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By
Shingareva, Inna; LizárragaCelaya, Carlos
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Linear algebra is the algebra of linear spaces and linear transformations between these spaces. Linear algebra is one of the fundamental areas of modern mathematics that has extensive applications in the natural and social sciences and in engineering, since nonlinear models can be studied by using approximated linear models.
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By
Shingareva, Inna; LizárragaCelaya, Carlos
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Maple and Mathematica perform complex arithmetic automatically, all operations are performed by assuming that the basic number system is the complex field ℂ. In both systems, the imaginary unit i of the complex number x+y*I is denoted by I.
By
Shingareva, Inna; LizárragaCelaya, Carlos
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We know that scientific computing and numerical analysis are concerned with constructing and investigating approximate methods to obtain numerical solutions to complicated mathematical, scientific, and engineering problems using computers. Numerical analysis is one of the most important fields of mathematics that has numerous applications in all fields of engineering and sciences.
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By
Shingareva, Inna; LizárragaCelaya, Carlos
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Algebra (or abstract algebra) is one of the important areas of the mathematics that studies various algebraic structures, such as sets, groups, fields, spaces and other.
By
Shingareva, Inna; LizárragaCelaya, Carlos
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In this Chapter we consider real functions of real variables, f:ℝ^{n}→ℝ^{n} (n ∈ ℕ). At first, let n = 1 and we consider various forms of definition, visualization, and operations on real functions of the real variable in both systems (in more detail about functions, see Sect. 4.8).
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By
Shingareva, Inna; LizárragaCelaya, Carlos
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Graphs of real values of expr or the functions f(x), f(x, y), x ∈ [x_{1}, x_{2}], (x, y) ∈ [x_{1}, x_{2}] × [y_{1}, y_{2}].
By
Shingareva, Inna; LizárragaCelaya, Carlos
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In 1979–1981, Stephen Wolfram constructed SMP (Symbolic Manipulation Program), the first modern computer algebra system (SMP was essentially Version Zero of Mathematica).
By
Shingareva, Inna; LizárragaCelaya, Carlos
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In this chapter we consider the most important geometric concepts in a Euclidean space ℝ^{n},where ℝ^{2} represents the two dimensional plane and ℝ^{3}, the three dimensional space.
By
Shingareva, Inna; LizárragaCelaya, Carlos
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Special functions is a set of some classes of particular functions that have attractive or useful properties arising from solutions of theoretical and applied problems in different areas of mathematics.
By
Shingareva, Inna; LizárragaCelaya, Carlos
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In Maple, the integral transforms (e.g., Fourier, Hilbert, Laplace, Mellin integral transforms) can be studied with the aid of the inttrans package.
