Mathematics

Download e-book for kindle: Algebraic Combinations in Mathematical Chemistry: Methods by Klin M., Rucker Ch.

By Klin M., Rucker Ch.

Show description

Read or Download Algebraic Combinations in Mathematical Chemistry: Methods and Algorithms PDF

Similar mathematics books

New PDF release: Biomathematik: Mathematische Modelle in der Medizinischen

Die Phänomene in Medizin und Computational lifestyles Sciences lassen sich in wachsendem Maße mit mathematischen Modellen beschreiben. In diesem Buch werden Mechanismen der Modellbildung beginnend von einfachen Ansätzen (z. B. exponentielles Wachstum) bis zu Elementen moderner Theorien, wie z. B. unterschiedliche Zeitskalen in der Michaelis-Menten-Theorie in der Enzymkinetik, vorgestellt.

Extra info for Algebraic Combinations in Mathematical Chemistry: Methods and Algorithms

Sample text

Tr`es bien. Then I can find a by taking cube roots. I also can find b in the same way, or by using b = m/3a. Therefore, x = a − b is the solution to the cubic equation. Am I correct? Well, I substitute x into the original cubic equation and see if it’s true. I could ask Antoine-August to show my analysis to his tutor. He would tell me if I’m doing this correctly. Friday | September 25, 1789 Autumn is slowly making an entrance. The weather is so nice, and the colors of the foliage are changing. After lunch my sisters and I went for a stroll to the Jardin des Tuileries.

Master” — 2012/3/8 — 13:19 — page 35 — #47 ✐ ✐ 1. Awakening 35 What am I missing? I will not sleep well if I do not solve it. I will attempt a different approach. First I see that (a − b)3 + 3ab(a − b) = a3 − b3 . Then, if a and b satisfy 3ab = m, and a3 − b3 = n, then a − b is a solution of x3 + mx = n. Now b = m/3a, so a3 − m3 /27a3 = n, which I can also write as a6 − na3 − m3 /27 = 0. This is like a quadratic equation in a3 , (a3 )2 − n(a3 ) − (m3 )/27 = 0. So, I can solve for a3 using the formula for a quadratic equation.

Is this correct? Oh, how can I be certain? If a polynomial is a mathematical expression involving a series of powers in one or more variables multiplied by coefficients, then I can write a polynomial in one variable with constant coefficients as: an xn + · · · + a3 x3 + a2 x2 + a1 x + a0 = 0. The highest power in the polynomial is called its order. And it makes more sense if I write the polynomial as: x3 + 2x2 + 3x + 5 = 0. ✐ ✐ ✐ ✐ ✐ ✐ “master” — 2012/3/8 — 13:19 — page 20 — #32 ✐ ✐ 20 Sophie s' Diary Then I say that this is a third-order polynomial.

Download PDF sample

Algebraic Combinations in Mathematical Chemistry: Methods and Algorithms by Klin M., Rucker Ch.


by Christopher
4.2

Rated 4.72 of 5 – based on 11 votes