Ostrowski's Method for Finding Roots
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Calculating Numerical Roots = = 1.37480222744
#10 in Fundamentals of Applied Math Series Calculating Numerical Roots Richard J. Nelson Introduction – What is a root? Do you recognize this number(1)? 1.41421 35623 73095 04880 16887 24209 69807 85696 71875 37694 80731 76679 73799 07324 78462 10703 88503 87534 32764 15727 35013 84623 09122 97024 92483 60558 50737 21264 41214 97099 93583 14132 22665 92750 55927 55799 95050 11527 82060 57147 01095 59971 60597 02745 34596 86201 47285 17418 64088 91986 09552 32923 04843 08714 32145 08397 62603 62799 52514 07989 68725 33965 46331 80882 96406 20615 25835 Fig. 1 - HP35s √ key. 23950 54745 75028 77599 61729 83557 52203 37531 85701 13543 74603 40849 … If you have had any math classes you have probably run into this number and you should recognize it as the square root of two, . The square root of a number, n, is that value when multiplied by itself equals n. 2 x 2 = 4 and = 2. Calculating the square root of the number is the inverse operation of squaring that number = n. The "√" symbol is called the "radical" symbol or "check mark." MS Word has the radical symbol, √, but we often use it with a line across the top. This is called the "vinculum" circa 12th century. The expression " (2)" is read as "root n", "radical n", or "the square root of n". The vinculum extends over the number to make it inclusive e.g. Most HP calculators have the square root key as a primary key as shown in Fig. 1 because it is used so much. Roots and Powers Numbers may be raised to any power (y, multiplied by itself x times) and the inverse operation, taking the root, may be expressed as shown below. -
Calculating Solutions Powered by HP Learn More
Issue 29, October 2012 Calculating solutions powered by HP These donations will go towards the advancement of education solutions for students worldwide. Learn more Gary Tenzer, a real estate investment banker from Los Angeles, has used HP calculators throughout his career in and outside of the office. Customer corner Richard J. Nelson Learn about what was discussed at the 39th Hewlett-Packard Handheld Conference (HHC) dedicated to HP calculators, held in Nashville, TN on September 22-23, 2012. Read more Palmer Hanson By using previously published data on calculating the digits of Pi, Palmer describes how this data is fit using a power function fit, linear fit and a weighted data power function fit. Check it out Richard J. Nelson Explore nine examples of measuring the current drawn by a calculator--a difficult measurement because of the requirement of inserting a meter into the power supply circuit. Learn more Namir Shammas Learn about the HP models that provide solver support and the scan range method of a multi-root solver. Read more Learn more about current articles and feedback from the latest Solve newsletter including a new One Minute Marvels and HP user community news. Read more Richard J. Nelson What do solutions of third degree equations, electrical impedance, electro-magnetic fields, light beams, and the imaginary unit have in common? Find out in this month's math review series. Explore now Welcome to the twenty-ninth edition of the HP Solve Download the PDF newsletter. Learn calculation concepts, get advice to help you version of articles succeed in the office or the classroom, and be the first to find out about new HP calculating solutions and special offers. -
HP Solve Calculating Solutions Powered by HP
MHT mock-up file || Software created by 21TORR Page 1 of 2 HP Solve Calculating solutions powered by HP » HP Lesson Plan Sweepstakes for Issue 20 teachers! August 2010 Teacher Experience Exchange is a free resource for teachers that offers discussion Welcome to the forums, lesson plans, and professional twentieth edition development tutorials. Visit the site and of the HP Solve upload your own lesson plan for a chance to newsletter. Learn win an HP Mini PC in our weekly drawing. calculation concepts, get advice to help you Your articles succeed in the office or the classroom, and be the first to find out about new HP calculating solutions and special offers. » Download the PDF version of newsletter articles. » Next generation financial » SmartCalc 300s Scientific calculator NOW AVAILABLE Calculator available for a » Contact the editor HP Announces its most limited time innovative calculator to date: Math and science students will From the Editor the 30B Business appreciate the logical, Professional. Available at accurate, and dependable HP Office Depot USA and Staples SmartCalc 300s Scientific Europe while supplies last. Calculator now available at Staples in the USA through September (while supplies last) and at several retailers in Europe. As HP Solve grows, the current structure will adapt as well. Learn more about current » RPN Tip #20 » Come Join Us At The HHC articles and feedback Gene Wright 2010 HP Handhelds from the latest Solve newsletter. 20 Useful Tips for the 30b Conference! Jake Schwartz Business Professional. This Learn more » article gives RPN user tips and Jake, official historian of HP helps explain differences Handheld Calculator Customer Corner between an RPL-based Conferences, provides his machine and a legacy RPN unique perspective and » Meet an HP machine. -
HP Calculator Programming Richard J
HP Calculator Programming Richard J. Nelson Introduction Do you use an HP calculator that has a programming capability, and do you actually use it? Of the 24 models, see Table 1 below, 23 are on the HP website 13, or 54.2%, are programmable. If the Home and Office machines are omitted, the numbers are: 17 models, and 13 or 76.5%, are programmable. What does this mean? A program is a sequence of instructions (functions and/or data) that are keyed (or loaded) into the calculator’s memory that will solve a particular problem or provide specific information. A program capability also includes special instructions that provide prompting for inputs and labeling for outputs. Another aspect of a program capability is the ability to perform decision logic so the particular parts of a program may be changed depending on the results of previous instructions. This capability provides “intelligence” to the program. The program capability of the 10 current models ranges from very simple such as the HP-12C to very complex (and very powerful) such as the HP 50g. Older HP calculators such as the HP-71B or HP-75C used a computer like programming language called BASIC. The HP-12C and HP-15C programing language is an RPN FOCAL(1) like language, and the HP 50g uses an RPL programming language. The algebraic calculators use what may be called an Aplet programming language. Table 1 – Current HP Calculator Products (24) # Financial Calculators Scientific & Graphing Home & Office 1 HP 10bII HP 10s HP Calcpad 100 2 HP 10bII+ HP-15C Limited Edition HP CalcPad 200 3 HP 20b HP 33s OfficeCalc 100 4 HP 30b HP 35s OfficeCalc 200 5 HP-12C HP 39gs OfficeCalc 300 6 HP-12C 30th Anniversary HP 39gII PrintCalc 100 7 HP-17bII+ HP 40gs QuickCalc 8 HP 48gII 9 HP 50g 10 SmartCalc HP 300s 5 of 7 = 71% programmable 8 of 10 = 80% programmable None programmable Note: Programmable calculators are in blue. -
HP Solve Calculating Solutions Powered by HP
HP Solve Calculating solutions powered by HP » Next generation financial calculator Volume 17 At the Consumer Electronics Show in February 2010 January, HP Calculators announced their most innovative financial calculator to date, Welcome to the the 30b Business Professional Calculator. seventeenth edition of the HP Solve Learn more » newsletter. Learn calculation concepts, get advice to help you Your articles succeed in the office or the classroom, and be the first to find out about new HP calculating solutions and special offers. Download the PDF version of newsletter » RPN Tip #17 »The HP-71B "Math Machine" articles. This issue starts the third year Only 25 years young, the HP- of HP Solve and RPN Tips. 71B has been around for Featured Calculator See a helpful summary of all generations. Read a historical the previous RPN tips from the review of this Gen3 HP first two years. "calculator." » Feature Calculator of the month: HP 12c » The HP 30b Business » HP 48 one minute marvel – Platinum financial Professional No. 4, Chinese New Year calculator What are the differences Marvel in these One Minute Tax time is here and between the HP 30b and HP Marvels from HP. This month, HP Calculators can 20b? Read a detailed review learn about prompting and help! The HP 12c on the features found on HP's labeling using the Chinese Platinum financial newest mid-range financial New Year! calculator is at your calculator. service to make sure your taxes are done right! Learn more » The Calculator Club Join the Calculator Club and take advantage of: » The HP 20b Business » Solver Menus on the HP 30b Consultant Frequently use the Date-menu • Calculator games & Learn more about HP's function? Learn a more Aplets financial calculator, the 20b. -
Measuring Calculator Current Richard J
Measuring Calculator Current Richard J. Nelson Introduction The most important measurement of a semiconductor or semiconductor device is its current usage. I once visited an assembly house in Asia that packaged integrated circuits, IC’s, (commonly called chips) into plastic packages. The finished IC’s were then 100% tested using a massive computer controlled very expensive digital signal tester. I noticed that the tester wasn’t in use and I asked why. The test engineer explained that they had found that they could simply measure the quiescent current and they could determine 99.9% of the time that the circuit was working. Besides, the hundreds (and often thousands) of specific digital conditions of the IC functions took much longer by a factor of at least ten. Calculators are semiconductor products and measuring the current that they draw under various usage/mode conditions provides a good indication of what is happening. Pressing “on” with a blank calculator display just doesn’t tell you very much. Current is the most problematic basic electronics measurement – vs. voltage or resistance. Modern digital nultimeters, DMMs, are cheap, accurate, and readily available. All too often, however, you will find that the current range doesn’t work – usually because of a blown internal fuse. Most electrical measurements are made by placing the probes across two points on the component or circuit under test. Measuring current, however, requires that you insert the meter into the circuit. This means that you must cut or un solder the circuit and this is usually not convenient. Current Range An interesting aspect of electronics is the very wide range of values that are involved. -
HP Solve Calculating Solutions Powered by HP
HP Solve Calculating solutions powered by HP In the Spotlight Issue 25 » 30th Anniversary Edition of the HP 12c October 2011 Performance never goes out of style. Celebrate 30 years of this one of a kind Welcome to the twenty- business calculator with a limited edition fifth edition of the HP collector's special. Solve newsletter. Learn calculation concepts, get advice to help you Your articles succeed in the office or the classroom, and be the first to find out about new HP calculating solutions and special offers. » Download the PDF version » The HP 15c Limited Edition » The HP-12C, 30 Years and of newsletter articles. calculator Counting One of nine machines in the Richard J. Nelson and Gene Wright » Contact the editor Voyager Series of HP Read this extensive review of calculators, HP announces a how the HP-12C calculator From the Editor re-release of their legendary has withstood the test of HP 15c calculator. professionals and time longer than any other calculator. » Calculator » Converting Decimal Learn more about Programmability—How Numbers to Fractions current articles and Important is it in 2011? Joseph K. Horn feedback from the latest Richard J. Nelson Joseph explains the Solve newsletter In this article, learn if there is continued Fraction Algorithm including One Minute an advantage to having a and provides an RPN HP- Marvels and a new scientific calculator 15C program that quickly column, Calculator programmable as well as the converts any decimal to a Accuracy. reasons for programmability. fraction to the accuracy set by the FIX display value. Learn more ‣ » Limited Edition HP 15c » How Large is 10^99? » Fundamentals of Execution Times Richard J. -
HP Solve Calculating Solutions Powered by HP
MHT mock-up file || Software created by 21TORR Page 1 of 2 HP Solve Calculating solutions powered by HP Hot Deals Issue 24 July 2011 » Back-To-School Summer Savings 10% off Calculators at the HP Home & Welcome to the twenty- Home Office Store and more! forth edition of the HP Solve newsletter. Learn calculation concepts, get advice to help you succeed in the office or Your articles the classroom, and be the first to find out about new HP calculating solutions and special offers. » Download the PDF version of newsletter articles. » HP Mobile Calculating Lab » Customization Kits Richard J. Nelson » Contact the editor Learn how the HP Mobile One of HP’s greatest Calculating Lab (MCL) helps contributions to calculators is From the Editor educators teach math and the feature of customization. science in a dynamic way. Read through a list of features found on HP calculators past and present. » Using PROOT with Duplicate » Repurposing the HP 20b/30b Learn more about Roots Calculator Platform current articles and Namir Shammas Jake Schwartz feedback from the latest In this article, Namir focuses As mentioned in the Solve newsletter on how the function PROOT Customization article, including One Minute handles polynomials that have repurposing is a form of Marvels and other duplicate roots in addition to customizing your calculator. community news. studying and comparing errors Jake provides an updated within the function PROOT. overview of an interesting user Learn more ‣ community repurposing project. » How Fast is Fast? Richard J. Nelson » HP’s Calculator Manuals Calculator speed is a » Fundamentals of Applied calculator technical mhtml:file://U:\HP\01_Newsletters\HP_Calculator_eNL\07_July_2011\Content\Design\R.. -
HP 20B Business Consultant HP 30B Business Professional Financial Calculator User’S Guide
HP 20b Business Consultant HP 30b Business Professional Financial Calculator User’s Guide HP Part Number: NW238-90001 Edition 1, March 2010 i Legal Notice This manual and any examples contained herein are provided "as is" and are subject to change without notice. Hewlett-Packard Company makes no warranty of any kind with regard to this manual, including, but not limited to, the implied warranties of merchantability, non- infringement and fitness for a particular purpose. In this regard, HP shall not be liable for technical or editorial errors or omissions contained in the manual. Hewlett-Packard Company shall not be liable for any errors or for incidental or consequential damages in connection with the furnishing, performance, or use of this manual or the examples contained herein. Copyright © 2010 Hewlett-Packard Development Company, L.P. Reproduction, adaptation, or translation of this manual is prohibited without prior written permission of Hewlett-Packard Company, except as allowed under the copyright laws. Hewlett-Packard Company 16399 West Bernardo Drive MS 66M-785 San Diego, CA 92127-1899 USA ii HP 20b Business Consultant iii HP 30b Business Professional iv Keyboard Map Legend Number Feature Number Feature 1 2-line, alphanumeric scrolling 9 Common Mathematical display screen functions and Math (Math) menu 2 Time Value of Money keys 10 Program menu* (TVM) RPN Swap/Close parenthesis 3 Cash Flow, IRR and NPV keys 11 Backspace key/Reset menu 4 Data and Statistics menus 12 Percent/Percent calculation (business) and Date menus 5 Input key and Memory menu 13 Recall and Store 6 Insert and Delete/scroll (up 14 Black-Scholes** and Bond and down) menus 7 Shift key 15 Amortization/Depreciation menus 8 On/Off/Cancel 16 Annunciators * Only applies to HP 30b. -
Measuring Calculator Current – Nine Measurement Examples Richard J
Measuring Calculator Current – Nine Measurement Examples Richard J. Nelson Introduction In HP Solve, issue #28 page 30, I described the importance and problems of measuring the current that a calculator draws from its “battery(1).” In that article I gave an example of the HP-41 and the current it draws under a very few selected conditions. I also described how the current a calculator draws frequently changes, often quite rapidly and drastically, depending on what the calculator is doing. Low power consumption is essential Nearly every reader has an extremely complex battery operated device such as a cell phone, game device, tablet, etc. Since we use these battery operated devices every day the need for drawing a minimum amount of current is a critical aspect of their design. Using the lowest possible power is the mantra for every circuit designer for battery operated products these days. What is amazing is the fact that since the digital circuits are able to operate so fast, and the sloth like human operators are so slow, that the circuit may be turned “off” and back on again while the human “decides” what to do, or how to deal with the previous result. Modern circuit design utilizes this current shut down concept in as many situations as possible throughout the complex circuitry. One of the reasons to measure the current draw – in addition to troubleshooting – is to be able to estimate the battery life of the machine. In terms of doing this you have to be careful, however, because of the many possible operating conditions, and that they may change faster than your meter can respond. -
RPN Tutorial, Incl. Some Things HP Did Not Tell
RPN Tutorial, incl. some things HP did not tell Copyright © 2014 by Hans Klaver, The Netherlands RPN , postfix notation or stack logic , the calculator logic system used in many Hewlett-Packard (HP) calculators and simulations thereof (like the standard Calculator in Mac OS X in RPN-mode, start with ⌘R or Command+R), is easy to use and saves you time because there is no need to use brackets or =. What’s better, it gives you more insight into your calculations than using the ‘algebraic’ systems used by other calculators and it keeps you and not your calculator (see Appendix D ) in command of what is calculated. In 1972, more than 40 years ago, HP launched the HP -35 , the first pocket calculator with transcendental functions and the first with RPN. This same RPN is used in calculators sold by HP nowadays, like the HP -12C , HP -12C Platinum , HP -15C LE , HP 17bII+ and HP 35s , also in the amazing WP 34S and WP 31S , and in a slightly modified version in the HP 20b and 30b and in graphing calculators like the HP 50g and HP Prime . This tutorial is a tribute to the HP -35 and especially to the lay-out of the beautiful and informative HP -35 Operating Manual . As far as possible it uses the colours of the keys as they appear in that Manual, so the colours of your calculator’s keys will almost always differ; don’t get confused by that. The ‘Cheat Sheet’ below serves as a table of contents and as a summary for this tutorial. -
WP 34S Owner's Manual
3.0 Owner’s Manual This file is part of WP 34S. WP 34S is free software: you can redistribute it and / or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. WP 34S is distributed in the hope that it will be useful, but without any warranty; without even the implied warranty of merchantability or fitness for a particular purpose. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with WP 34S. If not, please see http://www.gnu.org/licenses/ . This manual contains valuable information. It was designed and written in the hope that it will be read by you. Here is, however, first aid for those getting caught in an unexpected or unwanted calculator mode while playing before reading: (i.e. + ) will bring you back to default floating point mode. For those who don’t even read this: Sorry, we can’t help you. WP 34S Owner’s Manual Edition 3.0 Page 1 of 118 TABLE OF CONTENTS Welcome ..................................................................................................................... 5 Getting Started ............................................................................................................ 7 The User Interface ...................................................................................................... 8 Keyboard Basics ................................................................................................................