MATHCAD For Beginners. Course Slides PowerPoint

Slide 2: Course Syllabus: First Day: Introduction; Starting Mathcad;Mathcad Toolbars; Navigating the Resource Center; Building Mathematical Expressions; Variables and Functions;Vectors and Matrix; Entering Text and Math; Individual Practicing. Second Day: Creating Graphs: 2D- plots with one and more functions; Formatting 2D-graphs;3D Graphing; Formatting 3D graphs; Animating a graph. Individual Practicing Third Day: Symbolic Calculations;Units 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. User’s Guide with Reference Manual. Mathcad 2001 Professional. Mathsoft Inc.,2000. Minor modifications may take place.

Slide 3:MATHCAD

????? ?????: ?????? ??????? ?? MathCad ????? ?????? ???????: -????? ????? -??????? ????????? -??????? ????????, ???????????? ???????????? -??????? ????????? -?????? ?MathCad ?????? ????? ??????? ?????? ??????? ?????? ??? ????? ?????.

Slide 4:????? ??????

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

Slide 5:1. ???????? ??????? ?? MathCad

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

Slide 6:1. ???????? ??????? ?? 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

Slide 7:2. ????? ?????? ??????

????? ???? Resource Center ?? ????? Working Sheet ???? ? MATHCAD: Help

Slide 8:2.1 ????? ????

???? Mathcad 2001 - ???? ???? ?? Main Menu Math Tool Bar Tool Bar Format Bar Status Line Working Sheet Cursor

Slide 9:2.1 ????? ???? (????)

Main Menu Math Tool Bar Tool Bar

Slide 10:2.1 ????? ???? (????2)

Launches the Resource Center Formatting Toolbar (View=>Toolbars=>Formatting) Status Line

Slide 11:2.2 Resource Center

Slide 12:2.2 Resource Center(????)

Resource Center Navigational Controls

Slide 13:2.3 ?? ????? Working Sheet

???? ?? Working Sheet ?????? ???????? ?? ?????? ??? ??? – ????? ?????? ?????? ????? 15-8/1104.5= ?Enter

Slide 14:2.4 ???? ? MATHCAD: Help

???? ????

Slide 15:3. ??????? ????????? ?????????

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

Slide 16:3.1 ????? ?????? ??????? ?????? ???????

+ - * / ^ ?????? ?????? ????????? ????? := ???? ??????/ ????? ?????? ?????: ??? x=(-b+?(b2-4ac))/2a ???? a=5 b=6 c=-4

Slide 17:3.1 ????? ?????? ??????? ?????? ??????? (????)

???? (X2+3)/5 ? X2+3/5 Without Spacebar

Slide 18:3.1 ????? ?????? ??????? ?????? ??????? (????2)

??????? ?????? ????????

Slide 19:3.2 ????????

??????? ?????? ????????

Slide 20:3.2. ???????? (????)

?????? ??????? ????? ‘.. ‘(range operator)

Slide 21:?????: ?????? ?????? ??????? (????? ???????)

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

Slide 22:????? (????):

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

Slide 23:4. ??????? ????????

?????? ?? ??????? ???????

Slide 24:4. ??????? ????????

?????? ?????/?????? ?? ?????? 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

Slide 25:??????/????? ???? ??????/?????? ?????? : Type v and left square bracket [ or use Xn button in the Calculator toolbar ??????: v(1)=-4.3 Type See on screen v[1= v1=-4.3 v(0)=2001 Type See on screen v[0= vo =2001 i:0;2 i[I= v[I=

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

Slide 26:?????:

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

Slide 27:Vector-Matrix Toolbar ??????? ?? ???????

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

Slide 28:4.1 ?????? ?? ??????? (????)

???????

Slide 29:4.1 ?????? ?? ??????? (????)

???? ???? ??-????? ???? ???????) sin( x*y

Slide 30: 1. ???? ?????? ???? ?????? M????? ??????? ???? ???????? ????? ??? ???? ??????, ????? ????? ??????? ? ?????? M 2. ???? ?????? 1x4 ?? ?????? ????? ????? ?????? 3. ??? ??????? f(v)=?v/(9*b2)*v|+a ???? a=2,b=5,v=1,-2,3 4. ??? ??????? f(x)=sin(x) ???? x=-10,-9.9,…,10

4.2 ???????

Slide 31:5.

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

Slide 32:????? ???? Y-X ?????? ??? ??????

5. ?????? ?MATHCAD

Slide 33:MATHCAD ????? : ????? ?????? ??-?????? ????? ?????? ??? ?????? ???????? ?? ??????

5. ?????? ?MATHCAD

Slide 34:?????? ???? ???? ??????? sinX - ???? ?? ????? (x)sin ?????? ????

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

Slide 35:????? ???? Y-X ???? ????? ?? ???? ????????:

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

Slide 36: ?????: ???? grid 4x4 ?? ??????? ?????? ???? ???? ?? ????? ???? Grid Lines ?X Axis ??YAxis ???? ????? ?Auto Grid ???? 4 ?4 ?Number of Grid

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

Slide 37:???? Y-X ???? ?????

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

Slide 38:?????: ???? ???? ?? ??? ??????? – ??? ??? ????

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

Slide 39:???? 3 ?????? ?????? ???? ???????? ???? ???? ??? ???? ???????? ???? ???? ???? ???????? ??? ????? 2, ???? z=-10,-9.9…10 ???? ??????? ?????? ?z=-2,-1.9…2 ???? ??????? ????

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

Slide 40:3D -??????

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

Slide 41:3D –?????? ????????

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

Slide 42:

5.2 ?????? ??? ?????? (????2)

Slide 43:

5.2 ?????? ??? ?????? (????3)

Slide 44:????? ??????? ???????? –??????? FIND Nonlinear Least Square Fitting – ??????? Minerr ???????????: ???????? interp ?spline ???????

6. ??????? ???????? ????????

Slide 45: Find(z0,z1,…), ???? z0,z1,… - ?????? ??? ?????? ? find ????: ??? ????? ???????? ???? ?? ??? ??????? ????? ???? GIVEN ??? ????? ???????? ????? ????? ??????? ????? ??????? Find ????? (???? ????)

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

Slide 46:?????: ???? ????? ?? ????? ???????: ?????

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

Slide 47: Minerr(var1,var2,…) ???? var1,var2,… - ?????? ????? ? Minerr ???? ?????? ?Find ?????:

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

Slide 48:????? (????):

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

Slide 49:6.3 ???????????: ???????? interp ?spline

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

Slide 50:6.3 ???????????: ???????? interp ?spline(????)

????? ???? ????? ????????? interp ?spline

Slide 51: 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

Slide 52: 6.4 ??????? (????)

????? ???????? (oC) ?? ??? ??? 12 ???? ??????? ??: 16 18 15 19 25 29 31 30 22 25 27 24 ????? ?interp ??? ???? ???????? ?? 1/10 ??? ?????? ???? ??? ?? ?????? ?????. ??? x ???? ax2+bx+c=0 ???? initial x=1 ?: - a=3.1,b=5,c=-7.81 a=1,b=55.1,c=0 – ???? ???? ????? ????? ?????? root ????: ????? ?help ?????? ????? ????? root

Slide 53:???? ????????, ???????? ??????

7. ?????????

Slide 54:???????. 1. ???????? sin 2. ???????? sin ?? ??? ?????

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

Slide 55:8. ?????? ????? ?MATHCAD

????? ?????? SI ????? ?????? ??????? ???????

Slide 56: 8.1 ????? ?????? SI

??? ????? ????? MATHCAD ?????? ??????? SI ????? ?????? ????? ???????: ?????? ????? ???? ????: - ??? ??? ?????? (*) -???? ?? ?? ????? ?????? ?????? – ?INSERT->UNIT ?????:

Slide 57:8.2 ????? ??????

?????? ?????? ?????? ?????:

Slide 58:8.3 ???????

????? ??????? : ???????

Slide 59:8.4 ???????

??????? ?????? ?????? : 1. 2. 3.

Slide 60:9. ??????? ?????????

Evaluate ????????? ??????? ???? ??????? ???? ?????? ???????

Slide 61:9.1 Evaluate

???????? ????????? : ?????

Slide 62:9.2 ?????????

Slide 63:9.3 ???????

??????? ?? ?????:

Slide 64:9.4 ???? ??????? ???? ??????

Slide 65:9.5 SUBSTITUTION

Slide 66:9.6 ???????

1. 2.

Slide 67:9.6 ??????? (????)

3. 4.

Slide 68:10. ??????? ????????????.

ODESOLVE ??????? RKFIXED ???????

Slide 69:10.1 ODESOLVE

?????? ????? ?? ?????? ?? ????? ??????? ???????????? ??????? ? ???? GIVEN ?????? ODESOLVE

Slide 70:10.1 ODESOLVE (????)

THE ODESOLVE BLOCK

Slide 71:10.1 ODESOLVE (????2)

Initial Value Problem. High Order Differential Equations:

Slide 72:10.1 ODESOLVE (????3)

Boundary Value Problem. :

Slide 73:10.2 ???????

1.

Slide 74:10.2 ??????? (????)

2. 3.

Slide 75:10.3 RKFIXED

????? ??????? ???????????? ???? ?????

Slide 76:10.3 RKFIXED (????)

??????? rkfixed

Slide 77:10.4 ???????(????2)

1. 2.

Slide 78:

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