高等應(yīng)用數(shù)學(xué)問題的matlab求解02

1、星期三, 2008-4- 23, 20:08:07,Slide 1 (of 103) Dingyü Xue and YangQuan Chen, Solving Applied Mathematical Problems with MATLAB, CRC Press, 2008,Chapter 2Fundamentals of MATLAB

2、Programming,Solving Applied Mathematical Problems with MATLAB,CRC/Taylor & Francis PressChinese version by Tsinghua University Press,PPT by Wenbin Dong and Jun Peng, Northeastern University, PRCProofread by Dingyu

3、Xue & YangQuan Chen,星期三, 2008-4- 23, 20:08:07,Slide 2 (of 103) Dingyü Xue and YangQuan Chen, Solving Applied Mathematical Problems with MATLAB, CRC Press, 2008,Chapter 2

4、 Fundamentals of MATLAB Programming,Fundamentals of MATLAB ProgrammingFundamental Mathematical CalculationsFlow Control Structures of MATLAB LanguageWriting and Debugging MATLAB FunctionsTwo-dimensional GraphicsThre

5、e-dimensional GraphicsChapter summary,星期三, 2008-4- 23, 20:08:07,Slide 3 (of 103) Dingyü Xue and YangQuan Chen, Solving Applied Mathematical Problems with MATLAB, CRC Press,

6、 2008,MATLAB has the following advantages:Clarity and high efficiencyScientific computation, covers almost all the useful topics in math and engineeringGraphics facilitiesComprehensive toolboxes and block-sets, desig

7、ned by experts of almost all disciplines Powerful simulation facilities, unite the sub-systems of different domains together,星期三, 2008-4- 23, 20:08:07,Slide 4 (of 103) Dingyü Xue and Yan

8、gQuan Chen, Solving Applied Mathematical Problems with MATLAB, CRC Press, 2008,2.1 Fundamentals of MATLAB Programming,Variables and constants in MATLABData structuresBasic structure of MATLABColon expres

9、sions and sub-matrices extraction,星期三, 2008-4- 23, 20:08:07,Slide 5 (of 103) Dingyü Xue and YangQuan Chen, Solving Applied Mathematical Problems with MATLAB, CRC Press, 2008

10、,2.1.1 Variables and constants in MATLAB,Variables in MATLABStarting with a letter followed by other characters:Case-sensitive:Valid variable names: MYvar12, MY_Var12 and MyVar12_Invalid variable names: 12MyVar, _My

11、Var12Constants in MATLAB:eps, i, j, pi, NaN, Inf, i=sqrt(-1)lastwarn, lasterr,星期三, 2008-4- 23, 20:08:07,Slide 6 (of 103) Dingyü Xue and YangQuan Chen, Solving Applied Mat

12、hematical Problems with MATLAB, CRC Press, 2008,2.1.2 Data structures,Double-precision data typeSymbolic data typeOther data types,星期三, 2008-4- 23, 20:08:07,Slide 7 (of 103) Dingyü Xue

13、and YangQuan Chen, Solving Applied Mathematical Problems with MATLAB, CRC Press, 2008,Double-precision data type,IEEE standard, 64 bits (8 bytes)，11 bits for exponential and 53 bits for numerical and a sign

14、 bit.Use double() to convert other types to double.Data range:Other data types:int8(), int16(), int32(), uint16(), uint32(),星期三, 2008-4- 23, 20:08:07,Slide 8 (of 103) Dingyü Xue and

15、YangQuan Chen, Solving Applied Mathematical Problems with MATLAB, CRC Press, 2008,Symbolic data type,Usually used in formula derivations and analytical solutionsvariable declarationdisplay the symbolic

16、variables in any precisionThe default value: 32 decimal digits.,星期三, 2008-4- 23, 20:08:07,Slide 9 (of 103) Dingyü Xue and YangQuan Chen, Solving Applied Mathematical Prob

17、lems with MATLAB, CRC Press, 2008,Example 2.1,Display the first 300 digits of .MATLAB commandOne may further increase the number of digits to display. For extremely large number of digits, process may be slow,星期

18、三, 2008-4- 23, 20:08:07,Slide 10 (of 103) Dingyü Xue and YangQuan Chen, Solving Applied Mathematical Problems with MATLAB, CRC Press, 2008,Other data types,Strings:String v

19、ariables are used to store messages.Multi-dimensional arrays:a direct extension of matrices with multiple indices.Cell arrays:to put a set of data of different types under a single variable, expressed by { }.Classe

20、s and objects:used in Object-Oriented Programming.,星期三, 2008-4- 23, 20:08:07,Slide 11 (of 103) Dingyü Xue and YangQuan Chen, Solving Applied Mathematical Problems with MATL

21、AB, CRC Press, 2008,2.1.3 Basic structures of MATLAB,Direct assignmentThe basic structure of this type of statement isA semicolon can prevent the results from display.Reserved variable: ansstore the latest statemen

22、ts without left-hand-variable,星期三, 2008-4- 23, 20:08:07,Slide 12 (of 103) Dingyü Xue and YangQuan Chen, Solving Applied Mathematical Problems with MATLAB, CRC Press, 2008,Ex

23、ample 2.2,Enter matrix into MATLABCommandsOther commands,星期三, 2008-4- 23, 20:08:07,Slide 13 (of 103) Dingyü Xue and YangQuan Chen, Solving Applied Mathematical Problems

24、 with MATLAB, CRC Press, 2008,Example 2.3,Enter complex matrix into MATLABMATLAB commands Things to avoid:,星期三, 2008-4- 23, 20:08:07,Slide 14 (of 103) Dingyü Xue and YangQuan Che

25、n, Solving Applied Mathematical Problems with MATLAB, CRC Press, 2008,Function call statementFunction call examplesOne function may be called in different waysBuilt-in functions, *.m functions, Anon

26、ymous functions, inline functionsOverload functions,Function call statements,星期三, 2008-4- 23, 20:08:07,Slide 15 (of 103) Dingyü Xue and YangQuan Chen, Solving Applied Mathe

27、matical Problems with MATLAB, CRC Press, 2008,2.1.4 Colon expressions and sub-matrices extraction,Colon expression is an effective way in defining row vectors.Start value , increment and final value .defau

28、lt increment: 1,星期三, 2008-4- 23, 20:08:07,Slide 16 (of 103) Dingyü Xue and YangQuan Chen, Solving Applied Mathematical Problems with MATLAB, CRC Press, 2008,Example 2.4,For

29、 different increments, establish vectors for,星期三, 2008-4- 23, 20:08:07,Slide 17 (of 103) Dingyü Xue and YangQuan Chen, Solving Applied Mathematical Problems with MATLAB, CRC

30、 Press, 2008,Sub-matrix Extraction,Basic format numbers of the rows numbers of the columns:, all the columns or rows, depending on the position of it,星期三, 2008-4- 23, 20:08:07,Slide 18 (of 103)

31、 Dingyü Xue and YangQuan Chen, Solving Applied Mathematical Problems with MATLAB, CRC Press, 2008,Example 2.5,Different sub-matrices can be extracted from the given matrixMATLAB co

32、mmand,星期三, 2008-4- 23, 20:08:07,Slide 19 (of 103) Dingyü Xue and YangQuan Chen, Solving Applied Mathematical Problems with MATLAB, CRC Press, 2008,2.2 Fundamental Mathematic

33、al Calculations,Algebraic operations of matricesLogic operations of matricesRelationship operations of matricesSimplifications and presentations of analytical resultsBasic number theory computations,星期三, 2008-4- 23,

34、 20:08:07,Slide 20 (of 103) Dingyü Xue and YangQuan Chen, Solving Applied Mathematical Problems with MATLAB, CRC Press, 2008,2.2.1 Algebraic operations of matrices,Matrix t

35、ransposeMatrix addition and subtractionMatrix multiplicationsMatrix divisionsMatrix flip and rotationsMatrix powerMatrix dot operations,星期三, 2008-4- 23, 20:08:07,Slide 21 (of 103) Dingy&

36、#252; Xue and YangQuan Chen, Solving Applied Mathematical Problems with MATLAB, CRC Press, 2008,Matrix transpose,Matrix representation:Matrix A, n rows and m columns, is referred to as an mat

37、rixHermitian transposeSimple transpose,星期三, 2008-4- 23, 20:08:07,Slide 22 (of 103) Dingyü Xue and YangQuan Chen, Solving Applied Mathematical Problems with MATLAB, CRC P

38、ress, 2008,Mathematical representationsDifficult to program under C, like A*BMATLAB implementationNote: any variable can be a scalarIf not compatible, error messages given,Matrix addition and subtraction,星期三, 2008

39、-4- 23, 20:08:07,Slide 23 (of 103) Dingyü Xue and YangQuan Chen, Solving Applied Mathematical Problems with MATLAB, CRC Press, 2008,Math expressionMATLAB expressionNo

40、te: the dimension compatibility auto-checked,Matrix multiplication,星期三, 2008-4- 23, 20:08:07,Slide 24 (of 103) Dingyü Xue and YangQuan Chen, Solving Applied Mathematical Pro

41、blems with MATLAB, CRC Press, 2008,Matrix left divisionSolve the linear equations:MATLAB solution:Least squares solutionIf A is a non-singular square matrix. Then,,Matrix division,星期三, 2008-4- 23, 20:08:07,Sli

42、de 25 (of 103) Dingyü Xue and YangQuan Chen, Solving Applied Mathematical Problems with MATLAB, CRC Press, 2008,Matrix right divisionSolve the linear equations:MATLAB solut

43、ion:Least squares solutionIf A is a nonsingular square matrix. Then,More precisely,,星期三, 2008-4- 23, 20:08:07,Slide 26 (of 103) Dingyü Xue and YangQuan Chen, Solving Applied

44、 Mathematical Problems with MATLAB, CRC Press, 2008,left-right flip:up-down flip:Rotate :How to rotate ?,Matrix flip and rotation,星期三, 2008-4- 23, 20:08:07,Slide 27 (of 103)

45、 Dingyü Xue and YangQuan Chen, Solving Applied Mathematical Problems with MATLAB, CRC Press, 2008,A is a square matrix, determine the matrix A to the power x.Math descriptionMATLAB command:

46、,Matrix power,星期三, 2008-4- 23, 20:08:07,Slide 28 (of 103) Dingyü Xue and YangQuan Chen, Solving Applied Mathematical Problems with MATLAB, CRC Press, 2008,Matrix Dot operati

47、on,Element-by-element operationFor example:Another example,means,means,星期三, 2008-4- 23, 20:08:07,Slide 29 (of 103) Dingyü Xue and YangQuan Chen, Solving Applied Mathemati

48、cal Problems with MATLAB, CRC Press, 2008,Example 2.6,Cubic root of MATLAB commandsThe other two roots,星期三, 2008-4- 23, 20:08:07,Slide 30 (of 103) Dingyü Xue and YangQuan Chen, Sol

49、ving Applied Mathematical Problems with MATLAB, CRC Press, 2008,2.2.2 Logic operations of matrices,Logical variablesFor new version of MATLABNon-zero means logic 1Logical Operations (element-by-element)“

50、And” operation“Or” operation“Not” operationExclusive Or,星期三, 2008-4- 23, 20:08:07,Slide 31 (of 103) Dingyü Xue and YangQuan Chen, Solving Applied Mathematical Problems wi

51、th MATLAB, CRC Press, 2008,2.2.3 Relationship operations of matrices,Allowed comparisons: >, >=, <, <=, ==,~=, find(), all(), any()Examples:,星期三, 2008-4- 23, 20:08:07,Slide 32 (of 103)

52、 Dingyü Xue and YangQuan Chen, Solving Applied Mathematical Problems with MATLAB, CRC Press, 2008,2.2.4 Simplifications and presentations of analytical results,Function simple() can be used to s

53、implify mathematical formula:Other commonly used simplification functionsnumden(), collect(), expand(), factor(),星期三, 2008-4- 23, 20:08:07,Slide 33 (of 103) Dingyü Xue and YangQuan C

54、hen, Solving Applied Mathematical Problems with MATLAB, CRC Press, 2008,Example 2.7,Find the simplest form of the polynomialProcess it with various functionsExpand it,星期三, 2008-4- 23, 20:08:07,Slide

55、 34 (of 103) Dingyü Xue and YangQuan Chen, Solving Applied Mathematical Problems with MATLAB, CRC Press, 2008,Two commands to use It is run on the dot operation basisCon

56、vert to LATEX expression,Variable substitution,星期三, 2008-4- 23, 20:08:07,Slide 35 (of 103) Dingyü Xue and YangQuan Chen, Solving Applied Mathematical Problems with MATLAB, C

57、RC Press, 2008,Example 2.8,FunctionUse taylor() to evaluate its Taylor expression and convert the results in LATEX,星期三, 2008-4- 23, 20:08:07,Slide 36 (of 103) Dingyü Xue and YangQuan Ch

58、en, Solving Applied Mathematical Problems with MATLAB, CRC Press, 2008,By MATLAB \cos \left( b \right) -\sin \left( b \right) at+ \left( -1/2\,\cos \left( b \right) {a}^{2}+cd \right) {t}^{2}+1/6\,\sin \

59、left( b \right) {a}^{3}{t}^{3}+ \left( 1/24\,\cos \left( b \right) {a}^{4}-1/6\,c7wyaxk1^{3}-1/6\,{c}^{3}d \right) {t}^{4}-{\frac {1}{120}}\,\sin \left( b \right) {a}^{5}{t}^{5}By LaTeX,星期三, 2008-4- 23, 20:08:07,Slide 37

60、 (of 103) Dingyü Xue and YangQuan Chen, Solving Applied Mathematical Problems with MATLAB, CRC Press, 2008,2.2.5 Basic number theory computations,星期三, 2008-4- 23, 20:08:07,Sl

61、ide 38 (of 103) Dingyü Xue and YangQuan Chen, Solving Applied Mathematical Problems with MATLAB, CRC Press, 2008,Example 2.9,Data set -0.2765, 0.5772,1.4597, 2.1091, 1.191,-1

62、.6187Observe the results from different rounding functions.,星期三, 2008-4- 23, 20:08:07,Slide 39 (of 103) Dingyü Xue and YangQuan Chen, Solving Applied Mathematical Problems

63、with MATLAB, CRC Press, 2008,Example 2.10,Hilbert matrix can be specified with the statement A=hilb(3), perform the rational transformation.result,星期三, 2008-4- 23, 20:08:07,Slide 40 (of 103)

64、 Dingyü Xue and YangQuan Chen, Solving Applied Mathematical Problems with MATLAB, CRC Press, 2008,Example 2.11,1856120 , 1483720, get the GCD (greatest common divider), LCM (least common multiplier)

65、and prime factor decomposition to the least common multiplier,星期三, 2008-4- 23, 20:08:07,Slide 41 (of 103) Dingyü Xue and YangQuan Chen, Solving Applied Mathematical Problems

66、 with MATLAB, CRC Press, 2008,Example 2.12,Prime numbers in 1-1000The prime numbers obtained,星期三, 2008-4- 23, 20:08:07,Slide 42 (of 103) Dingyü Xue and YangQuan Chen, Solving Applied

67、 Mathematical Problems with MATLAB, CRC Press, 2008,2.3 Flow Control Structures of MATLAB Language,Loop control structuresConditional control structuresSwitch structureTrial structure,星期三, 2008-4- 23, 20

68、:08:07,Slide 43 (of 103) Dingyü Xue and YangQuan Chen, Solving Applied Mathematical Problems with MATLAB, CRC Press, 2008,2.3.1 Loop control structures,The for loop structures

69、If v is a matrix, i pick up one column at a time,星期三, 2008-4- 23, 20:08:07,Slide 44 (of 103) Dingyü Xue and YangQuan Chen, Solving Applied Mathematical Problems with M