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| Preface | |
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| List of mfiles | |
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| Basic MATLAB: The Command Line | |
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| First steps | |
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| Vectors and matrices | |
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| Array operations | |
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| Matrix multiplication and linear systems | |
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| MATLAB functions | |
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| Symbolic calculations | |
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| Two-dimensional graphs | |
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| Managing the workspace and getting help | |
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| Basic MATLAB: mfiles | |
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| Creating and editing files in MATLAB | |
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| Mfiles | |
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| Function functions | |
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| Script mfiles | |
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| MATLAB documents | |
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| Vectors, Lines, and Planes | |
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| Vectors | |
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| Plotting lines in two- and three-dimensional space | |
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| Planes | |
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| Viewing three-dimensional graphs | |
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| Curves in Space | |
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| Parametric representation of curves | |
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| Tangent vectors and velocity | |
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| Arc length | |
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| The geometry of curves | |
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| Rotations in the plane | |
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| Numerical differentiation | |
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| Functions of Two Variables | |
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| Defining numerical functions of several variables | |
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| Graphing numerical functions of two variables | |
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| Level curves | |
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| Graphing techniques for symbolically defined functions | |
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| Partial derivatives and the directional derivative | |
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| The gradient vector and level curves | |
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| The tangent plane approximation | |
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| More about colormaps | |
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| Cutting off a graph | |
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| The subplot command | |
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| Functions of Three Variables and Parametric Surfaces | |
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| Level sets and surfaces | |
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| Color slices of a solid | |
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| The gradient vector field | |
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| Parametric representation of surfaces | |
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| Normal vectors and tangent planes in parametric form | |
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| Solving Equations | |
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| Symbolic solutions | |
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| Numerical solutions in one dimension | |
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| Solving a single equation in two variables | |
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| Newton's method in two dimensions | |
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| Optimization | |
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| Critical points and the second-derivative test | |
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| Estimating the maximum and minimum | |
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| Constrained maximum and minimum problems | |
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| Functions of three variables | |
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| Multiple Integrals | |
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| Double integrals over rectangles | |
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| Nonrectangular regions of integration | |
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| Change of variable in double integrals | |
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| Triple integrals | |
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| Scalar Integrals Over Curves and Surfaces | |
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| Scalar integrals along curves | |
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| Scalar integrals on surfaces | |
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| Integrals over surfaces given parametrically | |
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| Surfaces composed of triangles | |
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| Integrals of Vector Fields Over Curves and Surfaces | |
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| Vector fields | |
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| Line integrals | |
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| Curl and Green's theorem | |
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| Flux integrals | |
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| The divergence theorem | |
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| Problems from Electrostatics and Fluid Flow | |
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| An important tool | |
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| Electrostatics | |
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| The geometry of fluid flow | |
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| The Euler equations | |
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| Incompressible flow | |
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| More Features of MATLAB | |
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| Data classes | |
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| The command feval | |
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| Vectorizing computations | |
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| Programming | |
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| Instructor Demos | |
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| Solutions to Selected Exercises | |
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| Index | |