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shpRectVx##mcDocumentObjectState\mcPageModelK????mcHeaderFooterI@I0Created: Jan. 20, 1996|NUpdated: August 15, 2000|F|Npage |P1Authors: Sidney H. Young|NTheresa Julia Zielinski
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\deflang1033\pard\plain\f2\fs20 Created: Jan. 20, 1996\
Updated: September, 2001
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\deflang1033\pard\qr\plain\f2\fs20 Authors: Sidney H. Young\
Theresa Julia Zielinski
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*@U@[@hX``-@rSidney Young
Department of Chemistry
University of South Alabama
Mobile AL 36688-0002
syoung@jaguar1.usouthal.edu7
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@G*@UWNGG-B*What version of Mathcad should you use?
This depends on the type of computer you have and what you have available. This document was written and saved as a Mathcad 6.0+ document. You can open it with any higher version of Mathcad. Higher versions may have some differences in how higher powered features are performed. For simple applications encountered by students version 6.0 is adequate. However, if you have a choice you should use the highest version you have available. Macintosh computer users only have Mathcad 6.0+ available for their use. 7***@H<*@I8@G}0,0,128@J<@K8@G0,0,128@H@J@H9*@L<*@M:@W,1@N</*@O<*@P0@NormalArial
@Q*@USCCPCP-ANote to users of this document. The methods and procedures of this document may be different in your version of Mathcad. This may be an obstacle if you let it be one. However, instances of version incompatibility should be few. Every effort has been made to keep the exercises here in a form that crosses most levels of Mathcad. You may need to refer to your Mathcad manual for details for performance of certain operations on your particular version of Mathcad. 79@R<@S:@W,1@T</@U<@V0@NormalArial
@W PageBreakE@U(@0(@X*@UDbBPRRR-HPart I - Preliminary Exercises
1. Begin your MATHCAD session by opening the MathSoft Apps Group in Windows and double clicking on the MATHCAD icon. You may wish to work through the Mathcad Tutorial before you start the set of exercises in this document. Exit the tutorial session before doing this set of exercises. Many users have the Mathcad icon on their desktop. Double click on this one if it is available.
2. Simple keyboard practice. Notice the structure of a Mathcad page. It is like a white piece of paper. Sample the various pull down menus. Notice how groups of possible actions are grouped together.
Entering simple equations onto the MATHCAD page.
Enter 16-8/2=
Note how the division sign behaves. Pressing = produces the numerical result of the operation.
To produce (16-8)/2, one should either type the entry with the parentheses included, or type 16-8 and then highlight the entire operation, and then press the division button. What ever is highlighted, i.e. in the blue box, will appear in the numerator. Try this step now.
The hierarchy of operator evaluation follows the commonly used standards. Powers are followed by multiplication and division, followed by addition and subtraction.
Pressing the = evaluates the mathematical sequence and returns the numerical value to the right of the equal
sign.
To take the power of a function use the carat symbol (Shift-6). Evaluate 4 squared. Practice now with other squares. You can make your practice exercises right here in this document or print this document and create your own collection of answers to the exercises. Save your file periodically in case of a computer glitch. You can also annotate your document with text regions. This will give you a personalized tutorial document that you can refer to if you forget something you learned here. You can also add sample exercises to your personal document as the semester proceeds. This is important because you may need to refer to techniques from one exercise to the next and you don't want to waste time recreating a technique that was already constructed in your practice files.
Most users of Mathcad have a file of techniques that they can refer to for new work. Start your file or notebook of techniques today.77@Y<@Z8@X}Times New Roman0,0,128@[<@\8@XTimes New Roman0,0,128@Y@]<@^8@XwTimes New Roman0,0,128@[@_8A2}Times New Roman0,0,128A;A?<A@8A2Times New Roman0,0,128A=AA<AB8A2_Times New Roman0,0,128A?AC<AD8A2Times New Roman0,0,128AAAE<AF8A2_Times New Roman0,0,128ACAG^A@@
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pB@@BB@@dBTB@@B4.2B*@U#` PP-@First we define the parameters that we will use in the calculation. Notice that Mathcad uses the := to associate a number with a variable name. The same := is used to define functional relationships as shown here for P(V).79B <B
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pB@@BB@@dBaB@@BB@@tB3.41B@@BB@@tB10B@@B4B*@U3^C@`NN-@fNext we write the van der Waals equation. Notice how we write the equation with P as a function of V. 7f9fB:@W,1B?</<B@<<BA0@NormalArial
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pBD@@BCBE@@dBDiBF@@BDBG@@tBF0BH@@BF100BI*@U@7NHTHT-ANotice how we must be sure to specify each variable and its range of values. View the array Vi and examine its contents. Notice how you don't need to type in all these values if you can find a way to calculate them. Once the Vi are defined it is an easy step to define Pi. 7]BJ<]BK8BI0,0,128BL<BM8BI_0,0,128BJBN<BO8BI0,0,128BLBP<BQ8BI_0,0,128BNBR<+BS8BI0,0,128BPBT<BU8BI_0,0,128BRBV<BW8BI0,0,128BTBVBJ9BX<BY:@W,1BZ</B[<B\0@NormalArial
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pBo@@BnBp@@@BoBq@@dBpPBr@@BpiBs@@BoBt@@dBsPBu@@pBsBv@@BuBw@@dBvVBx@@BviBy*@USX`"e``-AWe already saw how easy it is to prepare graphs with Mathcad. Practice this in the space to the left. Fill in the place holders with Pi and Vi. Be careful about which type of subscript you use here. Remember that most of the time you will need only to place the x and y variable names in the place markers for them. Mathcad will generate the scale of the graph for you. However if you want to adjust the formatting of the graph then you can double click on the graph itself. Try this and see what happens. 7Bz<B{8By0,0,128B|<B}8By_0,0,128BzB~<B8By0,0,128B|B<B8By_0,0,128B~BT%PiB@@
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pB@@BB@@dBtimeB@@BB@@tB5B@@BsecB*@U{$ @@-@Units are important for checking equations to be sure a derivation is correct. If units are incompatible then Mathcad will give you an error message.79B<B:@W,1B</B<B0@NormalArial
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pB@@@BB@@@BB@@BB@@dBwrongB@@BB@@dBmassB@@BaccB*@U`#XXX0X0-@Exercise: Calculate the pressure when 200 grams of CO2 are confined to a volume of 2 liters at 400 oC. Include all required units. repeat the exercise using the van der Waals equation. Which equation do you think is better and why?7d5B<5B8B128,0,0B<B8B_128,0,0BB<-B8B128,0,0BB<B8B_128,0,0BB<C8B128,0,0BBB9C<C:@W,1C</C<C0@NormalArial
C@E@U0@80(C*@UK)Xz(!M!M-A9. Integrals: Numerical integrals are easily performed using MATHCAD. To evaluate an integral open the calculus palette and choose the definite integral symbol. Clicking this produces an integral sign with place holders for the upper and lower limits, the function and variable. Fill in this so that you evaluate the integral of exp(-x2) from 0 to 2. When you enter this expression be sure to remember that exp means e . Notice how the power of a power is handled by MATHCAD. 7C<C 8C}0,0,128C
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CA*@U:|8*@*@-A*10. Iterations: Sometimes we want to do a whole of set of steps in a single calculation. In this case you must create a vector in order to get a sequential set of iteration steps. You already examined examples of using an index in previous sections of this set of notes. Here we extend that idea. 7*CB<CC8CA}0,0,128CD<
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CM*@U(}f__-BcHere we define the first two elements of the vector F. F is a vector of a set of numbers such that the next number is the sum of two previous numbers. We would like to generate the remaining values without typing them in one by one. We can use an index and vary the index systematically. The subscript here is created using the [ key.
First define the range for the set of numbers you wish to calculate. Then define the function that creates each element in the vector. Typing F = immediately below the definition of Fi+2 produces the desired vector. Mathcad repeats the calculation until all i are exhausted.7cCN<CO8CM0,0,128CP<CQ8CM_0,0,128CNCR Root EntryaB.dK83mM=Contents9OlePres000`ard 0 \pRKQ
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T1c$ArialdI_D6]TArialdI_D6]TC@@C@XC@@CC*@Uc<p($`$`-A11. Solving equations. In physical chemistry we are often asked to solve equations by finding the roots that satisfy the equation. Here we see some simple examples of solving equations. Mathcad will even let you solve differential equations but that is a story for later.
When solving an equation with Mathcad we must help the software get started. We do this by providing an initial guess for the root in which we are interested. 7C<C8C}0,0,128C<C8C0,0,128CCC9C<C:@W,1C</C<C0@NormalArial
C*@U8D@ @ -@_Here we have a quadratic equation. We will use the root function of Mathcad to find the roots. 7_9_C<_C:@W,1C</_C<_C0@NormalArial
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pC@@CC@@@CC@@dCfC@@pCC@@CxC@@CC@@@CC@@@CC@@dCxC@@C2C@@CC@@tC4C@@CxC@@C3C*@UCsPpp0p0-@Prepare a graph of f(x) as a function of x. You might consider using a range for x of -3 to +10. Can you detect the two roots in this graph? Adjust the range and visually determine the roots.79C<C:@W,1C</C<C0@NormalArial
C*@UE65p5p-A;Now use your guesses to find what Mathcad says the roots are. Here to the right I have typed in 3.5 and 0.5. Replace these with your roots and try several other initial guesses. Get Mathcad's answer by typing ans= to the right of the root expression. ans is the variable name that holds the values of the roots. 7;C<C8C0,0,128C<C8C}0,0,128CC****</eD?:@W,1E?</0E@<0EA0@NormalArial
EB*@U8!"8"8ZZ-Differentiation7EC<ED8EB}0,0,1289EE<EF:@W,1EG</EH<EI0@NormalArial
EJ*@U";"("] ] -@xHighlight the variable x with a blue selection box and choose variable, differentiate from the Symbolic pull down menu.7x9xEK%(%@ -@`Notice the names of the variables and the use of mathematical symbols to do the multiplication. 7`9`F5<`F6:@W,1F7</`F8<`F90@NormalArial
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Acknowledgment: TJZ acknowledges the National Science Foundation for support of the
1997 NSF-UFE Workshop on "Numerical Methods in the Undergraduate Chemistry Curriculum Using the Mathcad Software" and the organizers (Jeff Madura, Andrzej Wierzbicki and Sidney Young, University of South Alabama).7*FL<FM8FK0,0,128FN<FO8FK}0,0,128FLFP<FQ8FK0,0,128FNFPFL9*FR<*FS:@W,1FT</*FU<*FV0@NormalArial
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