1. University of Pitesti Dolnośląska Wyższa Szkoła Przedsiębiorczości i Techniki w Polkowicach Numeric Computers Ion Paul Mihai Dr inż. ZDZISŁAW PÓLKOWSKI Polkowice, 2015

2. TOPICS MENU Why do we need a computer? What is Numerical Computation? Main Branches of Numerical Computation Real use of Numerical Computation Brief History

3. Why do we need a computer? Computers play many important roles in society, helping to promote communication and interaction with others as well as providing users a way to shop, play games and have access to education. Additionally, computers provide a convenient way to create and store valuable information along with media and files, making them particularly useful for businesses.There are several different types of computers, each of which is geared towards a specific audience. For example, there are desktops and laptops for home use along with smaller, more easily portable computers for work or travel. In an educational setting, a teacher or instructor may use computers to help convey information or to create an efficient way for students to interact and learn valuable information. Another advantage of the computer is enhanced connectivity, especially in mobile devices, which promotes sharing of data and information. http://www.ask.com/technology/need-computers-8115b8db0a2c1658#full-answer

4. What is Numerical Computation? Numerical analysis or scientific computing is the study of algorithms that use numerical approximation (as opposed to general symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). One of the earliest mathematical writings is a Babylonian tablet from the Yale Babylonian Collection (YBC 7289), which gives a sexagesimal numerical approximation of sqrt2, the length of the diagonal in a unit square. Being able to compute the sides of a triangle (and hence, being able to compute square roots) is extremely important, for instance, in astronomy, carpentry and construction.Numerical analysis continues this long tradition of practical mathematical calculations. Much like the Babylonian approximation of sqrt 2, modern numerical analysis does not seek exact answers, because exact answers are often impossible to obtain in practice. Instead, much of numerical analysis is concerned with obtaining approximate solutions while maintaining reasonable bounds on errors. http://en.wikipedia.org/wiki/Numerical_analysis

5. Main Branches of Numerical Computation • Linear Equations: Solve a system of n linear equations in n unknowns. • Linear Programming: Minimize a linear function subject to m linear constraints. • Optimisation: Minimize a function of several variables. • Numerical PDE: Numerically solve a Partial Differential Equation. http://www.cambridge.org/ba/academic/subjects/mathematics/ http://www.slideshare.net/milinda1100/numerical-computation

6. Real use of Numerical Computation • Computer-aided engineering (CAE) is an important subject within engineering, and some quite sophisticated PSEs have been developed for this field. A wide variety of numerical analysis techniques is involved in solving such mathematical models. • The models follow the basic Newtonian laws of mechanics, but there is a variety of possible specific models, and research continues on their design. • Another important application is atmospheric modeling. In addition to improving weather forecasts, such models are crucial for understanding the possible effects of human activities on the Earth’s climate http://www.britannica.com/EBchecked/topic/422388/numerical-analysis

7. The need for advances in applications, such as ballistics prediction, neutron transport, and nonsteady, multidimensional fluid dynamics drove the development of the computer and depended strongly on advances in numerical analysis and mathematical modeling. Modern numerical analysis and scientific computing developed quickly and on many fronts. Our current focus is on numerical linear algebra, numerical methods for differential and integral equations, methods of approximation of functions, and the impact of these developments on science and technology. Of particular current interest is the impact of mathematical software packages. http://history.siam.org/ http://www.computerhistory.org/collections/catalog/102622385

8. How Computers Have Changed the World Computers have changed the world in many ways. They allow huge amounts of information to be stored in a small space. They also allow a person to calculate mathematical problems with ease. Finally, computers allow people to communicate with one another through internet sites such as Facebook, My Space, and Twitter. Personal computers today can hold huge amount of memory. They can be used to store music, pictures, documents, videos, and much more. Computers are able to be reprogrammed to suit any user's needs. This is one of the key traits of a computer today. Computers were first designed to help a person calculate numbers; this function can be seen as far back as 2000 B.C. with the use of the abacus. Modern computers are simply very advanced calculators. Almost any mathematical function can be plugged into a computer, and the computer will solve almost instantaneously. https://sites.google.com/site/computersrrrcool/computers/how-computers-have-changed-the-world

9. Brief History Modern numerical analysis can be credibly said to begin with the 1947 paper by John von Neumann and Herman Goldstine, "Numerical Inverting of Matrices of High Order" (Bulletin of the AMS, Nov. 1947). It is one of the first papers to study rounding error and include discussion of what today is called scientific computing. Although numerical analysis has a longer and richer history, "modern" numerical analysis, as used here, is characterized by the synergy of the programmable electronic computer, mathematical analysis, and the opportunity and need to solve large and complex problems in applications. http://history.siam.org/

10. The use of a computer as a calculating device takes away the monotonous task of calculating by brute force. Finally, computers have changed the way that we communicate as a society. People can now talk to one another in almost no time at all through the use of social networking sites, and people can even live video chat with applications such as Skype. The use of a computer as a calculating device takes away the monotonous task of calculating by brute force. Finally, computers have changed the way that we communicate as a society. People can now talk to one another in almost no time at all through the use of social networking sites, and people can even live video chat with applications such as Skype. http://www.maclife.com/article/gallery/10_ways_apple_changed_world