Discovering Mathematics: A Problem-Solving Approach to by Jiří Gregor

Posted by

By Jiří Gregor

Discovering arithmetic: A Problem-Solving method of research with Mathematica and Maple presents a optimistic method of mathematical discovery via cutting edge use of software program know-how. Interactive Mathematica and Maple notebooks are critical to this books’ application as a realistic device for studying. Interrelated suggestions, definitions and theorems are hooked up via links, guiding the reader to numerous dependent difficulties and highlighting a number of avenues of mathematical reasoning.

Interactivity is extra better throughout the supply of on-line content material (available at extras.springer.com), demonstrating using software program and in flip expanding the scope of studying for either scholars and academics and contributing to a deeper mathematical realizing.

This publication will attract either ultimate 12 months undergraduate and post-graduate scholars wishing to complement a arithmetic path or module in mathematical problem-solving and research. it is going to even be of use as complementary interpreting for college kids of engineering or technological know-how, and people in self-study.

Show description

Read Online or Download Discovering Mathematics: A Problem-Solving Approach to Mathematical Analysis with MATHEMATICA® and Maple™ PDF

Similar mathematical analysis books

Understanding the fast Fourier transform: applications

This can be a educational at the FFT set of rules (fast Fourier rework) together with an creation to the DFT (discrete Fourier transform). it truly is written for the non-specialist during this box. It concentrates at the real software program (programs written in uncomplicated) in order that readers may be capable of use this expertise after they have complete.

Acta Numerica 1995: Volume 4 (v. 4)

Acta Numerica has demonstrated itself because the major discussion board for the presentation of definitive studies of numerical research issues. Highlights of this year's factor contain articles on sequential quadratic programming, mesh adaption, unfastened boundary difficulties, and particle tools in continuum computations.

Extra info for Discovering Mathematics: A Problem-Solving Approach to Mathematical Analysis with MATHEMATICA® and Maple™

Example text

E. Fn+2 = Fn+1 + Fn . (i) If gcd(Fm+1 , Fm ) = s > 1 then all Fn should be divisible by s, which is evidently wrong. PI 52 1. For any given integer m divide the interval (0, 2π) into m subintervals of equal length 2π/m. 2. Considering numbers k mod 2π , k = 1, 2, . . , m + 1, show that two of them belong to the same subinterval of length 2π/m. 3. Since π is not rational, all integer multiples of the difference of these two numbers (still mod 2π ) form a set, which has the following property: The distance from any point of the interval (0, 2π) to some point of this set is at most 1/m.

Periodicity in the behavior of various dynamical systems is the theme of P 14 – P 24. Compare results obtained for linear differential and difference equations. It is also recommended to formulate and solve actual examples for each of the problems. P 20 gives a simple outlook to the vast area of periodical motions of nonlinear systems. – Some basic examples of Fourier series are given in P 09, P 10, P 11. – More involved cases of the periodicity concept are dealt with in P 08, P 25, P 26, P 27 and periodicity of two variable sequences is a topic in P 28 – P 36.

Ii) What if only one of them is convergent? (iii) Can it happen that none of them is convergent? Concepts 35 Hint: Recall the basic theorems. I 08 •• ↓ PI 08 Consider a sequence {xn } with limn→∞ xn = A and the sequence yn = Show that limn→∞ yn = A. I 09 • ↓ I 09 x1 +x2 +···+xn . n ↑ I 08 Consider a sequence {xn } of positive numbers with limn→∞ xn = A and the sequences zn = √ n x 1 x 2 . . xn , wn = n 1 x1 + 1 x2 + ··· + 1 xn . Find limn→∞ zn and limn→∞ wn , if A > 0. Hint: Consider log zn and I 10 •• 1 wn .

Download PDF sample

Rated 4.42 of 5 – based on 16 votes