MATLAB MATRIX LABORATORY

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MathCad for Beginners
by Dr.Leonid Burstein
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• Course Syllabus
• First Day
• Introduction Starting MathcadMathcad Toolbars
  Navigating the Resource Center Building
  Mathematical Expressions Variables and
  FunctionsVectors and Matrix Entering Text and
  Math Individual Practicing.
• Second Day
• Creating Graphs 2D- plots with one and more
  functions Formatting 2D-graphs3D Graphing
  Formatting 3D graphs Animating a graph.
  Individual Practicing
• Third Day
• Symbolic CalculationsUnits in Mathcad
  Differential Equation Solver Initial Value
  Problem Boundary Value Problem Individual
  Practicing.

• Course Destination
• Course is destined for non-programmers
  engineers and scientists who whish to gain the
  skill in using Mathcad.
• Prerequisites
• Primary skill in Mathcad is not required.
• Course organization
• Three academic hours, including individual
  practicing. Examples will be performed in real
  time by the lecturer and by the students.
• Bonus Those who wish can receive home task or
  propose and solve any problem which would check
  by lecturer.
• Period
• 3 days during one week.
• Literature
• Mathcad. Users Guide with Reference Manual.
  Mathcad 2001 Professional. Mathsoft Inc.,2000.
• Minor modifications may take place.

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MATHCAD

• ????? ?????
• ?????? ??????? ?? MathCad ????? ?????? ???????
• -????? ?????
• -??????? ?????????
• -??????? ????????, ???????????? ????????????
• -??????? ?????????
• -?????? ?MathCad
• ?????? ????? ??????? ?????? ??????? ?????? ???
  ????? ?????.

You never stop using MathCad
4
????? ??????

• 1 ???????? ??????? ?? MathCad
• 2 ????? ?????? ??????
• 3 ??????? ????????? ?????????
• 4 ??????? ????????
• 5 ?????? ?Mathcad
• 6 ??????? ??????? ?????????
• 7 ????????
• 8 ?????? ????? ?MATHCAD
• 9 ??????? ?????????
• 10 ??????? ????????????

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1. ???????? ??????? ?? MathCad

• MathCad ?????
• ????? ?? ??????? ???????? ????? ?????, ??????
  ????????
• ????? ??? ???? ?
• - ????? ?????? ????????
• - ????? ??????
• - ????? ?????
• ????? ???? ??????? ??? ??? ????? ??????
• ??????????? ???? ????? ????????? ???????
  ??????????

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1. ???????? ??????? ?? MathCad

• ?????? Mathcad ????
• Pentium 133MHz or compatible CPU
• CD-ROM driver
• Widows 95 or higher Windows NT 4.0 or higher
• At least 32 Mb RAM, 64 Mb is recommended
• Internet Explorer 4.0 or higher

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2. ????? ?????? ??????

• ????? ????
• Resource Center
• ?? ????? Working Sheet
• ???? ? MATHCAD Help

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2.1 ????? ????

• ???? Mathcad 2001 - ???? ???? ??

Main Menu
Tool Bar
Format Bar
Working Sheet
Math Tool Bar
Cursor
Status Line
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2.1 ????? ???? (????)

• Main Menu
• Math Tool Bar
• Tool Bar

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2.1 ????? ???? (????2)

• Launches the Resource Center
• Formatting Toolbar (ViewgtToolbarsgtFormatting)
• Status Line

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2.2 Resource Center
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2.2 Resource Center(????)

• Resource Center Navigational Controls

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2.3 ?? ????? Working Sheet

• ???? ?? Working Sheet ?????? ???????? ?? ??????
• ??? ??? ????? ?????? ??????
• ????? 15-8/1104.5 ?Enter

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2.4 ???? ? MATHCAD Help

• ???? ????

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3. ??????? ????????? ?????????

• ????? ?????? ??????? ?????? ???????
• ????????
• Buid-in ????????

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3.1 ????? ?????? ??????? ?????? ???????

• - / ?????? ?????? ????????? ?????
• ???? ??????/ ????? ??????
• ?????
• ??? x(-b?(b2-4ac))/2a ???? a5 b6 c-4

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3.1 ????? ?????? ??????? ?????? ??????? (????)

• ????
• (X23)/5
• ? X23/5

Without Spacebar
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3.1 ????? ?????? ??????? ?????? ??????? (????2)

• ??????? ?????? ????????

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3.2 ????????

• ??????? ?????? ????????

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3.2. ???????? (????)

• ?????? ??????? ????? .. (range operator)

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3.3. Build-in????????

• ????? ?????? ??????
  ??????? (????? ???????)

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3.3. Build-in???????? (????)

• ????? (????)

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4. ??????? ????????

• ?????? ?? ???????
• ???????

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4. ??????? ????????

• ?????? ?????/?????? ?? ?????? 3.3, -1.2, 8
• Type vector name v
• Press Ctrl m or choose Matrix from the Insert
• Fill in the appropriate numbers of rows (3) and
  column(1).
• Click on Insert or OK.
• Fill in the placeholders
• with the appropriate
• values. Use Tab to move
• from placeholder to
• placeholder inside the
• vector

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4. ??????? ????????(????)

• ??????/????? ???? ??????/?????? ??????
• Type v and left square bracket or use
• Xn button in the Calculator toolbar
• ??????
• v(1)-4.3
• Type See on screen
• v1 v1-4.3
• v(0)2001
• Type See on screen
• v0 vo 2001
• i02
• iI
• vI

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4. ??????? ????????(????2)

• ?????

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4.1 ?????? ?? ???????

• Vector-Matrix Toolbar ??????? ?? ???????

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4.1 ?????? ?? ??????? (????)

• ???????

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4.1 ?????? ?? ??????? (????)

• ???? ???? ??-????? ???? ???????) sin( xy

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4.2 ???????

• 1. ???? ??????
• ???? ?????? M????? ??????? ???? ????????
  ?????
• ??? ???? ??????, ????? ????? ??????? ? ??????
  M
• 2. ???? ?????? 1x4 ?? ?????? ????? ????? ??????
• 3. ??? ??????? f(v)?v/(9b2)va ????
  a2,b5,v1,-2,3
• 4. ??? ??????? f(x)sin(x) ???? x-10,-9.9,,10

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4.2 ??????? (????)

• 5.

????? ???????? ?????? ??????? ??????? ??? ?????
???????? ????? ?????? ????? ??? ??????
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5. ?????? ?MATHCAD

• ????? ???? Y-X
• ?????? ??? ??????

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5. ?????? ?MATHCAD

• MATHCAD ?????
• ????? ?????? ??-??????
• ????? ?????? ??? ??????
• ???????? ?? ??????

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5.1 ????? ???? Y-X

• ?????? ???? ???? ??????? sinX - ???? ??
• ????? (x)sin ?????? ????

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5.1 ????? ???? Y-X (????)

• ????? ???? Y-X ???? ????? ?? ???? ????????

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5.1 ????? ???? Y-X. ???????

• ?????
• ???? grid 4x4 ?? ??????? ??????
• ???? ???? ?? ?????
• ???? Grid Lines ?X Axis ??YAxis
• ???? ????? ?Auto Grid
• ???? 4 ?4 ?Number of Grid

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5.1 ????? ???? Y-X ???? ?????

• ???? Y-X ???? ?????

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5.1 ????? ???? Y-X ???? ????? (????)

• ?????
• ???? ???? ?? ??? ??????? ??? ??? ????

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5.1 ????? ???? Y-X. ???????

• ???? 3 ?????? ?????? ???? ????????
• ???? ???? ??? ???? ????????
• ???? ???? ???? ???????? ??? ????? 2,
• ????
• z-10,-9.910 ???? ??????? ??????
• ?z-2,-1.92 ???? ??????? ????

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5.2 ?????? ??? ??????

• 3D -??????

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5.2 ?????? ??? ?????? (????)

• 3D ?????? ????????

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5.2 ?????? ??? ?????? (????2)
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5.2 ?????? ??? ?????? (????3)
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6. ??????? ???????? ????????

• ????? ??????? ???????? ??????? FIND
• Nonlinear Least Square Fitting ??????? Minerr
• ??????????? ???????? interp ?spline
• ???????

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6.1 ????? ??????? ????????.??????? FIND

• Find(z0,z1,),
• ???? z0,z1, - ??????
• ??? ?????? ? find ????
• ??? ????? ???????? ???? ?? ??? ???????
• ????? ???? GIVEN ??? ????? ????????
• ????? ????? ???????
• ????? ??????? Find
• ????? (???? ????)

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6.1 ????? ??????? ????????.??????? find (????)

• ?????
• ???? ????? ?? ????? ???????
• ?????

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6.2 Nonlinear Least Square Fitting - ???????
Minerr

• Minerr(var1,var2,)
• ???? var1,var2, - ??????
• ????? ? Minerr ???? ?????? ?Find
• ?????

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6.2 Nonlinear Least Square Fitting- ???????
Minerr (????)

• ????? (????)

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6.3 ??????????? ???????? interp ?spline

• interp(S,X,Y,x)
• cspline(X,Y)
• ????

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6.3 ??????????? ???????? interp ?spline(????)

• ????? ???? ????? ????????? interp ?spline

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6.4 ???????

• United States Population in millions of people
  Vs. Years
• 1900 75.995
• 1910 91.972
• 1920 105.711
• 1930 123.203
• 1940 131.669
• 1950 150.697
• 1960 179.323
• 1970 203.212
• 1980 226.505
• 1990 249.633
• ??? ???? ???????? ?USA ?1975 ??? ????? ?????? ???
  1900 ?1990

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6.4 ??????? (????)

• ????? ???????? (oC) ?? ??? ??? 12 ???? ???????
  ??
• 16 18 15 19 25 29 31 30 22 25 27 24
• ????? ?interp ??? ???? ???????? ?? 1/10 ???
  ?????? ???? ??? ?? ?????? ?????.
• ??? x ???? ax2bxc0 ???? initial x1 ?
• - a3.1,b5,c-7.81
• a1,b55.1,c0
• ???? ???? ????? ????? ?????? root
• ???? ????? ?help ?????? ????? ????? root

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7. ?????????

• ???? ????????, ???????? ??????

54
7. ????????? ?MATHCAD (????)

• ???????.
• 1. ???????? sin
• 2. ???????? sin ?? ??? ?????

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8. ?????? ????? ?MATHCAD

• ????? ?????? SI
• ????? ??????
• ???????
• ???????

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8.1 ????? ?????? SI

• ??? ????? ????? MATHCAD ?????? ??????? SI ?????
  ?????? ????? ???????
• ?????? ????? ???? ????
• - ??? ??? ?????? ()
• -???? ?? ?? ?????
• ?????? ??????
• ?INSERT-gtUNIT
• ?????

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8.2 ????? ??????

• ?????? ?????? ?????? ?????

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8.3 ???????

• ????? ???????
• ???????

59
8.4 ???????

• ??????? ?????? ??????
• 1.
• 2.
• 3.

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9. ??????? ?????????

• Evaluate
• ?????????
• ???????
• ???? ??????? ???? ??????
• ???????

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9.1 Evaluate

• ???????? ?????????
  
• ?????

62
9.2 ?????????

63
9.3 ???????

• ??????? ?? ?????

64
9.4 ???? ??????? ???? ??????
65
9.5 SUBSTITUTION
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9.6 ???????

• 1.
• 2.

67
9.6 ??????? (????)

• 3.
• 4.

68
10. ??????? ????????????.

• ODESOLVE
• ???????
• RKFIXED
• ???????

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10.1 ODESOLVE

• ?????? ????? ?? ?????? ?? ????? ???????
  ????????????
• ??????? ? ???? GIVEN ?????? ODESOLVE

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10.1 ODESOLVE (????)

• THE ODESOLVE BLOCK

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10.1 ODESOLVE (????2)

• Initial Value Problem. High Order Differential
  Equations

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10.1 ODESOLVE (????3)

• Boundary Value Problem.

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10.2 ???????

• 1.

74
10.2 ??????? (????)

• 2.
• 3.

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10.3 RKFIXED

• ????? ??????? ???????????? ???? ?????

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10.3 RKFIXED (????)

• ??????? rkfixed

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10.4 ???????(????2)

• 1.
• 2.

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????? ??? (??? ????? ????)