Foreword

Headings similar to the title of this book are possible in practically any computer edition: Tips for Programmers of Visual Basic or Tips for MS Office Users, etc.

These tips are conditionally divided into three groups:

1.        Recommendations that are in published documentation and in Help by the original vendor.

2.        Information provided by program developers, giving information about new and useful properties of the program and ways of defect neutralization after the beginning of commercial sale.

3.        Information about results of experiments on the program. One can speak of so-called undocumented (collateral) properties of the programs. Developers ask the end user to avoid these practices, but...

A naturalist, who wants to study the world, cannot address his questions to the Creator directly (to God or to Nature as you prefer), but he has to ask an investigated object. For this purpose the experiment is carried out[1] some disturbance is created in the object and the reaction is determined: Click a horse on the nose; it will whisk its tail!.

Each program has an author. As a rule, one cannot find the name of the author on the box with the distribution kit or in the documentation, but the author exists[2]. Hence, any experiments with the program are needless. Any questions that arise should be directed either to the documentation or to the author. But for example, if it is required to know whether the argument of a sine function must be in degrees or radians, one probably will not look for it in the documentation, but simply write x: = sin(90) and see the result. The user carries out similar experiments hourly, reading the documentation only in some sophisticated cases. Often, this does not lead to an answer. Turning to the Creator is too difficult. We can find the program's vendor on the hot-line, but not the author. Most probably, you will be asked to call back in a few days. During these days they will carry out their own experiments on the program and try to find the answer. As a rule, asking the author gives nothing because he has forgotten his brain-child already and now works on an entirely new project. Even if it is not the case, the author likely does not remember all the properties and nuances of the program. Moreover, in creating the program, the programmer himself continuously experiments on it, surprising himself with its new, unexpected properties, most of which never make it to the documentation.

Consequently, a user often forgets (involuntarily) that the program is a creation of the mind and hands of a man (Second Nature) and supposes that it is the fruit of the Creator's labor, anonymous and inaccessible on any hot-line, (First Nature).

One can consider that celestial mechanics was not discovered by man, but the Creator betrayed a secret of higher laws, throwing an apple and striking Newtons head. The merit of a genius (Newton) is just an ability to be at a certain time and in a certain place[3]. The programs fall to us from above, too. Hence, the vitality of idea freeware. Vendors and programmers are not necessarily fond of this concept. We can say, that God (Absolute World Reason) has created not only man, but also the computer. A man who writes a program for the computer simply exhales soul into the lifeless heap of hardware. Body trade (transplantation of organs, transfusion of blood, prostitution, at last) is a reality in our day. The theme of the purchase and sale of a soul is the stuff of only myths and legends and also in their literary treatment (Faust history, for example). When we get some software, we buy only the body disks, documentation, information and discounts under new versions, and the main thing service after the sale.

Before we return to the tips, we note once more that the division of the tips between correct and incorrect, wrong is rather conditionally owing to inevitable experiments on the particular program. Giving harmful tips, the author says to readers: Think and decide to have or not to have in your own program. The following group of tips can be classified by another name: crazy hands. The author's hope, after the reader becomes familiar with some tips, that he will then will tell himself: As an idea this is disputable, but it is very interesting. I shall do it a differently and even better![4].

A program may be suitability for application to some concrete practical problems. Also, a program can be considered an entertaining and difficult puzzle (a gymnastics for the mind[5]), that may be suitable for high intellectual leisure: I wonder what will I get, if I do it like this?! I do not know what this programming trick is for, but it looks amusing.

Now we want to say something else about authorship. Tips for working on a computer are like jokes. It is not easy to mention the name of the author of some successful tip or joke. The author is people. If a reader becomes familiar with some recommendation, he can tell: But I know a better ending for the joke, pardon, the tip this problem can be solved more easily and more effectively in Mathcad!. Another reaction may be following: Interesting reception. I must introduce it to my colleagues (I shall retell a joke) and I shall include it in my Mathcad-documents! The author (elementary part, bit of people) is prepared for the third reaction neutral or negative. In any case he will be glad to receive responses from readers. This way he can expand and perfect more tips for users of Mathcad. This book is duplicated on a site http://twt.mpei.ac.ru/ochkov/MC&MC.book/Sovet/sovet.htm. The readers can send new tips and publishable comments to the address ochkov@twt.mpei.ac.ru.

At first, it was attempted to separate tips into seven precise groups, covering various aspects of work in Mathcad. But, it turned out that it is not easy to do such gradation. A single tip can touch various aspects of work. Therefore, it was decided to give icons that can provide advance warning about what we are going to present after the name of a tip:

Input-output of the information in the Mathcad-worksheet

Work with variables, operators (built-in and user implemented)

Remarks in a Mathcad-worksheet

Units in a Mathcad-worksheet

Symbolic mathematics (analytical transformations)

Programming

Graphing

Also, these two icons mark the following features of some tips:

An undocumented method, which solves one problem, but may create a new one

If it is impossible, but we want it very much, it is possible! this icon marks quite legal use of old tools in new or unusual applications (Crazy hands see above).

There is no special order or alternation of the tips: from the current tip, references[6] both to subsequent and to previous tips can be made. From the referenced tip, it is possible go to a new one or an old one. It is possible to study a tip, following strings (web if we remember the abbreviation WWW) of links but not the table of contents. So, a reader can dive into the tips at random. He can choose something that may have intrigued him more than something else. Tips of the book are some elements of a scattered mosaic (Puzzle). From the mosaic, a reader can collect a his own pieces and build a picture that reflects a sphere of his interests. Such pictures were collected by the author, too. It is articles (etudes, sketch), where links are made:

      Color in the programs http://twt.mpei.ac.ru/ochkov/Color_in_Program/index.htm

      The story of the masterpiece (Mathcad and nonstandard graphics) http://twt.mpei.ac.ru/ochkov/Lace/Lace_eng.htm

      Boolean cubs http://twt.mpei.ac.ru/ochkov/Fuzzy%20logic/Bool_Cube/Logic.htm

      Mathcad and Maple Working with Units http://twt.mpei.ac.ru/ochkov/Unit_MC_MP/Unit_MC_MP_eng.htm

      Solving of algebraic equations and systems or Van Gogh in Mathcad http://twt.mpei.ac.ru/ochkov/Carpet/carpet_eng.htm

      Price of an Old Car or The Way from Correlation to Regression in Mathcad http://twt.mpei.ac.ru/ochkov/car/c_e.html

      The Invisible Variable http://twt.mpei.ac.ru/ochkov/Invisible/Eng/Index.htm etc see http://twt.mpei.ac.ru/ochkov/work2_eng.htm

As the author understands and quite supposes, it is difficult to think out any practical application for some tips of the book. But Coming back to the idea that the programming does not have to be of practical benefit (gymnastics for the mind[7]). It is possible to confirm that the work on the computer is some kind of high intelligence entertainment. The author gives a tip and asks the reader to find a practical application for it.

Well, and now we shall begin a statement of tips. There are exactly one hundred of them. We do not count those tips that a reader will find between the lines of the text and in the operators and figures of the Mathcad-documents.



[1] One definition of a science: It is satisfaction of private curiosity (knowledge of Nature) for the public (state) account. In modern understanding, science appeared in the beginning of XVIII century, when people began to mark out a separate base of knowledge of features of Nature that could be reproduced at any moment. Theoretical physics (chemistry, biology etc. and etc.) are successful and unsuccessful attempts of interpolation and extrapolation of experimental data (see, for example in tip 52).

[2] All serious commercial programs are created by the large collective of the developers (authors' collective), but the innovative ideas that are the foundation of them, have their own authors.

[3] One says that it is simple to play a piano. It is enough to press the necessary key at the necessary time. And ingenious pianists are only a few because the Creator cannot serve all players simultaneously. Problems of diligence of the musician (programmer) shall not concern us in this text.

[4] Many tips in this book do not solve old problems but raise new ones that are connected with the use of computers in scientific and technical calculations.

[5] As rule mathematics is considered the gymnastics for the mind.

[6] Automatic links (hyperlinks) are introduced into electronic variants of the text of the book, where they are marked with color and underlining. If such a fragment of the text (it looks following way see tip NN) is called (mouse click), then the reader will pass to the necessary place (to the tip NN). Certainly, color found itself into the book but underlining remained. As we have already noted after the book is published (it was the request of the editor), the text of the book will be published on the Internet, where all hyperlinks will work and will simplify and speed navigation in the text. This footnote the link about links is the simplest example of a hyperlink: you dropped your eyes to the bottom of the page, and then you could return to the basic text. It is a pity that Word, where the text of the book was written, does not allow nested links it is possible to make a hyperlink in a link. Certainly the author has used it. The author hopes that he does not abuse the hyperlinks. On the one hand, if we speak about the electronic version of the book, hyperlinks are very comfortable (you clicked with your mouse see the link, and then click once more you return without getting lost). On the other hand we have common (flat) text of the book.

[7] If there is An Art for The Art , then there are A Programming for the Programming too.