Approaching precalculus mathematics discretely: explorations in a computer environment
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge, Mass.
MIT Press
1990
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 557 S. graph. Darst. |
| ISBN: | 0262121387 |
Internformat
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Datensatz im Suchindex
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| adam_text | Contents
Foreword ix
Acknowledgments xiii
1 Transformations, Functions, and Problem Solving 1
Problem Solving: A Theme 3
Maps 6
Logo Procedures and the Machine Metaphor 7
2 Mapping the Plane to the Computer Screen 17
Mappings of the Plane into Itself 18
Composition in Both Logo and Algebraic Notation 28
Mappings Applied to Sets of Points 31
Applying any Function across a List 34
Procedures Defined in the Text of Chapter 2 38
3 Vectors and Vector Operations 41
Vectors and Points in the Plane 41
Trips, Navigation, and Vectors 41
Ordered Pairs as Vectors 51
Operating with Vectors 54
Addition 54
Scalar Multiplication 59
Linear Combinations 60
Vector Operations with Logo 63
More about Linear Combinations 68
Bases for the Plane 74
Procedures Defined in the Text of Chapter 3 81
Contents
4 Linear Transformations 83
Linear Transformations in Logo 85
Transformations Based on Collinear Vectors 86
Matrices in Mathematics 91
Difficulties with Logo Lists 98
Operations with Matrices 102
Matrix Composition 104
Linear Systems, Matrix Equations, and Inverses 107
Matrix Addition 120
Procedures Defined in the Text of Chapter 4 122
5 Recursion, Induction, and Logo Procedures 125
Recursive Definitions in Mathematics 127
The Induction Hypothesis 128
Proofs by Mathematical Induction 133
Sequences 138
Series 142
A Model for List Recursion 151
Drawing Routines 154
Recursive List Operations 157
Procedures Defined in the Text of Chapter 5 162
6 Transformations Extended to Three Dimensions 165
Vectors in 3 Space 165
Drawing Routines 176
Linear Transformations in 3 Space 181
Basis Vectors for 3 Space 183
Rotations 188
Procedures Defined in the Text of Chapter 6 195
7 Representing Functions Graphically 201
From the Discrete to the Continuous 201
Building a Graphing Utility 207
Graphing Functions 212
Exploring Polynomial Graphs 219
Symmetry and Transformations 228
Equations from Graphs 238
Transforming Equations to Fit Graphs 246
Reflections about the X and Y axes 253
Rotation Maps 255
Reflections about Lines 257
Procedures Defined in the Text of Chapter 7 265
vl
Contents
8 Vectors Applied to Algebra 269
Polynomials from a Vector Point of View 270
Synthetic Substitution (and Synthetic Division) 275
Evaluation, Division, and Related Topics 278
The Remainder Theorem 280
The Integral Zero Theorem 283
Rational Zeros 284
Polynomial Equations 293
Procedures Defined in the Text of Chapter 8 295
9 Toward (he Calculus: Rational Functions and Limits 299
Polynomial Rational Functions 300
Limits and Limit Notation 309
Oblique Asymptotes 314
Toward a Definition of Limit 321
Approaching a Real Number 334
Continuity 338
Procedures Defined in the Text of Chapter 9 340
10 The Trigonometric Functions from a Graphic Point of View 343
The Trigonometric Functions 343
Applying Transformation Theory to Offset Periodic Functions 350
A Look at Compound Functions 352
The Function Cofunction Relationships 358
Rotations and Matrices 359
Converses and Inverses of the Cyclic Functions 366
Trigonometric Identities 380
Trigonometric Equations 382
Procedures Defined in the Text of Chapter 10 385
11 Approaching the Calculus 387
Functions from Functions 387
The Derivative 410
Generalizing the Derivative for Polynomials 417
Area under the Curve 421
An Area Function 430
The Area under the Derived Function 436
The Integral Calculus 444
Procedures Defined in the Text of Chapter 11 448
vil
Contents
12 Projects 454
Two Dimensional Vectors 454
Complex Numbers 456
Matrices 457
Analytic Geometry in Logo 458
Polynomials 460
Three Dimensional Vectors 462
Three Dimensional Matrix Operations 463
Graphing Extensions 464
Parametric Equations 466
Projectile Motion 467
Trigonometry Projects 469
Three Dimensional Surfaces 470
Calculus 472
Appendix A Logo Fundamentals and Function Composition 473
Experiments with Elementary Logo Syntax 473
Building Your Own Functions in Logo 478
Function Composition 482
Inverses 489
Issues of Domain and Range 496
list Inputs to Functions 498
The Logo Turtle 502
Logo Variables 507
Appendix B A Model for Problem Solving 511
Constructing an Axis System for the Screen 511
Appendix C Mathematical Notes 524
Linear Combinations of Collinear and Non collinear Vectors 524
The Limit of a Function as x Approaches a Real Number 525
The General Triangle 529
Using the Second Derivative for Critical Points 540
Bibliography and References 543
Index 545
viii
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| isbn | 0262121387 |
| language | English |
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| spelling | Lewis, Philip G. Verfasser aut Approaching precalculus mathematics discretely explorations in a computer environment Philip G. Lewis Cambridge, Mass. MIT Press 1990 XIV, 557 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier LOGO (Langage de programmation) Mathématiques - Informatique Datenverarbeitung Mathematik LOGO (Computer program language) Mathematics Data processing Precalculus Data processing Mathematik (DE-588)4037944-9 gnd rswk-swf LOGO (DE-588)4036214-0 gnd rswk-swf Datenverarbeitung (DE-588)4011152-0 gnd rswk-swf LOGO (DE-588)4036214-0 s DE-604 Mathematik (DE-588)4037944-9 s Datenverarbeitung (DE-588)4011152-0 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003884764&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lewis, Philip G. Approaching precalculus mathematics discretely explorations in a computer environment LOGO (Langage de programmation) Mathématiques - Informatique Datenverarbeitung Mathematik LOGO (Computer program language) Mathematics Data processing Precalculus Data processing Mathematik (DE-588)4037944-9 gnd LOGO (DE-588)4036214-0 gnd Datenverarbeitung (DE-588)4011152-0 gnd |
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| title | Approaching precalculus mathematics discretely explorations in a computer environment |
| title_auth | Approaching precalculus mathematics discretely explorations in a computer environment |
| title_exact_search | Approaching precalculus mathematics discretely explorations in a computer environment |
| title_full | Approaching precalculus mathematics discretely explorations in a computer environment Philip G. Lewis |
| title_fullStr | Approaching precalculus mathematics discretely explorations in a computer environment Philip G. Lewis |
| title_full_unstemmed | Approaching precalculus mathematics discretely explorations in a computer environment Philip G. Lewis |
| title_short | Approaching precalculus mathematics discretely |
| title_sort | approaching precalculus mathematics discretely explorations in a computer environment |
| title_sub | explorations in a computer environment |
| topic | LOGO (Langage de programmation) Mathématiques - Informatique Datenverarbeitung Mathematik LOGO (Computer program language) Mathematics Data processing Precalculus Data processing Mathematik (DE-588)4037944-9 gnd LOGO (DE-588)4036214-0 gnd Datenverarbeitung (DE-588)4011152-0 gnd |
| topic_facet | LOGO (Langage de programmation) Mathématiques - Informatique Datenverarbeitung Mathematik LOGO (Computer program language) Mathematics Data processing Precalculus Data processing LOGO |
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