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Introduction to FX Equation 4 The Basic Idea FX Equation is DIFFERENT. Most equation editors use a point and click interface that has you searching for the right option. With FX Equation, you just type and it does all the formatting for you. FX Equation’s defining feature is its… e4 Accessing FX Equation FX Equation is normally accessed from within Word. FX Equation adds two toolbar buttons to your Word toolbar. Push the first toolbar button (circled) to load FX Equation. e4 Using FX Equation Just type your equation into the top box on the screen. Your equation will appear formatted in the bottom window. e4 Returning to Word When you have finished creating your equation, click on the green check mark (tick) on the FX Equation toolbar to return to Word. e4 Toolbar Equation Entry FX Equation 4 introduces a new toolbar equation entry system that can help you when you cannot quite remember the right command. e4 Powers FX Equation can automatically recognize and raise most powers. For example, if you type x2 and (3x+2)3 you will get… 2 3 x and (3x + 2) Some powers will not be automatically recognized. Use ^ in these cases. For example type 2^x and e^(2x+1) and get… 2 x and e – 2x + 1 e4 Fractions Fractions are entered using the / key. You will need to wrap numerators and denominators in brackets. 35x/42 35x 42 (3x+7)/(2x-1) 3x + 7 2x – 1 1/(a+1/x) 1 a+1 x e4 Spaces You can change how FX Equation interprets things by adding spaces. FX Equation only automatically raises powers when there is no space… sin2 x 2 sin x sin 2x sin 2x e4 Greek Letters Commonly used Greek letters can be entered by typing the first two letters of their name. Typing the letters in uppercase will produce the uppercase Greek letter. al th la SI DE Check the documentation for a complete list of supported letters. e4 Symbols - 1 FX Equation can produce most mathematical symbols. Some symbols are based on common mathematical conventions. <> * / (followed by a space) or · e4 Symbols - 2 Some symbols are “constructed” from various pieces of the final symbol or rely on similarities between the code and the symbol <= >= =/ =~ ~= ~~ -= +` or lowercase 'o' -> e4 Symbols - 3 Some symbol codes are based on words inf tri ang perp and or element notelement subset notsubset propersubset prop tf e4 Degrees Symbol Degrees symbols are entered so often, we have given them their own key on the keyboard! On most keyboards you will find a backwards facing dash `. It is NOT the single quote key next to the semicolon on most keyboards. The back-dash key is USUALLY to the left on the 1 key on most keyboards and is under the tilde (~). You just type this dash wherever you need a degrees symbol. All Efofex products use this convention. e4 Brackets FX Equation treats all brackets as logically equivalent. {, [, and ( can be used interchangeably. FX Equation treats some brackets as “logical” brackets and will not display them. For example, (x+2)/2 e^(2x2+1) T\(n+1) x+2 2 2x + 1 2 Tn + 1 e e4 Limits, Summation, Products & Integrals lim(x->8) lim x 8 10 sigma(i=1,10) i =1 10 product(i=1,10) i =1 3 int (-2,3) – 2 e4 Definite Integrals FX Equation can show the bounds of a definite integral. Type an ordered pair immediately after a closing square bracket ( ] ) and FX Equation will automatically format it to suit. [x2+4]2,3 2 x + 3 4 2 e4 Subscripts The backslash key ( \ ) is used to indicate subscripts. Think of it as "sliding downhill". Any character immediately following \ will be subscripted. T\n T\(n+1) Tn Tn + 1 Please Note: On some keyboards (for example the Swedish keyboard) the \ key is missing. In those cases it can be replaced by the § key. e4 Means & Complements You can add a straight line ABOVE a character by typing an underline ( _ ) immediately AFTER the character. x_ x You can type an underline immediately after a set of brackets to add a line above all the bracketed information. (x+y)_ x+y e4 Quoted Text You can prevent FX Equation from using its formatting system on a section of text by wrapping it in quotes. This allows you to type “then” without FX Equation turning it into θen! "If" x = 4 "then" x/8 = 1/2 If x = 4 then x = 1 8 2 e4 Dots You can add dots above characters by typing a colon (:) immediately AFTER the character. You can add a double dot above a character by typing two colons. x: x:: . x .. x e4 Recurring Decimals You can easily input recurring decimals using FX Equation's special formatting characters, _ and : 3.1: 3.234_ 6.874_1234 . 3.1 3.234 6.8741234 e4 Scientific Notation Scientific notation can be quickly entered using the "E" notation commonly used in computers and calculators. 3.2E12 12 3.2 10 -4.7E-2 -4.7 10 –2 e4 Square Roots FX Equation uses sr and sqrt to indicate square roots. These two codes are interchangeable. sr3 3 sqrt9x2 2 9x sr(b2-4ac) 2 b – 4ac sr(x2/2) 2 x 2 e4 nth Roots FX Equation can draw any root of an expression using the root code. root9 9 3rootx 3 x nroot(x2+1) n 2 x +1 (3x+1)root2 3x + 1 2 e4 Column Vectors FX Equation will automatically format anything with a comma as a column vector (2,3) (1,2,3,4,5) 2 3 1 2 3 4 5 {x2,2x+1,x3 x 2x + 1 3 x 2 e4 Ordered Pairs If you enter (2,3) into FX Equation, it will format it as a column vector. You probably should not be using FX Equation for ordered pairs, but if you really need to, just wrap the comma in quotes to prevent FX Equation from using it for formatting. (x2","y+1) 2 (x , y + 1) e4 Matrices Enter matrices column by column, separated by spaces [1,2,3 4,5,6 7,8,9 10,11,12 13,14,15] 1 4 7 10 13 2 5 8 11 14 3 6 9 12 15 FX Equation can draw matrices with any number of columns but is limited to 20 rows. e4 Lower Case Vectors FX Equation can automatically recognize most equations that include lower case vectors and will either bold the vectors or add a tilde or line – depending on your preference. r = 3i+2j r = 3i+2j r = 3i+2j r = 3i + 2j r = 3i + 2j ~r = 3~i + 2~j e4 Arrows Left, right and double arrows can be added to any equation components using the -->, <-- and <-> commands. -->m m ABC <--(ABC) <->(x2+2x+1) 2 x + 2x + 1 e4 Mixed Numerals Type a space between the whole number and the fraction and FX Equation will produce a mixed numeral. Best results are obtained when FX Equation is set to shrink non-algebraic fractions – see the Styles tab of the Options. 3 4/5 + 2 2/3 = 6 7/15 7 3 45 + 2 23 = 6 15 e4 Boxes FX Equation can include “fill in the blank” boxes or can place a box around any content 3+box = 7 box(x2)+3x=4 3+ = 7 2 x + 3x = 4 e4 Arcs You can add arcs over any equation components using the arc command arc(ABC) ABC e4 Equation Numbers You can number equations by typing (1), (2), (3)... There must be “white space” around the equation numbers for them to be formatted. 3x + 2y = 4 x – 3y = 5 3x – 9y = 16 = 3 e4 Combinations & Permutations Combinations and permutations are entered using a nCr format 12C4 (n+1)P(n) 12 C4 n+1 Pn e4 Short Division The div command allows you to create short division problems. (32)div(960) 32 960 e4 Vertical Alignment Vertically aligning equals signs is easy – it is all automatic. Just enter one equation per line and FX Equation will do the rest. 3x + 7 = 2x – 4 3x – 2x = -4 – 7 x = -11 e4 Highlighting Lines Individual lines in a system of equations can be highlighted by underlining, italicising or making bold. e4 Units FX Equation can automatically detect standard units and apply different formatting. You can change the standard units that FX Equation detects on the Units tab of the Options. x cm x cm e4 Shortcuts FX Equation can store “shortcuts” that provide quick access to common equations. For example, FX Equation will automatically expand qf to the full quadratic formula. You can define your own shortcuts in the Shortcuts tab of the FX Equation options. e4 Email Tutorials Efofex provides comprehensive training for FX Draw 3 available as convenient email tutorials. Register at www.efofex.com/emailtutes.php. The system will send an email a day for a few weeks. Email tutorials are available for all Efofex products. e4