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【PDF文档】Scientific Computing with MATLAB(英文原版)
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1 Computer Mathematics Languages | An Overview 1 2 Fundamentals of MATLAB Programming 5 3 Calculus Problems 27 4 Linear Algebra 51 5 Integral Transforms and Complex-valued Functions 73 6 Nonlinear Equations and Numerical Optimization Problems 89 7 Dierential Equation Problems 111 8 Data Interpolation and Functional Approximation Problems 145 9 Probability and Mathematical Statistics Problems 165 10 Topics on Nontraditional Mathematical Branches 177 Bibliography 193
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“math˙2nd˙solutions” — 2016/10/17 — 9:44 — page 1 — #1
Dingy¨u Xue and YangQuan Chen
Scientific Computing with
MATLAB
“math˙2nd˙solutions” — 2016/10/17 — 9:44 — page 2 — #2
“math˙2nd˙solutions” — 2016/10/17 — 9:44 — page 0 — #3
Contents
1 Computer Mathematics Languages — An Overview 1
2 Fundamentals of MATLAB Programming 5
3 Calculus Problems 27
4 Linear Algebra 51
5 Integral Transforms and Complex-valued Functions 73
6 Nonlinear Equations and Numerical Optimization Problems 89
7 Differential Equation Problems 111
8 Data Interpolation and Functional Approximation Problems 145
9 Probability and Mathematical Statistics Problems 165
10 Topics on Nontraditional Mathematical Branches 177
Bibliography 193
0
“math˙2nd˙solutions” — 2016/10/17 — 9:44 — page 1 — #4
Chapter 1
Computer Mathematics Languages — An
Overview
Exercise 1.1 Install MATLAB on your machine, and issue the command demo. From
the dialog boxes and menu items of the demonstration program, experience the powerful
functions provided in MATLAB.
Solution Execute the setup.exe file on the MATLAB DVD, and follow the instructions,
the MATLAB and the toolboxes licensed will be installed. Start MATLAB and run demo
command under the prompt >>, you may appreciate the beauty of MATLAB. A window
shown in Figure 1.1 can be opened, and various demonstrations can be selected from the
items on the list box.
FIGURE 1.1 : MATLAB demonstration interface
For instance, if 3-D Visualization is selected, the instructions in Figure 1.2 are displayed.
Click the Open this Example button,a demonstration interface in Figure 1.3 is shown, and
the demonstration can be displayed in a step-by-step manner.
Exercise 1.2 In order to understand the three-phase learning stage, please revisit Example
1.5, and see which statements belong to the second and third phases. Also please think about
what should be done for the first phase.
Solution In the first phase, the user should know what is the physical meaning of the
1
“math˙2nd˙solutions” — 2016/10/17 — 9:44 — page 2 — #5
2 Scientific Computing with MATLAB
FIGURE 1.2: An example of MATLAB demonstration program
FIGURE 1.3: Volume visualization interface in MATLAB
mathematical expression. That is to find a vector x, and the vector must satisfy all the
items in the constraints. And how to select such a vector to minimize the objective function.
Then comes the second and third phase, and in the second phase, the problem can be
described by the variable P.
>> P.f=[-2 -1 -4 -3 -1]; P.Aineq=[0 2 1 4 2; 3 4 5 -1 -1];
P.Bineq=[54 62]; P.lb=[0;0;3.32;0.678;2.57]; P.solver=’linprog’;
P.options=optimset; x=linprog(P) % solve linear programming problem
And in the third phase, the function linprog() can be called to solve the problem, with
>> x=linprog(P) % solve linear programming problem
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