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管理數學介紹 了解管理數學的詳細內容

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內容介紹

為什么要在管理活動中運用數學方法?怎樣理解各種圖表和數據?什么是數學模型?怎樣運用數學模型輔助解決管理中的難題?本書對上述問題及其他有關問題作了清楚而確切的解釋。

作品目錄

Contents

  1 EIementary algebra

  Introduction

  1.1 Algebraic expressions and equations

  1.2 The addition and subtraction of algebraic forms

  1.3 Products of positive and negative real numbers

  1.4 Expansion of bracketed terms

  1.5 Fractions

  1.6 Exponents

  1.7 Negative exponents

  1.8 Cancelling out tenms

  1.9 The order and hierarchy of operations

  1.10 Factorization

  1.11 Degree of an expression

  1.12 Perfect squares

  1.13 Applications

  Additional examples

  2 Solving equations

  Introduction

  2.1 Drawing graphs

  2.2 Straight-line or linear functions

  2.3 Quadratic functions

  2.4 Cubic functions

  2.5 Algebraic solution of equations

  2.6 Equations involving fractions

  2.7 Quadratic equations

  2.8 Formula for solving quadratic equations

  2.9 Solution of cubic equations

  2.10 Applications

  Additional examples

  3 Simultaneous equations and inequalities

  Introduction

  3.1 Simple equations with one variable

  3.2 Pairs of equations

  3.3 Using a set of equations as a model

  3.4 Sets of three or more equations

  3.5 Independent and dependent equations

  3.6 Linear and non-linear equations

  3.7 Inequalities

  3.8 Simultaneous inequalities

  3.9 Applications of inequalities

  Additional examples

  4 Series

  Introduction

  4.1 Arithmetic progression (AP)

  4.2 The sigma notation for summation

  4.3 Sum of terms of an AP

  4.4 Geometric progression (GP)

  4.5 Sum of terms of a GP

  4.6 Notation for interest calculations

  4.7 Compound interest

  Additional examples

  5 Logarithms and exponentials

  Introduction

  5.1 Logarithms and exponents

  5.2 How logarithms work

  5.3 Rules for combining logarithms

  5.4 The exponential function and continuous compounding

  5.5 Nominal interest rates and effective interest rates

  5.6 Negative growth

  5.7 Application

  Additional examples

  6 Matrices

  Introduction

  6.1 Matrix notafion

  6.2 Equality, addition and subtraction of matrices

  6.3 Multiplication of matrices

  6.4 Transposing matrices

  6.5 Matrix formulation of simultaneous equations

  6.6 The identity matrix and the inverse

  6.7 Determinants

  6.8 The inverse of a 2 x 2 matrix

  6.9 Summary

  Additional examples

  7 Differentiation

  Introduction

  7.1 The slope of a straight line

  7.2 Finding the equation of a straight line

  7.3 A numerical method for finding the slope of a curve

  7.4 The general method of differentiation

  7.5 Rules for derivatives

  7.6 The derivative of the redprocal of a function

  Additional examples

  8 More about ditterentiation

  Introduction

  8.1 The second and higher derivatives

  8.2 Alternative notation for the derivative

  8.3 Maxima and minima

  8.4 Points of inflexion

  8.5 The function of a function rule

  8.6 The product rule

  8.7 Mixing the function of a function and product rules

  8.8 Differentiating expressions containing fractions

  8.9 Continuous functions

  8.10 Partial derivatives

  Additional examples

  9 Integration

  Introduction

  9.1 Integration as the reverse of differentiation

  9.2 Rules for integration

  9.3 The definite integral

  9.4 The integral as the area between the curve and the x-axis

  9.5 A general remark on integration and differentiation

  Additional examples

  10 The application ofmathematics

  10.1 Mathematical style

  10.2 Taclding mathematical examination questions

  10.3 Formulating real-life problems

  10.4 Solving real-life problems

  Appendix The Greek alphabet

  Solutions to additional examples

展開全部下面的內容轉自我的百度空間,是我收集來的,在這里看起來如果覺得排62616964757a686964616fe58685e5aeb931333236383433版不好,可以直接看我的空間內的文章:http://hi.baidu.com/newkedison/blog/item/1c7d2c392cc192f63b87ce12.html有關UTF-8的一些資料2008年06月13日 星期五 08:17一, 最重要的,UTF-8和Unicode的轉換UTF-8 編碼是一種被廣泛應用的編碼,這種編碼致力于把全球的語言納入一個統一的編碼,目前已經將幾種亞洲語言納入。UTF 代表 UCS Transformation Format. UTF-8 采用變長度字節來表示字符,理論上最多可以到 6 個字節長度。UTF-8 編碼兼容了 ASC II(0-127), 也就是說 UTF-8 對于 ASC II 字符的編碼是和 ASC II 一樣的。對于超過一個字節長度的字符,才用以下編碼規范: 左邊第一個字節1的個數表示這個字符編碼字節的位數,例如兩位字節字符編碼樣式為為:110xxxxx 10xxxxxx; 三位字節字符的編碼樣式為:1110xxxx 10xxxxxx 10xxxxxx.;以此類推,六位字節字符的編碼樣式為:1111110x 10xxxxxx 10xxxxxx 10xxxxxx 10xxxxxx 10xxxxxx。 xxx 的值由字符編碼的二進制表示的位填入。只用最短的那個足夠表達一個字符編碼的多字節串。例如: Unicode 字符: 00 A9(版權符號) = 1010 1001, UTF-8 編碼為:11000010 10101001 = 0x C2 0xA9; 字符 22 60 (不等于符號) = 0010 0010 0110 0000, UTF-8 編碼為:11100010 10001001 10100000 = 0xE2 0x89 0xA0以上轉換例子已經確認是正確的,不用懷疑,如果看不懂請再仔細想想Unicode編碼和utf-8編碼之間的對應關系表 The table below summarizes the format of these different octet types. The letter x indicates bits available for encoding bits of the character number.Char. number range | UTF-8 octet sequence (hexadecimal) | (binary) --------------------+--------------------------------------------- 0000 0000-0000 007F | 0xxxxxxx 0000 0080-0000 07FF | 110xxxxx 10xxxxxx 0000 0800-0000 FFFF | 1110xxxx 10xxxxxx 10xxxxxx //////A///////// 0001 0000-0010 FFFF | 11110xxx 10xxxxxx 10xxxxxx 10xxxxxx這是一個Unicode編碼和utf-8編碼之間的對應關系表。中文的Unicode編碼范圍在0000 0800-0000 FFFF 中。二, 關于BOMUTF-8以字節為編碼單元,沒有字節序的問題。UTF-16以兩個字節為編碼單元,在解釋一個UTF-16文本前,首先要弄清楚每個編碼單元的字節序。例如收到一個“奎”的Unicode編碼是594E,“乙”的Unicode編碼是4E59。如果我們收到UTF-16字節流“594E”,那么這是“奎”還是“乙”? Unicode規范中推薦的標記字節順序的方法是BOM。BOM不是“Bill Of Material”的BOM表,而是Byte Order Mark。BOM是一個有點小聰明的想法: 在UCS編碼中有一個叫做"ZERO WIDTH NO-BREAK SPACE"的字符,它的編碼是FEFF。而FFFE在UCS中是不存在的字符,所以不應該出現在實際傳輸中。UCS規范建議我們在傳輸字節流前,先傳輸字符"ZERO WIDTH NO-BREAK SPACE"。 這樣如果接收者收到FEFF,就表明這個字節流是Big-Endian的;如果收到FFFE,就表明這個字節流是Little-Endian的。因此字符"ZERO WIDTH NO-BREAK SPACE"又被稱作BOM。 UTF-8不需要BOM來表明字節順序,但可以用BOM來表明編碼方式。字符"ZERO WIDTH NO-BREAK SPACE"的UTF-8編碼是EF BB BF(讀者可以用我們前面介紹的編碼方法驗證一下)。所以如果接收者收到以EF BB BF開頭的字節流,就知道這是UTF-8編碼了。三, VB實現UTF-8轉Unicode的函數1.不使用APIFunction Utf8ToUnicode(ByRef Utf() As Byte) As StringDim utfLen As LongutfLen = -1On Error Resume NextutfLen = UBound(Utf)If utfLen = -1 Then Exit FunctionOn Error GoTo 0Dim i As Long, j As Long, k As Long, N As LongDim B As Byte, cnt As ByteDim Buf() As StringReDim Buf(utfLen)i = 0j = 0Do While i <= utfLen B = Utf(i) If (B And &HFC) = &HFC Then cnt = 6 ElseIf (B And &HF8) = &HF8 Then cnt = 5 ElseIf (B And &HF0) = &HF0 Then cnt = 4 ElseIf (B And &HE0) = &HE0 Then cnt = 3 ElseIf (B And &HC0) = &HC0 Then cnt = 2 Else cnt = 1 End If If i + cnt - 1 > utfLen Then Buf(j) = "?" Exit Do End If Select Case cnt Case 2 N = B And &H1F Case 3 N = B And &HF Case 4 N = B And &H7 Case 5 N = B And &H3 Case 6 N = B And &H1 Case Else Buf(j) = Chr(B) GoTo Continued: End Select For k = 1 To cnt - 1 B = Utf(i + k) N = N * &H40 + (B And &H3F) Next Buf(j) = ChrW(N)Continued: i = i + cnt j = j + 1LoopUtf8ToUnicode = Join(Buf, "")End Function2. 使用API (包括Unicode轉UTF-8)Private Declare Function WideCharToMultiByte Lib "kernel32" (ByVal CodePage As Long, ByVal dwFlags As Long, ByVal lpWideCharStr As Long, ByVal cchWideChar As Long, ByRef lpMultiByteStr As Any, ByVal cchMultiByte As Long, ByVal lpDefaultChar As String, ByVal lpUsedDefaultChar As Long) As LongPrivate Declare Function MultiByteToWideChar Lib "kernel32" (ByVal CodePage As Long, ByVal dwFlags As Long, ByVal lpMultiByteStr As Long, ByVal cchMultiByte As Long, ByVal lpWideCharStr As Long, ByVal cchWideChar As Long) As LongPrivate Const CP_UTF8 = 65001Function Utf8ToUnicode(ByRef Utf() As Byte) As StringDim lRet As LongDim lLength As LongDim lBufferSize As LonglLength = UBound(Utf) - LBound(Utf) + 1If lLength <= 0 Then Exit FunctionlBufferSize = lLength * 2Utf8ToUnicode = String$(lBufferSize, Chr(0))lRet = MultiByteToWideChar(CP_UTF8, 0, VarPtr(Utf(0)), lLength, StrPtr(Utf8ToUnicode), lBufferSize)If lRet <> 0 Then Utf8ToUnicode = Left(Utf8ToUnicode, lRet)End IfEnd FunctionFunction UnicodeToUtf8(ByVal UCS As String) As Byte()Dim lLength As LongDim lBufferSize As LongDim lResult As LongDim abUTF8() As BytelLength = Len(UCS)If lLength = 0 Then Exit FunctionlBufferSize = lLength * 3 + 1ReDim abUTF8(lBufferSize - 1)lResult = WideCharToMultiByte(CP_UTF8, 0, StrPtr(UCS), lLength, abUTF8(0), lBufferSize, vbNullString, 0)If lResult <> 0 ThenlResult = lResult - 1ReDim Preserve abUTF8(lResult)UnicodeToUtf8 = abUTF8End IfEnd FunctionPrivate Sub Command1_Click()Dim byt() As Bytebyt = UnicodeToUtf8("測試")Debug.Print Hex(byt(0)) & Hex(byt(1)) & Hex(byt(2))Debug.Print Utf8ToUnicode(byt()) End Sub參考資料:http://hi.baidu.com/newkedison/blog/item/1c7d2c392cc192f63b87ce12.html*展開全部'復制下面文件到模塊中'調用:Text1.Text = UTF8_Decode(UTF8Zfc)'注意:文件下載后直接轉換,不能做任何其他轉換(如strconv)。'***************模塊代碼********************'Utf8字符轉化636f70793231313335323631343130323136353331333236383433成Unicode字符定義Public Declare Function MultiByteToWideChar Lib "kernel32" (ByVal CodePage As Long, ByVal dwFlags As Long, ByRef lpMultiByteStr As Any, ByVal cchMultiByte As Long, ByVal lpWideCharStr As Long, ByVal cchWideChar As Long) As LongPublic Const CP_UTF8 = 65001'獲得系統的類型定義Private Declare Function GetVersionExA Lib "kernel32" (lpVersionInformation As OSVERSIONINFO) As IntegerPrivate Type OSVERSIONINFO dwOSVersionInfoSize As Long dwMajorVersion As Long dwMinorVersion As Long dwBuildNumber As Long dwPlatformId As Long szCSDVersion As String * 128End Type'獲得系統的類型Public Function GetVersion() As String Dim osinfo As OSVERSIONINFO Dim retvalue As Integer osinfo.dwOSVersionInfoSize = 148 osinfo.szCSDVersion = Space$(128) retvalue = GetVersionExA(osinfo) With osinfo Select Case .dwPlatformId Case 1 Select Case .dwMinorVersion Case 0 GetVersion = "1Windows 95" Case 10 GetVersion = "1Windows 98" Case 90 GetVersion = "1Windows Mellinnium" End Select Case 2 Select Case .dwMajorVersion Case 3 GetVersion = "2Windows NT 3.51" Case 4 GetVersion = "2Windows NT 4.0" Case 5 If .dwMinorVersion = 0 Then GetVersion = "2Windows 2000" Else GetVersion = "2Windows XP" End If End Select Case Else GetVersion = "Failed" End Select End WithEnd Function'功能: 把Utf8字符轉化成Unicode字符Public Function UTF8_Decode(ByVal sUTF8 As String) As String Dim lngUtf8Size As Long Dim strBuffer As String Dim lngBufferSize As Long Dim lngResult As Long Dim bytUtf8() As Byte Dim n As Long If LenB(sUTF8) = 0 Then Exit Function If Left(GetVersion(), 1) = "2" Then On Error GoTo EndFunction 'bytUtf8 = StrConv(sUTF8, vbFromUnicode) bytUtf8 = sUTF8 lngUtf8Size = UBound(bytUtf8) + 1 On Error GoTo 0 'Set buffer for longest possible string i.e. each byte is 'ANSI, thus 1 unicode(2 bytes)for every utf-8 character. lngBufferSize = lngUtf8Size * 2 strBuffer = String$(lngBufferSize, vbNullChar) 'Translate using code page 65001(UTF-8) lngResult = MultiByteToWideChar(CP_UTF8, 0, bytUtf8(0), _ lngUtf8Size, StrPtr(strBuffer), lngBufferSize) 'Trim result to actual length If lngResult Then UTF8_Decode = Left(strBuffer, lngResult) End If Else Dim i As Long Dim TopIndex As Long Dim TwoBytes(1) As Byte Dim ThreeBytes(2) As Byte Dim AByte As Byte Dim TStr As String Dim BArray() As Byte 'Resume on error in case someone inputs text with accents 'that should have been encoded as UTF-8 On Error Resume Next TopIndex = LenB(sUTF8) ' Number of bytes equal TopIndex+1 If TopIndex = 0 Then Exit Function ' get out if there's nothing to convert 'BArray = StrConv(sUTF8, vbFromUnicode) BArray = sUTF8 i = 0 ' Initialise pointer TopIndex = TopIndex - 1 ' Iterate through the Byte Array Do While i <= TopIndex AByte = BArray(i) If AByte < &H80 Then ' Normal ANSI character - use it as is TStr = TStr & Chr$(AByte): i = i + 1 ' Increment byte array index ElseIf AByte >= &HE0 Then 'was = &HE1 Then ' Start of 3 byte UTF-8 group for a character ' Copy 3 byte to ThreeBytes ThreeBytes(0) = BArray(i): i = i + 1 ThreeBytes(1) = BArray(i): i = i + 1 ThreeBytes(2) = BArray(i): i = i + 1 ' Convert Byte array to UTF-16 then Unicode TStr = TStr & ChrW$((ThreeBytes(0) And &HF) * &H1000 + (ThreeBytes(1) And &H3F) * &H40 + (ThreeBytes(2) And &H3F)) ElseIf (AByte >= &HC2) And (AByte <= &HDB) Then ' Start of 2 byte UTF-8 group for a character TwoBytes(0) = BArray(i): i = i + 1 TwoBytes(1) = BArray(i): i = i + 1 ' Convert Byte array to UTF-16 then Unicode TStr = TStr & ChrW$((TwoBytes(0) And &H1F) * &H40 + (TwoBytes(1) And &H3F)) Else ' Normal ANSI character - use it as is TStr = TStr & Chr$(AByte): i = i + 1 ' Increment byte array index End If Loop UTF8_Decode = TStr ' Return the resultant string Erase BArray End IfEndFunction:End Function*www.545130.tw*?*?

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