Скачать или смотреть Computer Algebra Systems Engineering and Differentiation

Calculus, the mathematical study of continuous change, is an invaluable field utilized almost routinely by scientists in every discipline. It is built around the idea of infinitesimally small increments, which is notably applied in finding derivatives and integrals. These fundamental concepts of calculus are incredibly important and utilized frequently in modern science and engineering. As mathematics grows increasingly more complex and calculations more time consuming, the use of computers becomes increasingly more viable and necessary. Mathematics and computer science are very closely intertwined, and thus, can be utilized in conjunction effectively. A computer, in its most basic state, can only work with numbers by feeding certain instructions to the ALU (Arithmetic Logic Unit). To do calculus, a computer would have to understand Symbolic Algebra which is composed of letters in addition to numbers. To accomplish this task, a computer library capable of manipulating algebraic expressions was written centered around the fundamental concept of a polynomial being a computer data type. By utilizing principles of Object Orientated Programming, the creation of custom data types usable by the library is relatively simple, thus making the library incredibly adaptable. Its functionality was demonstrated by passing an expression into a program utilizing the library that it then differentiated. The program performed as expected under each test.