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Inroductory Examples

Here you will find a selection of examples introducing some of the key features of DreamCalc. For information concerning any specific function, refer to the Function Index page.

Most examples in this User Guide are given using the prefix algebraic input order, and you should compensate as required to suit the input order of your choice. The financial sections are an exception, and generally give examples using Reverse Polish Notation (RPN).

Algebraic Examples Example: Determine the result of sin(-35) using degrees. First ensure the calculator is in the degrees mode by clicking Modes->Trigonometry->Degrees from the main menu. If you are using Prefix Algebraic (MAL) input mode, key in the following: [sin] [+/(-)] (acts as (-), see note) 35 [ENTER] Displays: -0.5735764363510461 If using Postfix Algebraic (CAL) input mode, key in the following: 35 [+/(-)] (toggle sign) [sin] [ENTER] (optional) Displays: -0.5735764363510461

Reverse Polish Example This example applies only if DreamCalc is set to use RPN input order. Example: Determine (3 + 5) × (2 + 4). 3 [ENTER] 5 [+] (sum 3 + 5) [ENTER] 2 [ENTER] 4 [+] (sum 2 + 4) [×] (multiplies the two sums) Answer: 48 If you wish to learn more about RPN, refer to Input Order Notation.

When your press [ENTER] you will see the calculation added automatically to the Paper Roll. Simply press F11 to toggle the Paper Roll at any time.

Note. In prefix algebraic input mode, the [+/(-)] key acts as a minus sign input, rather than a sign toggle. Press it where you would use (-) on your hand-held calculator.

Storing & Copying Values

Simply press CTRL-C to copy the screen value into the clipboard at any time, or CTRL-V to paste a value from the clipboard.

To store a value in DreamCalc memory, use [STO] and [RCL] with keys marked MEM, A-F and 0-9.

Example 3: Store and Recall 5.76.

5.76
[STO] [MEM] (value now stored)

[AC] (clear screen)

[RCL] [MEM] (recalls mem)
Displays: 5.76

You can also view and edit values held in memory directly from the Memory Register tab of the Paper Roll window.

Conversions & Constants

Conversions are performed by selecting one from the Insert main menu. All conversions operate in a postfix manner, meaning that you input the conversion after the value, irrespective of what input mode you are using.

Example: What is 45 degree Farenheit expressed as degrees Celsius?

45
[Farenheit-Celsius] (use Insert->Temperature menu)
Displays: 7.222...

Constants can also be inserted using the Insert main menu. DreamCalc supports over 630 constants, and the range of constants available from Insert menu is configurable from the "Miscellaneous" page of the Options Window.

Alternatively, if the constant you want is a commonly used scientific one, you will find it on the numeric keypad.

Example: Proton Mass

Key in:

[CONST] [1] (mp)
Displays: 1.6726231E-27 (Proton Mass kg)

Complex Number Example

DreamCalc handles complex numbers naturally. Use the semi-colon key [;] to separate between real and imaginary components when entering complex values.

Example:

5 [;] 3
[+]
23 [;] -2 (always use [+/(-)] for negative imaginary input)
[ENTER]
Displays: 28 + 1i

There is no need to explicitly use parentheses with complex values as they are "atomic", meaning that DreamCalc treats them as a single entity. DreamCalc will automatically show braces around complex values when they displayed in the calculator paper roll and numeric display.

All mathematical functions support complex numbers where applicable. Where real solutions exist, these will be returned in preference to a complex result. For example, 3 √ -216, which is equivalent to -216^1/3, will yield a real result of -6. You should also bear in mind that where complex solutions exist, the result returned by DreamCalc maybe one of many possible solutions.

In addition, DreamCalc supports copying and pasting of complex numbers via the clipboard and can store complex values in memory registers.

Example: Copy & paste a complex value.

As a demonstration, select and copy the following string into your clipboard with CTRL-C.

33 - 3i

Now in DreamCalc, press CTRL-V and the complex value should appear on screen. When pasting complex values, ensure that the imaginary component follows the real component and is suffixed with "i". Do not copy any braces around the complex value.

Polynomial Solutions

Example: Find the solutions to the cubic equation, x³ + 5x² - 29x - 105 = 0.

[POLY] (Initiates the polyonomial solver)
3 [ENTER] (Enter order 3)
1 [ENTER] (Enter coefficients in sequence)
5 [ENTER]
-29 [ENTER]
-105 [ENTER]

At this point, the solutions will be given in sequence: +5, -3, and -7, and pressing [ENTER] will page through them. Use the [STO] key at any time to store values you want to keep. For more information, refer to the section on Solving Polynomials.

Natural Fractions When you press the [a b/c] key, the result of a previous calculation will be shown as a natural (or common) fraction. The natural fraction form will also be shown if you input a decimal point. Example: Show Π as a fraction. [CONST] Π [a b/c] Displays: 3 + 16/113 (aprx) The 'aprx' indication signifies that the fraction cannot be represented precisely, and it is thus an approximate conversion. You can modify the precision of fraction conversions by changing the 'Max Denominator' setting in the Options Window. Inputing & Reducing Fractions The [a b/c] key may also be used to input values in common fraction form. Pressing it again will show the result of the reduction. Example: Reduce 1 + 8/6. 1 [a b/c] 8 [a b/c] 6 (input fraction) [ENTER] (convert to decimal*) Displays: 2.333333... [a b/c] (press again to convert decimal) Displays: 2 + 1/3 Additionally, we can show this as an improper fraction by pressing [d/c]: Displays: 2 + 1/3 (previous result) [d/c] Displays: 7/3 *It was not was not strictly necessary to press [ENTER] here, but it demonstrates the conversion to decimal.

Degrees, Minutes, Seconds The DMS [° ' ''] key behaves in much the same way as the [a b/c] natural fraction key--you can use it to both input values and display results in degrees, minutes and seconds. Example: Enter 5° 30' 15''. 5 [° ' ''] 30 [° ' ''] 15 [ENTER] Displays: 5.50416666666666667 Example : Show 67.2376 in degrees, minutes, seconds. 67.2376 [° ' ''] Displays: 67 : 14' : 15.360'' Engineering Example The [ENG] key provides a convenient way to view values in engineering form, without having to enable the dedicated engineering mode. Simply press [ENG] any time. Example: 564000000 [ENG] Displays: 564E6 (Mega) Press [ENG] multiple times to decrement the exponent by 3, or use with [SHIFT] to increment by 3.

Financial Example (Bond Price)

Professional Edition Only

Reverse Polish Notation is commonly used by financial calculators; for this reason financial examples in the financial sections of this User Guide using RPN. DreamCalc, however, can perform financial calculations in any input order, and here we show the same calculation in both RPN and algebraic inputs.

Example: What price should you pay on April 25th 2005 for a 6.75% U.S. Treasury bond that matures on June 1st 2015, if you want a yield of 8.25%. Assume that you normally express dates in the month-day-year format.

Reverse Polish Notation:

2 [n] (semi-annual)
8.25 [i] (enters YTM)
6.75 [PMT] (enters coupon rate)
4 [DATE] 25 [DATE] 2005 (settlement date)
[ENTER]
6 [DATE] 1 [DATE] 2015 (maturity date)
[PRICE]
Displays: 89.85 (price as percentage par)
[+]
Displays: 92.55 (total price inc. accrued interest)

Algebraic Modes:

2 [n] (semi-annual)
8.25 [i] (enters YTM)
6.75 [PMT] (enters coupon rate)
4 [DATE] 25 [DATE] 2005 (settlement date)
[PRICE]
6 [DATE] 1 [DATE] 2015 (maturity date)
[ENTER]
Displays: 89.85 (price as percentage par)
[+]
[RCL] [K] (recalls accrued interest)
Displays: 2.70
[ENTER]
Displays: 92.55 (total price inc. accrued interest)

For more information, refer to the Introduction to Financial Calculations section, or to Bond Calculations for specific information about the example.

See also: Getting Started, Graphing Examples, Graphing & List Window

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