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? MathCAD 2.5 ONLINE HELP ?????? TO LEAVE HELP, PRESS [Esc] ? ? ARRAYS ? EQUATIONS ? MOVING ? ? A ? Matrices ? E ? Editing ? M ? Move Cursor ? ? A ? Vectors ? G ? Disabling ? M ? Search/Replace ? ? O ? Operators ? N ? Formatting ? ? ? B ? Functions ? S ? Solving ? NAMES ? ? ? ? G ? Subscripts ? ? CONFIGURATION ? FUNCTIONS ? G ? Built-in Variables ? ? C ? Command Files ? F ? Built-in ? X ? Defining Variables ? ? W ? Display Options ? B ? FFT ? G ? Greek Letters ? ? C ? DOS Subshell ? L ? Statistical ? ? ? W ? Memory ? X ? User-defined ? OPERATORS ? ? ? F ? Conditional ? O ? Fundamental ? ? DATA ? ? J ? Deriv/Integrals ? ? D ? Disk I/O ? GRAPHICS ? J ? Sums/Products ? ? I ? Input Table ? P ? Graphs (2D) ? V ? Vectorize ? ? H ? Sorting ? P ? Surface Plots ? S ? Boolean ? ? ? Q ? Format 2D Plots ? ? ? DOCUMENT MANAGEMENT ? R ? Format 3D Plots ? TEXT ? ? C ? Pagebreaks ? K ? Sketch Import ? T ? Editing ? ? C ? Printing ? ? ? ? C ? Save, Load ? ITERATION ? UNITS ? ? C ? Split Screens ? I ? Range Variable ? U ? Defining ? ? W ? Calculate ? I ? Seeded ? U ? Conversions ? `???? FOR HELP ON A TOPIC, PRESS CORRESPONDING LETTER ????? ????? CREATING A MATRIX ?????????????? ADDING OR DELETING ROWS/COLUMNS ???????? Press [Alt]M, enter dimensions DELETE: Put cursor on row or column and fill in placeholders to be deleted. Press [Alt]M ? ? ? ??Ŀ ? ADD ROW: Put cursor just above where new A :=?????? row will be, then press [Alt]M ???? ? ? ADD COL: Put cursor left of where new col Or, define explicitly: will be, then press [Alt]M i := 0..2 -type i:0;2 ?????????????? ARRAY ORIGIN ??????????????ͻ ? ? j := 0..1 ? To offset indices of an array, press ? ? [Esc] set ORIGIN ? A := i+j -type A[(i,j):i+j ? EXAMPLE: ? i,j ? If ORIGIN=0, top left element is A ? ? ? (use "[" for ? 0,0 ? ?0 1? subscripts) ? but... ? A = ?1 2? ? ? ?2 3? ? if ORIGIN=1, top left element is A ? ? ? ? 1,1 ? ??????????????????????????????????????????ͼ MAIN HELP MENU [F1] More Info...Ch 10 TO LEAVE HELP [Esc] ??????? VECTOR FUNCTIONS ??????????????????????? MATRIX FUNCTIONS ????????????? ? ? ? min(V)=1 ? ? ? rows(M)=3 ?1? max(V)=8 ? ?7 2 2? cols(M)=3 ?8? length(V)=5 Number of ? M = ?6 5 4? min(M)=1 V = ?4? elements in V ? ?3 1 8? max(M)=8 ?6? last(V)=4 Index of last ? ? ? tr(M)=20 Sum of elements ?2? element in V ? on the diagonal ? ? V =1 Because ORIGIN ? M = 7 Because ORIGIN 0 is set to 0 ? 0,0 is set to 0 ? ?????? JOINING MATRICES ??????????????????????? FOURIER TRANSFORMS ???????????? ? m m-1 ? ? ? ? ? V & W have 2 elements, U has 1+2 ?7 2 2? ?9? ? ? M = ?6 5 4? V = ?9? ? U=fft(V) ? ? ? ? ? ? ? Use when V is real ? ? ? V=ifft(U)? ?7 2 2 9? ? ? augment(M,V) = ?6 5 4 9? ? ? ? ? ? W=cfft(V) ? ? ? Use when V is ? V=icfft(W)? complex ? ? MAIN HELP MENU [F1] More Info...Ch 10,13 TO LEAVE HELP [Esc] ???????? DOCUMENT MANAGEMENT ?????????????????? PAGEBREAKS ???????????????????? Load document [F5] ? Every n lines [Esc] pagelength n Save document [F6] ? Insert [Esc] pagebreak Append document [Esc] append ? Delete [F3] with cursor placed Delete document use DOS delete ? on pgbreak at column 0 Quit MathCAD [Ctrl]Q ? To prevent To DOS w/o quit [Esc] dos ? regions from [Esc] breakpage Save configuration [Esc] config ? being split Split/unsplit screen [F7],[Ctrl][F7] ? by pagebreak Jump between screens [F8] ? ? ?????????? COMMAND FILES ????????????????????? PRINTING ??????????????????????? ? Text files containing valid ? 1. Set left margin by typing [Esc] margin MathCAD commands can be ? (default is 0) executed as macros by typing ? 2. Select printer by typing [Esc] select ? 3. Press [Ctrl]O [Esc] exec filename.mcc ? 4. Select print area or press [Return] ? to print the entire document MCAD.MCC is a command file ? 5. Select output device. Press [Return] containing your most recently ? for defaults: PRN for printers saved configuration. ? COM1 for plotters ? or specify a filename to write to. MAIN HELP MENU [F1] More Info...Ch 3,6 TO LEAVE HELP [Esc] ? STRUCTURED DATA FILES ????????????????? STRUCTURED DATA FILES ??????????????? ? Rectangular array of numbers ? Non-rectangular array of numbers stored as ASCII text ? ? i := 0 ..N Range variable M := READPRN(f) Data in F.PRN is ? put into M array ? V := READ(f) Data in F.DAT is ? i put into V vector WRITEPRN(f) := M Data from M array ? is written to the ? WRITE(f) := V Data from V vector file F.PRN ? i is written to the ? file F.DAT APPENDPRN(f) := M Data from M array ? added to existing ? APPEND(f) := V Data from V added data in F.PRN ? i to existing F.DAT ? ? DATA IN DIFFERENT DISK/DIRECTORY ?????? FORMATTING YOUR OUTPUT ?????????????? ? Ex: Read the file A:\MA\BUH.AY ? 3.1 -> 3.14 [Esc] set prnprecision ? Press [Esc] filename f A:\MA\BUH.AY ? 1 2 -> 1 2 [Esc] set prncolwidth and use "f" as shown above ? ? MAIN HELP MENU [F1] More Info...Ch 15 TO LEAVE HELP [Esc] COPY, CUT OR PASTE ONE OR MORE REGIONS ? COPY, CUT, OR PASTE PART OF AN EQN ? A region can be an equation, plot, ? TO DELETE AN EXPRESSION, move cursor imported drawing, or text. ? to the top-level operator of the ? expression and press [Ctrl][F3] TO DELETE A REGION, move the cursor ? TO MOVE AN EXPRESSION, delete it, into the region and press [F3]. ? move the cursor to an empty place- TO MOVE A REGION, delete it, move the ? holder (?) and press [Ctrl][F4] cursor to the new location, press [F4]. ? TO COPY AN EXPRESSION, follow the TO COPY A REGION, follow instructions ? instructions for moving but use for moving but use [F2], not [F3]. ? [Ctrl][F2] instead of [Ctrl][F3] ? TO DELETE, MOVE, OR COPY MULTIPLE REGIONS ? If you don't know the top-level 1. Mark the first region by moving the ? operator, experiment with [Ctrl] cursor into it and pressing [Ctrl]Y. ? [F3]. Remember that an immediate 2. Mark the last region with [Ctrl]Y. ? [Ctrl][F4] will undo whatever you 3. Press [F2] to cut, [F3] to copy, or ? just did with [Ctrl][F3]. [F4] to paste. ? ? TO CREATE A MATCHED PAIR OF TO DELETE A CHARACTER, place the cursor ? PARENTHESES with an empty on the character and press [Del]. ? placeholder, use the apostrophe. TO INSERT A CHARACTER, place cursor ahead ? of where character should be and type ? (?) ? Press ' it in. ? MAIN HELP MENU [F1] More Info...Ch 5 TO LEAVE HELP [Esc] ?????????????????????????? BUILT-IN MATH FUNCTIONS ???????????????????????????? NOTE: All angles are expressed in RADIANS. z,w may be COMPLEX; x,y must be REAL; i,j,k,m, and n must be INTEGER. ???? TRIGONOMETRIC ????????? COMPLEX FUNCTIONS ??????? EXPONENTIAL/LOG ???????? sin(z) asin(z) Re(z) = real part exp(z) = e raised to x cos(z) acos(z) Im(z) = imag part ln(z) = natural log tan(z) atan(z) arg(z) = ? z=exp(i?) log(z) = base 10 log ???? HYPERBOLIC ???????????? BESSEL ???????????? MISC (integer arguments) ????? sinh(z) asinh(z) J0(x) Y0(x) ?(m,n) = 1 if m=n and 0 if m?n cosh(z) acosh(z) J1(x) Y1(x) ?(i,j,k) = antisymmetric tensor tanh(z) atanh(z) Jn(n,x) Yn(n,x) of rank three ???? MISC (real arguments) ???????????????? CONDITIONAL FUNCTIONS ????????????? ?(x) = 1 if x ? 0, 0 otherwise ? ceil(x) = smallest integer ? x ? z if cond is true, floor(x) = greatest integer ? x if(cond,z,w) = ? mod(x,y) = remainder of x/y ? w if cond is false with sign of y ? angle(x,y) = positive angle from until(x,z) = z halts iteration x axis to (x,y) when x < 0 MAIN HELP MENU [F1] More Info...Ch 13 TO LEAVE HELP [Esc] ?? GREEK LETTERS ???????????? PRIME ?????????????? DISABLING EQUATIONS ???????? ???????????????????????ͻ ??????????????ͻ ???????????????????????????????????ͻ ? ? [Alt]A ? [Alt]N ? ? ? ? To prevent unecessary evaluation ? ? ? [Alt]B ? [Alt]O ? ? Type the [`] ? ? of an equation (for example, when ? ? ? [Alt]D ? [Alt]P ? ? (backquote) ? ? it is for documentation only) ? ? ? [Alt]E ? [Alt]Q ? ? not the ['] ? ? ? ? ? [Alt]F ? [Alt]R ? ? (apostrophe) ? ? 1. Enter manual mode by typing ? ? ? [Alt]G ? [Alt]S ? ? ? ? [Esc] manual ? ? ? [Alt]H ? [Alt]T ? ??????????????ͼ ? ? ? ? [Alt]I ? [Alt]U ? ? 2. Type the equation as ? ? ? [Alt]L ? [Alt]W ? ? you ordinarily would. ? ???????????????????????ͼ ? ? ? 3. With cursor in eq, press ? ? [Esc]eq ? ???????????????????????????????????ͼ ?????? BUILT-IN VARIABLES ???????????????????????? LITERAL SUBSCRIPTS ????????? ????????????????????????????ͻ ??????????????????????????????????ͻ ? 307 ? ? Type V.GC:5 and ? ? ? = 10 [Alt]i ? ? V := 5 move cursor out ? ? ? = 3.14159... [Alt]p ? ? GC of equation. The ? ? e = 2.71828... ? ? GC will drop down. ? ? % = .01 ? ? ? ????????????????????????????ͼ ??????????????????????????????????ͼ MAIN HELP MENU [F1] More Info...Ch 7,8 TO LEAVE HELP [Esc] ????????????????????????????? SORTING A MATRIX ???????????????????????????????? ? ? ? ? ? ? ?0 1 5? ?6 2 0? ?5 0 1? M = ?3 7 1? csort(M,2) = ?3 7 1? rsort(M,1) = ?1 3 7?Ŀ ?6 2 0? ?0 1 5? ?0 6 2? ? ? ? ? ^? ? ? ? ? ? Rows are swapped such that??? Columns are swapped such ??? column 2 is in ascending that row 1 is in ascending order order ????????????????????????????? SORTING A VECTOR ???????????????????????????????? ? ? ? ? ? ? ?1? ?1? ?8? ?6? ?5? ?5? V = ?9? sort(V) = ?6? reverse(V) = ?9? ?5? ?8? ?6? ?8? ?9? ?1? ? ? ? ? ? ? Returns vector sorted Returns vector with in ascending order elements in reverse order MAIN HELP MENU [F1] More Info...Ch 13 TO LEAVE HELP [Esc] ??? DEFINING A RANGE VARIABLE ????????????????? USING A RANGE VARIABLE ???????? ???????????? First value ? ? ? Type t= sinh(t)= ? ??????????Next value ? ? ? ? ? (optional, default ? ___t___ _sinh(t)_ ? ? is 1 + first value) ? ?__1____? ?__1.175__? ? ? ? ?__1.1__? ?__1.336__? ? ? ????Last value ? ?__1.2__? ?__1.509__? ? ?__1.3__? ?__1.698__? t := 1,1.1 ..1.3 type t:1,1.1;1.3 ? ? ??? SEEDED ITERATION ????????????????????????? ENTERING A TABLE OF VALUES ????? ? Example: Fibonacci Sequence ? To enter data values into an array ? n ? 2 ..4 ? ? ? i := 0 ..3 ?1? ? x ? 1 x ? 1 ?1? ? s Type 0 1 x = ?2? ? ___i___ s[i:11,29,15,56 ?3? ? ?__11___? ^ ^ ^ x ? x + x ?5? ? ?__29___? ????????Ŀ n n-1 n-2 ? ? ? ?__15___? separate data ? ? ?__56___? values with commas ? MAIN HELP MENU [F1] More Info...Ch 11 TO LEAVE HELP [Esc] ? INTEGRATION ?????????????????????????????????? DIFFERENTIATION ?????????????? Press & and fill in Press ? and fill in the placeholders ????? the placeholders. ? ? ????>1 ???integrand ? Value of TOL ? x := 3?Point at which deriv ? ? ? controls the ? will be evaluated. ? ? sin(??x) dx = ? accuracy of ? ? ? ^ ? int & deriv. ? d 4 ????>0 ? ? ? ?? x = 108 ? variable of ? To change it, ? dx ^ limits of integration ? type ? ^ ???function to be integration ? ? ? differentiated ? [Esc] set TOL ? ? ? ? differentiation variable ????? ? SUMMATION ???????????????????????????????????? ITERATED PRODUCT ????????????? Press $ and fill in ? Press # and fill in the placeholders ? the placeholders ? ? x ? ? x i ^i ? i ^i range ^ ? ? range ^ ? term to be variable?? summand ? variable?? ??? multiplied ? MAIN HELP MENU [F1] More Info... Ch 12 TO LEAVE HELP [Esc] ????????????????? IMPORTING DRAWINGS FROM CAD SOFTWARE ???????????????????????? ? 1. Create an HPGL output file ? 3. From MathCAD, press [Alt]5 with your CAD software ? to create a sketch region. ? 2. From DOS, type ? 4. Putin the placeholder. MCSTRANS . ? to create a MathCAD readable ? 5. For files on other disks/directories, file called .MCS ? use [Esc]filename. (For Help, press [F1]D) ? ????????????????????????? FORMATTING A DRAWING ???????????????????????????????? To format a single drawing: ? move cursor into sketch region and press "f" ? To format all ? subsequent drawings: ?????? ? ? Size=15,30 ???ı????? Size in rows,columns ? Type ? Magnification=1,1 ????? Scale y,x dimensions ? ? Center=.5,.25 ??ı????? Center is ? way on y ? [Esc] sketchformat ? Box=y ?????????ı??Ŀ and ? way on x ? ? Global Default ?ı?Ŀ?? Set to n to hide frame ? A menu similar to ? Revert ??????ıĿ??? Use default values ? that on the left ? Done ??????????ı????? Cancel all changes ? will appear. ??????????? No further changes ? ? MAIN HELP MENU [F1] More Info...Ch 17 TO LEAVE HELP [Esc] ???????????????????????????? STATISTICAL FUNCTIONS ???????????????????????????? ??????????????????????????????????????????????????????????????????????????????ͻ ? UPPERCASE = VECTORS ? Y,Z complex ? W,X real ? F integer ? ? Lowercase = scalars ? z complex ? x real ? i integer ? ??????????????????????????????????????????????????????????????????????????????ͼ SAMPLE STATISTICS ?????????? LINEAR REGRESSION ???? SPECIAL FUNCTIONS ???????? mean(Z) var(Z) slope(Z,Y) cnorm(x) Cum normal dist stdev(Z) corr(Y,Z) intercept(Z,Y) erf(x) Error function ?(z) Gamma function INTERPOLATION ?????????????? HISTOGRAMS ??????????? RANDOM NUMBERS ??????????? ??? ??? Linear -> linterp(Z,Y,z) ? F = hist(X,W) ? rnd(x)=uniform distribution ? ????????? ? between 0 and x Cubic Spline Example ? Vector of intervals ? ? requires W >W ? To start a different Choose one: ? i i-1 ? sequence, change seed by ? ? ? ?cspline(Z,Y) cubic ends ? F = # of "X" values ? [Esc] randomize i VS=?lspline(Z,Y) linear " ? i falling in the ? ? ?pspline(Z,Y) parab " ? interval ? To restart the same ? ? ? ? sequence, use [Esc] ????????????Ŀ ? W ? X < W ? randomize but do not f(z)=interp(VS,Z,Y,z) ? i i-1 ? change the seed value. ??? ??? MAIN HELP MENU [F1] More Info...Ch 13 TO LEAVE HELP [Esc] ? MOVING TO A STRING ? ^ ?? MOVING LARGE DISTANCES ?? ? ? ? ? ? ? Find a string ? [Ctrl][PgUp] -19 ? move cursor ?r rows and ? ? ? ? ? ?c col's from current loc ? ? [Ctrl][F5] ? ? ? [Esc] move ?r ?c ? ? ? ? ? go to row r and column c ? ? Find, then replace ? ? ? [Esc] goto r c ? ? ? ? ? beginning or end of doc. ? ? [Ctrl][F6] ? [PgUp] ? -10 ? [Ctrl][Home] [Ctrl][End] ? ? ? ? ? ? ??????? ? ????????? [^] [Ctrl]E??????[Ctrl][<]??????[<] [>]?????[Ctrl][>]??????????[Ctrl]G???> -80 -10 [ ] +10 +80 ?? FAST SCROLLING ?? ? ? ? ? ?? SHORTCUTS IN EQUATIONS ?? ? To avoid needless ? [PgDn] ? +10 ? ? ? recalc while scrolling,? ? ? [Tab] next operator or ? ? ? ? ? ? [Shift][Tab] previous oper or ? ? ? [Esc] manual ? ? ? [Home],[End] 1st/last oper or ? ? ? ? [Ctrl][PgDn] +19 ? ? ? Then [F9] to recalc ? ? ????????? ??????? MAIN HELP MENU [F1] More Info...Ch 3 TO LEAVE HELP [Esc] ?????? GLOBAL FORMAT ???????????????????????? LOCAL FORMAT ???????????????????? Type [Esc]format to see the menu ? Move cursor into displayed result and below. Use ? and ? followed by ? type "f" to see a subset of the menu below. [Return] to change an item. All ? Use ? and ? followed by [Return] to change displayed results are affected. ? an item. Only this equation is affected. ? Show 3 decimal ??????Ŀ ??????? ?? d=decimal,h=hex,o=octal places ? ? Radix = d ? ???>? Displayed Precision=3 ? Show z in exponential ?-1=i or j ????????????Ŀ ? Exponential Threshold=3?? form if z?1000 or z?.001 -15 ?>? Imaginary Symbol=i ? Show z as 0 if z<10 ???>? Zero Tolerance=15 ? ??? Show z as real if ? Complex Tolerance=2 ?? ?Re(z)?Im(z)? < .01 Restore to defaults ?????>? Overall Default ? Show z as imag if ????>? Revert ? ?Im(z)?Re(z)? < .01 ? ? Done ??Ŀ Ignore all changes ??? ??????? ???? Return to document, implement changes ?????????????????????????????? ALLOWED VALUES ????????????????????????????????? ??????????????????????????????????????????????????????????????ͻ ? Displayed Precision ? 15 Zero Tolerance ? 307 ? ? Exponential Threshold ? 15 Complex Tolerance ? 307 ? ??????????????????????????????????????????????????????????????ͼ MAIN HELP MENU [F1] More Info...Ch 8 TO LEAVE HELP [Esc] ????????????????????????????? OPERATORS ??????????????????????????????????????? Some operators share the same keystroke (for example | means magnitude or determinant). MathCAD applies whichever operator makes sense in context. ? BINARY SCALAR OPERATORS ?????????????????????? UNARY SCALAR OPERATORS ??????? ^ Exponentiation \ Square root / Division ! Factorial * Multiplication | Magnitude - Subtraction " Complex conjugate + Addition [Ctrl][Enter] Addition w/ linebreak ? BINARY ARRAY OPERATORS ??????????????????????? UNARY ARRAY OPERATORS ???????? * Vector dot product | Vector magnitude * Matrix multiplication | Matrix determinant [Alt]* Vector cross product [Alt]! Transpose [Alt]^ Extracts column from array [Alt]$ Sum of vector elements ^ Matrix inverse when exponent is -1 [Alt]- Vectorize operator ^ Integer powers of a matrix Press [F1]V for more + Vector/matrix addition help on this operator - Vector/matrix subtraction MAIN HELP MENU: [F1] More Info...Ch 12 TO LEAVE HELP: [Esc] ????????????? GRAPHS ???????????????????????????? SURFACE PLOTS ??????????????? ??? TO CREATE: Press @ and fill ? TO CREATE: Press [Alt]2 and put ?'s as shown below ? name of matrix in ? ? ???????????????Ŀ ??? use comma for ? ? ? ? multiple traces ? ? /??/??/??/ ? ? ?????????????Ŀ ? ? /??/??/??/ ? ?+ ?Ŀ ++ ڿ ? ? ?/??/??/??/ ? f(x),z ? ??+?+ڿ+??ij ? ????????????????? ??> i ??? +????? ? ? ? ? 0??????????????? ??????????????????????????????????????? ? 0 x,i 10 ? ? ??? ? TO DELETE: Place cursor in plot, ? ? ??range variables ? then press [F3] ? ? ? ? ? axis limits (optional, ? TO MOVE: Delete as described above, ? MCAD will autoscale if ? move cursor to new location and ? these are left blank) ? press [F4] ? ? ??????? subscript required when ? TO FORMAT: For help on 2D plots, plotting an array ? press [F1]Q. For help on 3D ? plot, press [F1]R ??? MAIN HELP MENU [F1] More Info...Ch 16,17 TO LEAVE HELP [Esc] ?? TO FORMAT A SINGLE PLOT ????????????????? TO FORMAT ALL SUBSEQUENT PLOTS ??? Move cursor into plot region and ? Type [Esc] plotformat to see menu, press f to see menu below. Then ? Then use or followed by [Return] use or followed by [Return] ? to change settings. to change settings. ? ??????????????????????????????????????????????????????????????????????????????ͻ ? 15 rows high ? ? 30 cols wide ????? ??? Gridlines: 4 subdiv on Y axis ? ? ????????????>? Size=15,30 ? ? 1 subdiv on X axis ? ? "l" connects pts ??>? Trace Types=l ? ? (On log axis, only 1, 2 or ? ? with lines. See ??>? Log Cycles=0,3 ? ? 9 subdivisions are allowed) ? ? table below for ? ? Subdivisions=4,1??? ? ? additional types ? ? Global Default ????????? Use global default ? ? ? ? Revert ????????? Undo all changes ? ? Y axis linear ??? ? Done ????????? Return to document and ? ? X axis logarithmic ????? implement all changes ? ? w/ 3 cycles ? ??????????????????????????????????????????????????????????????????????????????ͼ ADDITIONAL TRACE TYPES ?????????????????????? MULTIPLE TRACES ???????????????? ???????????????????????????????????????Ŀ ??????Ŀ ? d ? ? s=step ? p + ? P ?+?+? ? Trace Types=sp ?+ڿ+ +? ? x x ? e=error bar ? v ? V ? ? ? ? X drawn as steps X ,Y ??ٳڿڳ ? X x?x?x ? b=bar chart ? o ? ? O ????? ? Y drawn as + i i??+???ٳ ????????????????????????????????????????? ???????? MAIN HELP MENU [F1] More Info...Ch 16 TO LEAVE HELP [Esc] ?????? TO FORMAT A SINGLE PLOT ??????????? TO FORMAT ALL SUBSEQUENT SURFACES ?? ? Move cursor into the plot region and ? Press [Esc] surfaceformat to see press f to see the menu below. Then ? a menu similar to that shown below. use ? or ? followed by [Return] to ? Use ? or ? followed by [Return] to change settings. ? change an item. ? ? ??????????????????????????????????????????????????????????????????????????????ͻ ? ? ? 15 rows high ?Ŀ Rotation=0 views along ? ? 30 cols wide ? ?????? columns ? ? ???>? Size=15,30 ? Rotation=90 views along ? ? Tilt=90 views surface ? ? Rotation=10 ??? rows ? ? from above ????>? Tilt=35 ? ? ? Tilt=0 views surface ??>? Vertical Scale=3 ? ? ? edge on ? ? Global Default ?? Use global default ? ? ? ? Revert ?? Undo all changes ? ? Reducing this flattens ? ? Done ?? Return to document ? ? variations in plot ???? ?????? and implement changes ? ? ? ??????????????????????????????????????????????????????????????????????????????ͼ MAIN HELP MENU [F1] More Info...See Ch 17 TO LEAVE HELP [Esc] ?????????? SYSTEMS OF EQUATIONS ?????????????????? ROOTS OF AN EQUATION ??????? ???????????????????????????????????????????????????????????????????????????????? ? To find x satisfying ?????? ? ? ?? Guess values ? tan(x) = x ? x := 1 y := 2?ı? ? ? ? Keyword to mark the ? ???????? ? Given ???????????ı? beginning of a solve ? ? ? ? ? block ? ? x := 12.15 ? Guess val ? ? x ? 2 <Ŀ ? ? ? ? ? ? ? Constraints x,y ? ? root(tan(x)-x,x) = -0.139 ? ? x-y ? 2???????ı? must satisfy ? ? ???????? ? ? ? ? ? (Use [Alt]= to ? ???????? ? x?y ? 6? ? type the ?) ? ? ? ? ? ? ? ? ? ? Equation whose ? Solve for x ? ?3.646? ? ?x? ? root is sought ? Find(x,y) =? ?<ı? ? ? Solution vector ? ? ^ ^ ?1.646? ? ?y? ? ? COMPARISON OPERATORS ? ? ? ? ? ? ? ? ? ? ? ? ? ??????????????ı? Variables to be ? ? ? [Alt]= ? [Alt]) ? ? ? solved for ? ? ? [Alt]# ? [Alt]( ? ?????? ? ? ? ? ??????? ???????????????????????????????????????????????????????????????????????????????? MAIN HELP MENU [F1] More Info...Ch 14 TO LEAVE HELP [Esc] ???????? TEXT REGIONS ?????????????????????????? TEXT BANDS ??????????????????? ? USE TEXT REGIONS for small amounts of ? USE TEXT BANDS for significant amounts text having varying widths. ? of text stretching across the page. TO CREATE, press ". Type text between ? TO CREATE, press [Ctrl]T and type text pair of double-quotes. ? between pair of double-quotes. TO SET WIDTH, place cursor in region ? TO SET WIDTH for all text bands in the and type [Esc] width ? document, type [Esc] linelength ? ???? MOVING IN TEXT ?????????????????????????? EDITING TEXT ??????????????????? ? LEAVE a text [>][<][^][ ] ? TO MARK A TEXT BLOCK: Press [Ctrl]X, then band or region ? move to end of text block, [Ctrl]X again. Move by WORD [Ctrl]W or [Tab] ? TO COPY OR CUT: First mark the text, then Move by LINE [Ctrl]L ? press [Ctrl][F2] or [Ctrl][F3]. Move by SENTENCE [Ctrl]S ? TO COPY, CUT OR PASTE A TEXT BAND/REGION: Move by PARAGRAPH [Ctrl]P ? Put cursor in text band/region. Press Move by CHARACTER [>][<][^][ ] ? [F2],[F3], or [F4] to copy, cut, or paste Move FORWARD [Ctrl]F ? TO PASTE TEXT INTO A TEXT BAND/REGION: Move BACKWARD [Ctrl]B ? Move cursor to where text is to be placed ? and press [Ctrl][F4]. Ex: Move back 1 word, down 1 line ? TO CENTER TEXT: Press [Ctrl]C [Ctrl]B [Ctrl]W [Ctrl]F [Ctrl]L ? TO REWRAP TEXT: Press [Ctrl]N ? TO START A NEW LINE: Press [Return] MAIN HELP MENU [F1] More Info...Ch 4 TO LEAVE HELP [Esc] ????????? DIMENSIONS ???????????????????? DEFINING UNITS ?????????????????????? ? ? The built in dimensions are: ? g := 1M ? ? cm := 1L???? Define M = mass ? s := 1T ? fundamental units L = length ? ? T = time ? ? Q = charge ? m := 100?cm ? ? kg := 1000?g ???? Define To change their names, type ? -2 ? derived units ? N := kg?m?s ? [Esc] dimension ? ? ???????????????????????????? UNIT CONVERSION ?????????????????????????????????? Place N here and -2 -2 press [Enter] F := 6300?g?cm?s F = 6300?mass?length?time ?????????? -2 ? N := kg?m?s ? MathCAD converts from CGS to MKS lbf := 4.45?N F = .063?N?? Replace N by lbf ? ? MathCAD converts to pounds force F = .014?lbf MAIN HELP MENU [F1] More Info...Ch 9 TO LEAVE HELP [Esc] ?????????????????????????? VECTORIZE OPERATOR ????????????????????????????????? Use the "vec" operator, [Alt]-, to apply a function or operator element by element to an array. Examples of its use are shown below: ??Example 1??????????????????????ͻ ??Example 2???????????????????????????ͻ ? ? ? ? ? ? ? ? 0 ? ? ? The dot product of x and x is ... ? ? x := ?.25?? ? ? ? ? ?.5?? ? ? ? x?x = 3.084 ? ? ? ? ? ? ? ? ? ? ? ? but the term by term product is ... ? ? Press [Alt]- ?????> ? 0? ? ? ? ? ? ? and type sin(x) = ?.707? ? ? ??> ? 0? Press [Alt]- and ? ? sin(x) in ? ? 1? ? ? x?x = ?0.617? type (x*x) in ? ? ? ? ? ? ? ?2.467? ? ?????????????????????????????????ͼ ? ? ? ? ??????????????????????????????????????ͼ ??Example 3????????????????????????????????????????????ͻ ? ????> ? ? ? ? Press [Alt]- and type i?x ? 1? ? ? (e^(1i*x)) in ? e = ?.707 + .707i? ? ? ? i? ? ? ? ? ? ???????????????????????????????????????????????????????ͼ MAIN HELP MENU [F1] More Info...Ch 10 TO LEAVE HELP [Esc] ?? STARTUP OPTIONS ??????????????????????? SCREEN UPDATE COMMANDS ????????????? /M Start in MathCAD in manual ? mode ? [F9] Update screen ? /Lnnnn Use nnnn KB of LIM memory ? [Esc] process Update entire document ? /Rname Execute the commands found ? [Esc] auto Update eqns as required in NAME.MCC upon startup. ? Press [F1]C for more help ? [Esc] sep Separate overlapping ? regions (see Ch 3) /Fnn Set foreground color to nn ? /Bmm Set background color to mm ? [Ctrl]R Redraw screen ? ?? DISPLAY OPTIONS ??????????????????????? MISC COMMANDS ?????????????????????? ? To override MCAD's choice of display ? [Esc] memory Check available adaptor, use one of the following: ? memory (see Ch 6) ? /V VGA /EH EGA w/256K card ? [F10] Show MathCAD's /E EGA at highest res ? pull-down menu /C CGA /EM EGA, monochrome ? (see Ch 1) /T Toshiba monitor ? /A AT&T 6300 /EC EGA 640x200 res ? /H Hercules /VM VGA mono ? MAIN HELP MENU [F1] More Info...Appendix A, Ch 7 TO LEAVE HELP [Esc] ?? LOCAL DEFINITIONS ??????????????????? GLOBAL DEFINITIONS ??????????????????? u := 6 Type u:6 ^ x = 66 Evaluated even though ???????Ŀ definition appears below x := 11?u Since u is defined earlier, x can u ? 6 Type u~6 x = 66 be evaluated ^ ^ ??????Ŀ Definition for u must still ??????Type x= to evaluate x ? 11?u precede its use ?????????????????????????? USER DEFINED FUNCTIONS ????????????????????????????? ??u must be defined Example: S(V,n) returns nth partial sum of the sequence in V f(?) := 11?u?cos(?) f(0) = 66 ^ i := 0 ..10 V := i ? ? in arg list need not be defined i g(w,?) := 11?w?cos(?) g(6,0) = 66 S(V,n) := ?(i ? n)?V ^ i i ?? Neither ? nor w need be defined S(V,3) = 6 MAIN HELP MENU [F1] More Info...Ch 1,7 TO LEAVE HELP [Esc]