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Multivariable Calculus with MATLAB®: With Applications to Geometry and Physics 1st ed. 2017 [Kõva köide]

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  • Formaat: Hardback, 276 pages, kõrgus x laius: 235x155 mm, kaal: 712 g, 86 Illustrations, color; 1 Illustrations, black and white; XII, 276 p. 87 illus., 86 illus. in color., 1 Hardback
  • Ilmumisaeg: 18-Dec-2017
  • Kirjastus: Springer International Publishing AG
  • ISBN-10: 3319650696
  • ISBN-13: 9783319650692
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Multivariable Calculus with MATLAB®: With Applications to Geometry and Physics 1st ed. 2017Suurem pilt
  • Formaat: Hardback, 276 pages, kõrgus x laius: 235x155 mm, kaal: 712 g, 86 Illustrations, color; 1 Illustrations, black and white; XII, 276 p. 87 illus., 86 illus. in color., 1 Hardback
  • Ilmumisaeg: 18-Dec-2017
  • Kirjastus: Springer International Publishing AG
  • ISBN-10: 3319650696
  • ISBN-13: 9783319650692
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9783319650692.html
Märksõnad:

This comprehensive treatment of multivariable calculus focuses on the numerous tools that MATLAB® brings to the subject, as it presents introductions to geometry, mathematical physics, and kinematics. Covering simple calculations with MATLAB®, relevant plots, integration, and optimization, the numerous problem sets encourage practice with newly learned skills that cultivate the reader’s understanding of the material. Significant examples illustrate each topic, and fundamental physical applications such as Kepler’s Law, electromagnetism, fluid flow, and energy estimation are brought to prominent position. Perfect for use as a supplement to any standard multivariable calculus text, a “mathematical methods in physics or engineering” class, for independent study, or even as the class text in an “honors” multivariable calculus course, this textbook will appeal to mathematics, engineering, and physical science students.

MATLAB® is tightly integrated into every portion of this book, and its graphical capabilities are used to present vibrant pictures of curves and surfaces. Readers benefit from the deep connections made between mathematics and science while learning more about the intrinsic geometry of curves and surfaces. With serious yet elementary explanation of various numerical algorithms, this textbook enlivens the teaching of multivariable calculus and mathematical methods courses for scientists and engineers.

Arvustused

The book is addressed to students as well as to instructors of calculus. It helps to understand multivariable analysis utilysing visualization of such geometric structures like domains, curves and surfaces. It also develops the skill of students to use a powerful software for solving modern problems. (Ivan Podvigin, zbMATH 1400.26001, 2019)

Preface v
1 Introduction
1(14)
1.1 Benefits of Mathematical Software
2(1)
1.2 What's in This Book
3(2)
1.2.1
Chapter Descriptions
3(2)
1.3 What's Not in This Book
5(1)
1.4 How to Use This Book
6(1)
1.5 The MATLAB Interface
7(1)
1.5.1 A Word on Terminology
8(1)
1.6 Software Versions
8(7)
Problem Set A Review of One-Variable Calculus
9(3)
Glossary of MATLAB Commands
12(1)
Options to MATLAB Commands
13(1)
References
13(2)
2 Vectors and Graphics
15(18)
2.1 Vectors
15(4)
2.1.1 Applications of Vectors
17(2)
2.2 Parametric Curves
19(4)
2.3 Graphing Surfaces
23(2)
2.4 Parametric Surfaces
25(8)
Problem Set B Vectors and Graphics
27(4)
Glossary of MATLAB Commands
31(1)
Options to MATLAB Commands
31(2)
3 Geometry of Curves
33(28)
3.1 Parametric Curves
33(3)
3.2 Geometric Invariants
36(6)
3.2.1 Arclength
36(1)
3.2.2 The Frenet Frame
37(2)
3.2.3 Curvature and Torsion
39(3)
3.3 Differential Geometry of Curves
42(19)
3.3.1 The Osculating Circle
42(1)
3.3.2 Plane Curves
43(1)
3.3.3 Spherical Curves
44(1)
3.3.4 Helical Curves
44(1)
3.3.5 Congruence
45(2)
3.3.6 Two More Examples
47(4)
Problem Set C Curves
51(8)
Glossary of MATLAB Commands
59(2)
4 Kinematics
61(14)
4.1 Newton's Laws of Motion
61(3)
4.2 Kepler's Laws of Planetary Motion
64(1)
4.3 Studying Equations of Motion with MATLAB
65(10)
Problem Set D Kinematics
67(5)
Glossary of MATLAB Commands
72(1)
Reference
73(2)
5 Directional Derivatives
75(20)
5.1 Visualizing Functions of Two Variables
75(5)
5.1.1 Three-Dimensional Graphs
76(1)
5.1.2 Graphing Level Curves
77(3)
5.2 The Gradient of a Function of Two Variables
80(5)
5.2.1 Partial Derivatives and the Gradient
80(2)
5.2.2 Directional Derivatives
82(3)
5.3 Functions of Three or More Variables
85(10)
Problem Set E Directional Derivatives
89(5)
Glossary of MATLAB Commands and Options
94(1)
Options to MATLAB Commands
94(1)
6 Geometry of Surfaces
95(28)
6.1 The Concept of a Surface
95(7)
6.1.1 Basic Examples
96(6)
6.2 The Implicit Function Theorem
102(3)
6.3 Geometric Invariants
105(7)
6.4 Curvature Calculations with MATLAB
112(11)
Problem Set F Surfaces
115(6)
Glossary of MATLAB Commands and Options
121(1)
Options to MATLAB Commands
121(1)
References
121(2)
7 Optimization in Several Variables
123(24)
7.1 The One-Variable Case
123(4)
7.1.1 Analytic Methods
123(1)
7.1.2 Numerical Methods
124(1)
7.1.3 Newton's Method
125(2)
7.2 Functions of Two Variables
127(7)
7.2.1 Second Derivative Test
128(2)
7.2.2 Steepest Descent
130(3)
7.2.3 Multivariate Newton's Method
133(1)
7.3 Three or More Variables
134(2)
7.4 Constrained Optimization and Lagrange Multipliers
136(11)
Problem Set G Optimization
139(7)
Glossary of MATLAB Commands
146(1)
8 Multiple Integrals
147(38)
8.1 Automation and Integration
147(9)
8.1.1 Regions in the Plane
148(3)
8.1.2 Viewing Simple Regions
151(1)
8.1.3 Polar Regions
152(4)
8.2 Algorithms for Numerical Integration
156(4)
8.2.1 Algorithms for Numerical Integration in a Single Variable
156(1)
8.2.2 Algorithms for Numerical Multiple Integration
157(3)
8.3 Viewing Solid Regions
160(5)
8.4 A More Complicated Example
165(4)
8.5 Cylindrical Coordinates
169(1)
8.6 More General Changes of Coordinates
170(15)
Problem Set H Multiple Integrals
173(10)
Glossary of MATLAB Commands
183(2)
9 Multidimensional Calculus
185(20)
9.1 The Fundamental Theorem of Line Integrals
186(4)
9.2 Green's Theorem
190(2)
9.3 Stokes' Theorem
192(2)
9.4 The Divergence Theorem
194(2)
9.5 Vector Calculus and Physics
196(9)
Problem Set I Multivariate Calculus
199(3)
Glossary of MATLAB Commands
202(1)
Options to MATLAB Commands
203(1)
References
203(2)
10 Physical Applications of Vector Calculus
205(30)
10.1 Motion in a Central Force Field
205(3)
10.2 Newtonian Gravitation
208(4)
10.3 Electricity and Magnetism
212(3)
10.4 Fluid Flow
215(3)
10.5 Heat and Wave Equations
218(17)
10.5.1 The Heat Equation
218(1)
10.5.2 The Wave Equation
219(2)
Problem Set J Physical Applications
221(11)
Glossary of MATLAB Commands and Options
232(1)
Options to MATLAB Commands
233(1)
Appendix: Energy Minimization and Laplace's Equation
233(1)
References
234(1)
11 MATLAB Tips
235(6)
12 Sample Solutions
241(28)
12.1 Problem Set A: Problem 10
241(2)
12.2 Problem Set B: Problem 21
243(2)
12.3 Problem Set C: Problem 14
245(3)
12.4 Problem Set D: Problem 6
248(3)
12.5 Problem Set E: Problem 5, Parts (b) and (c)
251(3)
12.6 Problem Set F: Problem 10, Part (e)
254(2)
12.7 Problem Set G: Problem 10, Part (b)
256(4)
12.8 Problem Set H: Problem 2, Parts (c) and (d)
260(3)
12.9 Problem Set I: Problems 4(b) and 5(a)
263(2)
12.10 Problem Set J: Problem 3, Parts (a) and (b), but only subpart (ii)
265(4)
Index 269
Ronald Lipsman retired in 2010 after a 41-year career as Professor of Mathematics at the University of Maryland. During his last decade on campus, he served as Senior Associate Dean of the College of Computer, Mathematical and Physical Sciences. His research interests include group representations and harmonic analysis on Lie groups. He received his Ph.D. from MIT in 1967 and was a Gibbs Instructor at Yale University, 1967-1969.



Jonathan Rosenberg is Ruth M. Davis Professor of Mathematics at the University of Maryland, a Fellow of the American Mathematical Society, and a Managing Editor of Annals of K-Theory. His research interests include geometry, topology, and mathematical physics.  He received his Ph.D. from the University of California, Berkeley, in 1976, and joined the faculty at Maryland in 1981.

Professors Lipsman and Rosenberg have collaborated on numerous research and educational projects. Among their educational texts is: A Guide to MATLAB, 3rd&n

bsp;ed, 2014.