Elsevier S & T

A Matlab Companion for Multivariable Calculus

Cooper, Jeffery

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Table of contents
  • Contentsv
  • Prefaceix
  • List of mfilesxv
  • Chapter 1. Basic MATLAB: The Command Line1
  • 1.1 First steps1
  • 1.2 Vectors and matrices3
  • 1.3 Array operations6
  • 1.4 Matrix multiplication and linear systems8
  • 1.5 MATLAB functions10
  • 1.6 Symbolic calculations12
  • 1.7 Two-dimensional graphs16
  • 1.8 Managing the workspace and getting help19
  • Chapter 2. Basic MATLAB: mfiles21
  • 2.1 Creating and editing mfiles in MATLAB21
  • 2.2 Mfiles22
  • 2.3 Function functions24
  • 2.4 Script mfiles25
  • 2.5 MATLAB documents27
  • Chapter 3. Vectors, Lines, and Planes33
  • 3.1 Vectors33
  • 3.2 Plotting lines in two- and three-dimensional space35
  • 3.3 Planes37
  • 3.4 Viewing three-dimensional graphs41
  • Chapter 4. Curves in Space47
  • 4.1 Parametric representation of curves47
  • 4.2 Tangent vectors and velocity49
  • 4.3 Arc length54
  • 4.4 The geometry of curves56
  • 4.5 Rotations in the plane59
  • 4.6 Numerical differentiation61
  • Chapter 5. Functions of Two Variables69
  • 5.1 Defining numerical functions of several variables69
  • 5.2 Graphing numerical functions of two variables70
  • 5.3 Level curves76
  • 5.4 Graphing techniques for symbolically defined functions78
  • 5.5 Partial derivatives and the directional derivative79
  • 5.6 The gradient vector and level curves83
  • 5.7 The tangent plane approximation86
  • 5.8 More about colormaps89
  • 5.9 Cutting off a graph90
  • 5.10 The subplot command93
  • Chapter 6. Functions of Three Variables and Parametric Surfaces101
  • 6.1 Level sets and surfaces101
  • 6.2 Color slices of a solid105
  • 6.3 The gradient vector field108
  • 6.4 Parametric representation of surfaces110
  • 6.5 Normal vectors and tangent planes in parametric form118
  • Chapter 7. Solving Equations123
  • 7.1 Symbolic solutions123
  • 7.2 Numerical solutions in one dimension125
  • 7.3 Solving a single equation in two variables128
  • 7.4 Newton’s method in two dimensions130
  • Chapter 8. Optimization141
  • 8.1 Critical points and the second-derivative test141
  • 8.2 Estimating the maximum and minimum147
  • 8.3 Constrained maximum and minimum problems153
  • 8.4 Functions of three variables157
  • Chapter 9. Multiple Integrals169
  • 9.1 Double integrals over rectangles169
  • 9.2 Nonrectangular regions of integration177
  • 9.3 Change of variable in double integrals179
  • 9.4 Triple integrals188
  • Chapter 10. Scalar Integrals Over Curves and Surfaces197
  • 10.1 Scalar integrals along curves197
  • 10.2 Scalar integrals on surfaces199
  • 10.3 Integrals over surfaces given parametrically201
  • 10.4 Surfaces composed of triangles203
  • Chapter 11. Integrals of Vector Fields Over Curves and Surfaces219
  • 11.1 Vector fields219
  • 11.2 Line integrals223
  • 11.3 Curl and Green’s theorem227
  • 11.4 Flux integrals232
  • 11.5 The divergence theorem234
  • Chapter 12. Problems from Electrostatics and Fluid Flow241
  • 12.1 An important tool241
  • 12.2 Electrostatics242
  • 12.3 The geometry of fluid flow247
  • 12.4 The Euler equations254
  • 12.5 Incompressible flow257
  • Chapter 13. More Features of MATLAB271
  • 13.1 Data classes271
  • 13.2 The command feval274
  • 13.3 Vectorizing computations275
  • 13.4 Programming276
  • Appendix: Instructor Demos279
  • Solutions to Selected Exercises281
  • Index291
Book details
  • Vendor Elsevier S & T
  • SKU 9780121876258
  • ISBN-13 9780080489360
  • Author Cooper, Jeffery
  • Category Mathematics
  • Subject Calculus

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Description eBook delivery & access Reviews
Offering a concise collection of MatLab programs and exercises to accompany a third semester course in multivariable calculus, A MatLab Companion for Multivariable Calculus introduces simple numerical procedures such as numerical differentiation, numerical integration and Newton's method in several variables, thereby allowing students to tackle realistic problems. The many examples show students how to use MatLab effectively and easily in many contexts. Numerous exercises in mathematics and applications areas are presented, graded from routine to more demanding projects requiring some programming. Matlab M-files are provided on the Harcourt/Academic Press web site at http://www.harcourt-ap.com/matlab.html.

* Computer-oriented material that complements the essential topics in multivariable calculus
* Main ideas presented with examples of computations and graphics displays using MATLAB
* Numerous examples of short code in the text, which can be modified for use with the exercises
* MATLAB files are used to implement graphics displays and contain a collection of mfiles which can serve as demos