 502 S. zahlr. graph. Darst. |
| ISBN: | 0534163629 |
Internformat
MARC
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| 100 | 1 | |a Devitt, John S. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Calculus with Maple V |c John S. Devitt |
| 264 | 1 | |a Pacific Grove, Calif. |b Brooks/Cole Publ. Co. |c 1993 | |
| 300 | |a XXII, 502 S. |b zahlr. graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Brooks/Cole symbolic computation series | |
| 630 | 0 | 4 | |a Maple (Computer file) |
| 650 | 7 | |a MATEMÁTICA DA COMPUTAÇÃO |2 larpcal | |
| 650 | 7 | |a Maple (computerprogramma) |2 gtt | |
| 650 | 4 | |a Datenverarbeitung | |
| 650 | 4 | |a Calculus |x Data processing | |
| 650 | 0 | 7 | |a Maple V 4.0 |0 (DE-588)4407788-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Maple V 4.0 |0 (DE-588)4407788-9 |D s |
| 689 | 0 | |5 DE-604 | |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-006372437 | |
Datensatz im Suchindex
| _version_ | 1809768390222413824 |
|---|---|
| adam_text |
Contents
I The Basics and Interactive Computing 1
1.1 Introduction 1
1.1.1 Some Pointers to Better User Machine Communication 2
1.1.2 A Sample Session 3
1.1.3 Basic Objectives 6
1.1.4 Expressions and Equations 6
1.1.5 Graphical Representations 9
1.2 Plotting as an Aid to Understanding Inequalities 12
1.2.1 More on Inequalities 15
1.2.2 Type 1 Inequalities 15
1.2.3 Type 2 Inequalities 20
1.3 Equations Involving Two Variables 22
1.3.1 Equations of Straight Lines 23
1.3.2 Distances Between Points 26
1.3.3 Solving an Algebraic Equation Step by Step 27
1.3.4 Quadratic Equations and Their Graphs 29
1.3.5 Solving a Quadratic 30
1.3.6 Equations Involving x2 and y2 31
1.4 Functions 36
1.4.1 Defining a Function 36
1.4.2 Using Functions 37
1.4.3 Restricted Domains 39
1.4.4 Finding Domains of Functions 40
1.4.5 Absolute Values 42
1.4.6 Step Functions 43
1.4.7 Even Functions 44
1.4.8 Odd functions 44
1.4.9 Constant Functions 45
1.5 New Functions from Old 45
xvii
1.5.1 Arithmetic Operations 46
1.5.2 Composition of Functions 46
Exercise Set 1 48 |
C. Limits 57
2.1 Introduction 57 7
2.2 Limit Computations in Maple 61
2.3 Some Limit Computations 62
2.3.1 Ratios of Polynomials 62
2.3.2 Obscure Common Factors 66
2.3.3 Limits That Are Bounded but Do Not Exist 69
2.3.4 Unbounded Functions 69
2.4 A Formal Definition of a Limit 70
2.4.1 Computing 8 71
2.5 Properties of Limits 77
2.6 The Squeeze Theorem 81
2.7 Continuity 83
2.7.1 One Sided Limits 85
2.7.2 Combining Continuous Functions 88
2.8 The Intermediate Value Theorem 89
2.9 Exact Computations Versus Approximations 92
Exercise Set 2 93
O Derivatives 98
3.1 Introduction 98
3.1.1 Interpretations of the Derivative 101
3.1.2 Leibnitz Notation 110
3.2 Differentials 112
3.3 Differentiation Formulas 114
3.3.1 Some Fundamental Examples 115
3.3.2 Constants 116
3.3.3 Pure Powers 117
3.3.4 Laws for Addition and Multiplication 122
3.3.5 Derivatives of 126
g(x)
3.3.6 Summary 128
3.4 Expressions versus Functions 130
3.5 Trigonometric Functions 131 ;
3.5.1 Limits of Trigonometric Functions 131
I
3.5.2 Derivatives of Trigonometric Functions 135
3.6 The Chain Rule 137
3.6.1 Compositions Involving More Than Two Functions 146
3.6.2 Summary 147
3.7 Derivatives of Exponentials and Logarithms 148
3.7.1 Logarithms as Inverse Exponential Functions 150
3.8 Implicit Derivatives 152
3.8.1 Treating x and y as Functions of t 156
3.8.2 Related Rates 158
3.9 A Derivation of Newton's Formula 163
Exercise Set 3 167
** Optimal Solutions and Extreme Values 173
4.1 Maximums and Minimums 173
4.1.1 Optimizations in Maple 179
4.1.2 Local Maximums and Minimums 179
4.1.3 The Extreme Value Theorem 187
4.1.4 Summary 188
4.2 The Mean Value Theorem 188
4.2.1 The Average Slope 190
4.3 Monotonic Functions 197
4.3.1 The First Derivative Test 198
4.4 Concavity and Points of Inflection 202
4.5 Asymptotes 209
4.6 Applied Maximum and Minimum Problems 213
Exercise Set 4 223
0 Integration 227
5.1 Introduction 227
5.2 Summations 228
5.2.1 Summations and Area Under a Curve 231
5.2.2 Rules for Combining Sums 232
5.2.3 Formulas for Specific Sums 234
5.2.4 Discovering Formulas 235
5.3 Area 239
5.3.1 An Underestimate of the Area 239
5.3.2 An Overestimate of the Area 242
5.3.3 Better Estimates 243
5.4 The Definite Integral 245
5.4.1 Curves Above the Axis 246
5.4.2 Curves Below the Axis 247
5.4.3 Curves That Cross the Axis 249 ,
5.5 Shortcuts in Computation 250
5.5.1 The Basic Manipulations 250
5.5.2 Order Relationships 254
5.6 The Fundamental Theorem of Calculus 260
5.6.1 Indefinite Integrals 265 T
5.7 Applications of the Fundamental Theorem 268
Exercise Set 5 273 :'
0 Applications of Integration 278
6.1 Areas Between Curves 278 :
6.2 Volume 285
6.3 Solids of Revolution 288 !
6.4 Generalized Cross Sections 294
6.5 Cylindrical Shells 298
6.5.1 Visualizing Cylinders 301
6.5.2 Cylindrical Decompositions Off the Axis 303
6.6 Work 305
Exercise Set 6 309
1 Integration Techniques 313
7.1 Introduction 313
7.2 Changing Variables 314
7.2.1 Using a Change of Variables to Integrate 316
7.2.2 Summary 316
7.2.3 Additional Examples 317
7.2.4 The Effective Use of Change of Variables 318
7.2.5 Definite Integrals 321
7.3 Integration by Parts 326
7.3.1 Applications of Integration by Parts 328
7.3.2 Definite Integrals 331
7.3.3 Reduction Formulas 333
7.4 Trigonometric Substitutions 334
7.4.1 Mixtures of Sines and Cosines 338
7.4.2 Identities for Secant and Tangent 339
7.4.3 Integrating Secant 342
7.4.4 Sums and Differences of Angles 344
7.5 Square Roots of Quadratics 344
7.6 Partial Fraction Decompositions 352
7.6.1 Computing a Partial Fraction Decomposition 352
7.6.2 Patterns for Partial Fractions 354
7.6.3 Integrals with Quadratics in the Denominator 356
7.6.4 Partial Fractions in Action 357
7.7 Numerical Approximations 361
7.7.1 The Trapezoidal Rule 361
7.7.2 Simpson's Rule 366
Exercise Set 7 373
0 More Applications of Integration 380
8.1 Volumes Through Integration 380
8.1.1 Visualizing Stacks of Disks 385
8.1.2 Variations on Volume 388
8.2 Cylindrical Shells 396
8.3 Arc Length 398
8.4 Surface Area 405
Exercise Set 8 409
U Parametric Equations 413
9.1 Introduction 413
9.2 Parametric Curves 413
9.2.1 Finding Cartesian Representations 415
9.3 Tangents and Areas Revisited 420
9.3.1 Second Derivatives 424
9.3.2 Areas 426
9.4 Arc Length and Surface Area Revisited 427
9.4.1 Arc Length 428
9.4.2 Surface Area 429
9.5 Polar Coordinates 430
9.5.1 Curve Sketching in Polar Coordinates 431
9.5.2 Tangent Lines and Polar Coordinates 432
9.6 Areas in Polar Coordinates 435
9.7 Arc Lengths in Polar Coordinates 436
Exercise Set 9 440
1 U Sequences and Series 446
10.1 Introduction 446
10.2 Sequences 446
10.2.1 Recurrence Relations 447
10.2.2 Asymptotic Behavior of Sequences 449
10.3 Series 451
10.3.1 Arithmetic on Series 456
10.4 Testing for Convergence and Divergence 457
10.4.1 The Integral Test 457
10.4.2 Comparison Tests 460
10.4.3 Ratio Tests 463
10.4.4 The Root Test 465
10.5 Alternating Series 465
10.6 Power Series 468
10.7 Constructing Power Series 471
10.7.1 Algebraic Manipulations of Power Series 472 :
10.7.2 Constructing Coefficients 477
10.7.3 Taylor Series 480
10.8 Approximations 481
10.8.1 Error Analysis 483
Exercise Set 10 488 '
M The Computing Environment 495
A.I The Student Package 495
A.2 Production Notes 498 |
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| indexdate | 2024-09-10T00:53:51Z |
| institution | BVB |
| isbn | 0534163629 |
| language | English |
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| physical | XXII, 502 S. zahlr. graph. Darst. |
| publishDate | 1993 |
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| spelling | Devitt, John S. Verfasser aut Calculus with Maple V John S. Devitt Pacific Grove, Calif. Brooks/Cole Publ. Co. 1993 XXII, 502 S. zahlr. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Brooks/Cole symbolic computation series Maple (Computer file) MATEMÁTICA DA COMPUTAÇÃO larpcal Maple (computerprogramma) gtt Datenverarbeitung Calculus Data processing Maple V 4.0 (DE-588)4407788-9 gnd rswk-swf Maple V 4.0 (DE-588)4407788-9 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006372437&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Devitt, John S. Calculus with Maple V Maple (Computer file) MATEMÁTICA DA COMPUTAÇÃO larpcal Maple (computerprogramma) gtt Datenverarbeitung Calculus Data processing Maple V 4.0 (DE-588)4407788-9 gnd |
| subject_GND | (DE-588)4407788-9 |
| title | Calculus with Maple V |
| title_auth | Calculus with Maple V |
| title_exact_search | Calculus with Maple V |
| title_full | Calculus with Maple V John S. Devitt |
| title_fullStr | Calculus with Maple V John S. Devitt |
| title_full_unstemmed | Calculus with Maple V John S. Devitt |
| title_short | Calculus with Maple V |
| title_sort | calculus with maple v |
| topic | Maple (Computer file) MATEMÁTICA DA COMPUTAÇÃO larpcal Maple (computerprogramma) gtt Datenverarbeitung Calculus Data processing Maple V 4.0 (DE-588)4407788-9 gnd |
| topic_facet | Maple (Computer file) MATEMÁTICA DA COMPUTAÇÃO Maple (computerprogramma) Datenverarbeitung Calculus Data processing Maple V 4.0 |
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