By Cesar Perez Lopez
MATLAB Numerical Calculations specializes in MATLAB features to provide you numerical ideas to difficulties you are going to come across on your specialist or scholastic existence. It introduces you to the MATLAB language with functional hands-on directions and effects, permitting you to speedy in attaining your targets. beginning with a glance at simple MATLAB performance with integers, rational numbers and genuine and complicated numbers, and MATLAB's courting with Maple, you are going to remedy equations in MATLAB, and the way to simplify the implications. you will discover how MATLAB accommodates vector, matrix and personality variables, and services thereof. MATLAB is a robust instrument used to outlined, manage and simplify advanced algebraic expressions. With MATLAB you may also paintings comfortably in matrix algebra, applying instructions which let you locate eigenvalues, eigenvectors, determinants, norms and diverse matrix decompositions, between many different beneficial properties. finally, you will see that how one can write scripts and use MATLAB to discover numerical research, discovering approximations of integrals, derivatives and numerical ideas of differential equations.
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Extra info for MATLAB Numerical Calculations
It also allows you to express all kinds of numbers in different bases. info Chapter 2 ■ Integers, Divisibility and Number Systems maple(‘convert(decimal,octal,n)’) or dec2hex(decimal) converts to base 8 (octal) the specified decimal number with n digits of precision maple(‘convert(decimal,hex)’) converts the decimal number specified to base 16 (hexadecimal) maple(‘convert(binary,decimal,binary)’) or bin2dec (binary) converts the specified binary number to decimal maple(‘convert(octal,decimal,octal)’) converts the octal number to decimal maple(‘convert(hexadecimal,decimal,hex)’) or hex2dec (hexadecimal) converts the specified base 16 number to decimal maple(‘convert([a,b,…,c],base,old_base,new_base)’) converts the number whose digits in the old base are: c… ba, to the new base.
In all subsequent calculations involving 2^(1/2) and 3^(1/2) they will be operated on symbolically following the mathematical rules of calculation with radicals. Of course we can also work with decimal approximations of irrational numbers, as we pointed out above. info Chapter 3 ■ Real and Complex Numbers If we use the command maple(‘simplify’), the exact result is obtained. info Chapter 3 ■ Real and Complex Numbers EXERCISE 3-6 Simplify the following irrational expressions by rationalizing the denominators: a) 2 b) 2 3 2 2 3 a c) 3 d) e) 2 4 3 a In these cases of rationalization, the simple use of the command simplify solves the problem.
The commands for working with algebraic numbers are as follows: maple(‘convert(RootOf_expression,radical)’) converts a RootOf expression to a radical expression maple(‘convert(radical_expression, RootOf)’) converts a radical expression to a RootOf expression maple(‘simplify RootOf(expression)’) simplifies the RootOf expression EXERCISE 3-9 a) Convert the following radical expressions to RootOf expressions: i) 2 ii) 3 1 - 2 b) Perform the reverse conversions of (i) and (ii) above.