Download Analysis for Computer Scientists: Foundations, Methods, and by Alexander Ostermann, Michael Oberguggenberger PDF

By Alexander Ostermann, Michael Oberguggenberger

ISBN-10: 0857294466

ISBN-13: 9780857294463

Arithmetic and mathematical modelling are of principal value in desktop technological know-how, and for this reason it's important that machine scientists are conscious of the most recent strategies and techniques.

This concise and easy-to-read textbook/reference provides an algorithmic method of mathematical research, with a spotlight on modelling and at the functions of research. absolutely integrating mathematical software program into the textual content as an enormous part of research, the e-book makes thorough use of examples and reasons utilizing MATLAB, Maple, and Java applets. Mathematical idea is defined along the elemental options and strategies of numerical research, supported by means of desktop experiments and programming routines, and an in depth use of determine illustrations.

Topics and features:

* completely describes the basic techniques of research, masking genuine and intricate numbers, trigonometry, sequences and sequence, features, derivatives and antiderivatives, certain integrals and double integrals, and curves
* presents summaries and routines in every one bankruptcy, in addition to computing device experiments
* Discusses very important functions and complicated themes, equivalent to fractals and L-systems, numerical integration, linear regression, and differential equations
* offers instruments from vector and matrix algebra within the appendices, including additional details on continuity
* contains definitions, propositions and examples during the textual content, including an inventory of correct textbooks and references for extra reading
* Supplementary software program could be downloaded from the book’s website at www.springer.com

This textbook is vital for undergraduate scholars in computing device technology. Written to in particular tackle the desires of computing device scientists and researchers, it's going to additionally serve pros seeking to bolster their wisdom in such basics super good.

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Read or Download Analysis for Computer Scientists: Foundations, Methods, and Algorithms (Undergraduate Topics in Computer Science) PDF

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Extra info for Analysis for Computer Scientists: Foundations, Methods, and Algorithms (Undergraduate Topics in Computer Science)

Example text

5 Exercises 33 4. , n i3. i=1 Check your code against the direct formula n i=1 i3 = n(n + 1) 2 2 for different values of n, such as n = 3, n = 30, and n = 300. 5. Write an R program that counts the number of zeros of a given vector v ∈ Rn . Apply the program to an example vector as countzeros(matrix(c(4,0,3,0,0,3,-4,0,5,0),ncol=1)) 6. Write a program that finds the smallest element of a given vector v ∈ Rn . Apply the program to three different vectors as findminimum(matrix(c(4,0,3,0,0,3,-4,0,5,0),ncol=1)) findminimum(matrix(c(4,2,3,5,6,3,4,1,5,2),ncol=1)) findminimum(matrix(c(-4,-2,-3,-5,-6,-3,-4,-1,-5,-2),ncol=1)) Check that your program works correctly with −4, 1, and −6 outputs, respectively.

In other words, if the first input is smaller, then the program automatically switches the inputs in the first call of the recursion. In the program above, the recursion is controlled by an if statement. In any call of this program, if the smaller integer is zero, then the output is the other integer (see line 03). Note that, as a recursion continues and integers are subtracted from each other, this condition occurs eventually, leading to the termination of the recursion. 2 Example: Lowest Common Multiple The lowest common multiple (LCM) of two positive integers i and j is defined as the smallest integer that is the multiple of both i and j .

2 Nested Loops 23 We have seen different programs to calculate two different norms of a given vector. At this stage, the following question may arise: Is there any better way to calculate these norms instead of writing these programs? In fact, the answer is yes. For example, consider the following command for the ∞-norm: max(abs(v)) It is just a single line, and there is even no need to put this command in a function format. Alternative, if v is correctly defined as a column vector, using norm(v,"I") also works.

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