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E-raamat: Student's Introduction to Mathematica and the Wolfram Language

(Randolph-Macon College, Virginia), (Randolph-Macon College, Virginia)
  • Formaat: PDF+DRM
  • Ilmumisaeg: 16-May-2019
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9781108314046
  • Formaat - PDF+DRM
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  • Formaat: PDF+DRM
  • Ilmumisaeg: 16-May-2019
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9781108314046

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This book introduces Mathematica® and the Wolfram Language™ in the context of the standard university mathematics curriculum. It equips current and former students to harness these tools to explore ideas from pre-calculus, calculus, and linear algebra. Additional chapters on programming and 3D printing provide outlets for further exploration.

The unique feature of this compact student's introduction to Mathematica® and the Wolfram Language™ is that the order of the material closely follows a standard mathematics curriculum. As a result, it provides a brief introduction to those aspects of the Mathematica® software program most useful to students. Used as a supplementary text, it will help bridge the gap between Mathematica® and the mathematics in the course, and will serve as an excellent tutorial for former students. There have been significant changes to Mathematica® since the second edition, and all chapters have now been updated to account for new features in the software, including natural language queries and the vast stores of real-world data that are now integrated through the cloud. This third edition also includes many new exercises and a chapter on 3D printing that showcases the new computational geometry capabilities that will equip readers to print in 3D.

Arvustused

'This book is an easy-to-read introduction to Mathematica. It is interspersed with helpful hints that make interacting with Mathematica more efficient and examples to test the reader's comprehension. This book is good for learning how to use Mathematica to graph functions, perform algebraic manipulation, and approach topics from calculus and linear algebra. This new version shines some light on entity objects and accessing Wolfram's curated data which is needed because their structure is unintuitive and because of their growing prominence in the Wolfram ecosystem. The new final chapter on 3D printing gives readers the tools to quickly design and 3D print physical objects that embody mathematical surfaces. These two additions showcase recent advances in the Wolfram Language and ensure that the whole book remains relevant and up to date.' Christopher Hanusa, Queens College, City University of New York 'Mathematica has the power to unravel some of the current mysteries of mathematics but only if you know how to ask it the right questions. The 3rd edition of The Student's Introduction to Mathematica and the Wolfram Language can be your well-used guide for such exploration. Beginning and experienced Mathematica users will easily learn from the pages of this book especially given the recent changes to Mathematica. Even more, the 3rd edition moves into a new dimension, giving details on 3D printing! Grab one for yourself and another for a student you know.' Tim Chartier, Davidson College, North Carolina 'This text, including the exercises and solutions, is written in a student-friendly style Unlike most tutorial introductions to Mathematica, the authors go to significant lengths to provide explanations and rationales underlying what a newcomer would likely find confusing I believe that this book would be a useful addition to any student's library in a college or university that uses Mathematica.' Marvin Schaefer, MAA Reviews

Muu info

An introduction to Mathematica® and the Wolfram Language in the familiar context of the standard university mathematics curriculum.
Preface xi
1 Getting Started
1(26)
1.1 Launching Mathematica
1(1)
1.2 The Basic Technique for Using Mathematica
1(1)
1.3 The First Computation
2(1)
1.4 Commands for Basic Arithmetic
2(1)
1.5 Input and Output
3(1)
1.6 The Basic Math Assistant Palette
4(2)
1.7 Decimal In, Decimal Out
6(1)
1.8 Use Parentheses to Group Terms
7(1)
1.9 Three Well-Known Constants
8(1)
1.10 Mathematica Commands from Palettes
9(11)
1.11 Let Mathematica Do Your Typing
20(1)
1.12 Free-Form Input
21(1)
1.13 Computing with Real Data
22(1)
1.14 Saving Your Work and Quitting Mathematica
23(1)
1.15 Frequently Asked Questions About Mathematica's Syntax
24(3)
2 Working with Mathematica
27(24)
2.1 Opening Saved Notebooks
27(1)
2.2 Adding Text to Notebooks
27(3)
2.3 Printing
30(1)
2.4 Creating Presentations
31(1)
2.5 Sharing a Notebook
32(1)
2.6 Mathematical Kernel
32(2)
2.7 Tips for Working Effectively
34(7)
2.8 Working with Entities and Units
41(4)
2.9 Getting Help from Mathematica
45(3)
2.10 Troubleshooting
48(3)
3 Functions and Their Graphs
51(94)
3.1 Defining a Function
51(2)
3.2 Plotting a Function
53(6)
3.3 Using Mathematical Plot Options
59(17)
3.4 Investigating Functions with Manipulate
76(9)
3.5 Producing a Table of Values
85(8)
3.6 Working with Piecewise Defined Functions
93(3)
3.7 Plotting Implicitly Defined Functions
96(4)
3.8 Combining Graphics
100(8)
3.9 Enhancing Your Graphics
108(8)
3.10 Working with Data
116(6)
3.11 Managing Data: An Introduction to Lists
122(4)
3.12 Importing Data
126(13)
3.13 Working with Difference Equations
139(6)
4 Algebra
145(46)
4.1 Factoring and Expanding Polynomials
145(2)
4.2 Finding Roots of Polynomials with Solve and NSolve
147(8)
4.3 Solving Equations and Inequalities with Reduce
155(5)
4.4 Understanding Complex Output
160(8)
4.5 Working with Rational Functions
168(5)
4.6 Working with Other Expressions
173(5)
4.7 Solving General Equations with FindRoot
178(6)
4.8 Solving Difference Equations with RSolve
184(3)
4.9 Solving Systems of Equations and Inequalities
187(4)
5 Calculus
191(58)
5.1 Computing Limits
191(4)
5.2 Working with Difference Quotients
195(3)
5.3 The Derivative
198(3)
5.4 Visualizing Derivatives
201(1)
5.5 Higher-Order Derivatives
202(1)
5.6 Maxima and Minima
203(8)
5.7 Inflection Points
211(1)
5.8 Implicit Differentiation
212(3)
5.9 Differential Equations
215(3)
5.10 Integration
218(6)
5.11 Definite and Improper Integrals
224(10)
5.12 Numerical Integration
234(4)
5.13 Surfaces of Revolution
238(4)
5.14 Sequences and Series
242(7)
6 Multivariable Calculus
249(86)
6.1 Vectors
249(6)
6.2 Real-Valued Functions of Two or More Variables
255(47)
6.3 Parametric Curves and Surfaces
302(9)
6.4 Other Coordinate Systems
311(15)
6.5 Vector Fields
326(5)
6.6 Line Integrals and Surf ace Integrals
331(4)
7 Linear Algebra
335(1)
7.1 Matrices
335(10)
7.2 Performing Gaussian Elimination
345(2)
7.3 Matrix Operations
347(4)
7.4 Minors and Cofactors
351(3)
7.5 Working with Large Matrices
353(4)
7.6 Solving Systems of Linear Equations
357(6)
7.7 Vector Spaces
363(7)
7.8 Eigenvalues and Eigenvectors
370(5)
7.9 Visualizing Linear Transformations
375(8)
8 Programming
383(74)
8.1 Introduction
383(1)
8.2 FullForm: What the Kernel Sees
384(6)
8.3 Numbers
390(10)
8.4 Map and Function
400(11)
8.5 Control Structures and Looping
411(10)
8.6 Scoping Constructs: With and Module
421(8)
8.7 Iterations: Nest and Fold
429(11)
8.8 Patterns
440(17)
9 3D Printing
457(66)
9.1 Introduction
457(1)
9.2 3D Printing Basics
457(10)
9.3 MeshRegions
467(5)
9.4 MeshRegions from the Wolfram Knowledgebase
472(4)
9.5 Mesh Assembly, Modification, and Diagnostics
476(18)
9.6 Extrusion
494(10)
9.7 Printing a Solid of Revolution
504(5)
9.8 Printing a 3D Terrain Map
509(14)
Index 523
Bruce F. Torrence is the Garnett Professor of Mathematics at Randolph-Macon College, Virginia. In 2014, he received a Wolfram Innovator Award for his use of Mathematica in mathematics education, and in 2008 he received the John Smith Award for distinguished teaching from the Mathematical Association of America. Bruce served as a co-editor of Math Horizons magazine from 20082013, and his writings have twice appeared in the Best Writing on Mathematics series, in 2012 and 2014. Trained as an algebraic topologist, he has a longstanding interest in computer algebra systems. Eve A. Torrence is a Professor of Mathematics at Randolph-Macon College, Virginia. In 2013, she received an Outstanding Faculty Award from the State Council of Higher Education for Virginia, the highest honor for faculty at colleges and universities in the commonwealth. She has served as the president of Pi Mu Epsilon, the National Mathematics Honor Society, and is a member of the board for the Bridges Organization, which sponsors an international conference on mathematics and the arts. Eve is the author of Cut and Assemble Icosahedra: Twelve Models in White and Color (2011) and enjoys designing mathematical sculpture and incorporating the arts into teaching mathematics.