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# Lect.10

الكلية كلية الهندسة     القسم هندسة الكيمياوية     المرحلة 3
أستاذ المادة حسنين محسن علي جواد العبيدي       21/03/2017 08:26:49
Numeric analysis or briefly numerics has a distinct flavor that is different from basic
calculus, from solving ODEs algebraically, or from other (nonnumeric) areas. Whereas in
calculus and in ODEs there were very few choices on how to solve the problem and your
answer was an algebraic answer, in numerics you have many more choices and your
answers are given as tables of values (numbers) or graphs. You have to make judicous
choices as to what numeric method or algorithm you want to use, how accurate you need
your result to be, with what value (starting value) do you want to begin your computation,
and others. This chapter is designed to provide a good transition from the algebraic type
of mathematics to the numeric type of mathematics.
We begin with the general concepts such as floating point, roundoff errors, and general
numeric errors and their propagation. This is followed in Sec. 19.2 by the important topic
of solving equations of the type by various numeric methods, including the famous
Newton method. Section 19.3 introduces interpolation methods. These are methods that
construct new (unknown) function values from known function values. The knowledge
gained in Sec. 19.3 is applied to spline interpolation (Sec. 19.4) and is useful for understanding
numeric integration and differentiation covered in the last section.
Numerics provides an invaluable extension to the knowledge base of the problemsolving
engineer. Many problems have no solution formula (think of a complicated integral
or a polynomial of high degree or the interpolation of values obtained by measurements).
In other cases a complicated solution formula may exist but may be practically useless.
It is for these kinds of problems that a numerical method may generate a good answer.
Thus, it is very important that the applied mathematician, engineer, physicist, or scientist
becomes familiar with the essentials of numerics and its ideas, such as estimation of errors,
order of convergence, numerical methods expressed in algorithms, and is also informed