Differential Equations, Part 3: Elimination of Arbitrary Constants with a Single Variable in Two Factors
Par. 15, 16 has starvation, disease, America. The variable as two factors adds complexity but it can be handled by equating the elements of the vectors to zero at L10. A theorem makes it easier.
Par.18 has the suns rotational energy. Before we can raise a 4 x 4 matrix to a complex power, we must find its characteristic polynomial, which has, as the solutions to its roots, the eigenvalues of the matrix.
The Bible bugs me is at paragraph 14. Without a calculator you can approximately locate real roots, but the tangent lines of Newton's method will find them very quickly and very precisely.
John, lies and accuracy at par. 13. It required five hubs( grouped below) to derive this formula, but with it no term of the FS is beyond your reach. In fact we found the trillionth term in this hub.
Pursuing your dream at par. 8. The diagonal representation matrix, is a powerful engine of the matrix. With it you can raise a matrix to a very high power, or rational power, or a complex power.
A message from God begins at par. 7. Finding the inverse matrix is relatively easy for a 2x2 matrix, but it looks complicated in this hub because we need to retain the exact values for the final hub, A Formula for the...
Going to heaven? begins at par. 10. DEs finds functions. This hub works backwards. You are given a function, and you find a differential equation associated with it.
The Bible and sophistry begins at par. 10. The differential operator is a powerful mathematical technique. It enables one to solve differential equations very quickly under the right conditions.
Par. 15 : What does the UCG believe to be our destiny? A graphing calculator, and synthetic division can greatly expedite the factoring of any polynomial. Synthetic division can quickly give you the value of f( x),...
Salvation lost begins at par. 5. Anyone who has studied calculus knows the derivative of the exponential function, base e, but this hub gives two different derivations of it.
God, nuts, and bolts begin at par. 6. This hub gives the derivation of the derivative of a logarithmic function, and it gives a formula to find the derivative of a logarithmic function to any base.
Tornadoes, the ultimate manufacturer, begins at par. 8. This hub uses limits to define e, and it explains why 1 raised to an infinite power may not be anywhere near one when limits are involved.
Numbers and the Bible begins at par. 5. Euler's formula can be used to find the logarithm of a complex number. This hub shows you how it is done.
A RESULT OF WORMWOOD'S SUCCESS: Paragraph 3 of Intention of Demons contains these three sentences: "How do we prevent consistent love---in all its forms---from becoming as intrinsic part of their character, and of...
Assumptions about God at par. 12. It is not possible to take the logarithm of a negative number; however, if you are willing to leave the realm of real numbers and enter the field of complex numbers . . . well then, ...
God is not willing that any perish begins at par. 12. Inverse trigonometric functions would be difficult to integrate if you did not first convert them into their algebraic equivalent. After that--in many...
The Bible, not my opinion, begins at par. 12. The eigenvalues determine the eigenvectors, and the eigenvectors are the structures upon which the eigenvalues, the essence of a matrix, are built. The eigenvectors are the...
Par. 8 begins, Is God's love unconditional? Collectively the eigenvectors of a matrix represent a very powerful mathematical machine. This introduction will give you a good idea of how eigenvectors are determined, and...
DNA, A WITNESS FOR GOD IN DIVERSE WAYS 1. When I began doing the necessary research for this hub I came to the conclusion that I may have to title it, "DNA, A Witness for God, Part 1 of about 153." For example, Its 3...
The improbability of structure by chance begins at par. 9. Once you calculate the eigenfunction of a matrix, then find the roots( X values that give Y = 0) of that function, then those roots are the eigenvalues, which...
God's limits at par. 20. Math limits are very fascinating mathematical entities. Where you usually run into trouble is when the denominator approaches zero. If you can mathematically cancel that out with, for example,...
Information stored within the structure of space is at par. 21. This is the first step in finding the millionth or trillionth term of the Fibonacci sequence. This hub will take you to any term that your calculator can...
PART 2 OF HUB 10: 1. This hub is part 2 of hub 10( How to Generate Funds . . . ). WE HAVE 2 BILLION HOURS PER DAY OF LATENT TIME: 2. Americans have 2,000,000,000 hours of spare time on their hands, and that...
CHRISTIAN HEADS UP: 1. All math hubs have something about God in their final paragraph. In this hub it is actually the last 3 paragraphs, and they address how God's questions are over our heads( beyond our...
Fractal Geometry is mentioned in God's Word, the Bible? Absolutely! This hub presents a powerful argument to convince you that not only is Fractal Geometry mentioned in the Bible, but to this day we still have no idea...
God and America at par. 16. Problems involving Lagrange multipliers can be very complex and hard to solve. This hub gives a simple introduction into the basics of how they work, and what they are.
Finding the determinant and inverse of a matrix is essential in doing calculations using matrices. With them you can solve simultaneous equations, find the eigenvalues, and they are used in the process to raise a matrix...
You can easily solve two simultaneous equations without using matrices. Three is harder but it can be done. But 4 or more? Well, then you want to use matrices. Matrices are very powerful mathematical tools, and when...
A DESIRE TO SERVE 1. I know someone who, in my opinion, is a strong Christian, and wants to minister( Mt. 25:40) for Christ full-time but he cannot do that yet because he must keep the job that provides his family a...
One proof of God's omniscience is the informational content and density stored within the geometric stucture of DNA.
THE BIBLE: IT PRESENTS THE MOST ADVANCED SCIENCE EVER 1. We need no more proof than this that the Bible is God's Word; nevertheless, God gave us more proof. Long before our scientists have ever thought of it, or our...
THE NUMBERS IN PARENTHESES 2. The numbers enclosed within parentheses refer to footnotes giving pertinent documentation, calculations and annotations. They may also direct you to additional hubs( my own and others),...
Yes, a clear conscience, Pear Head, and my coffer pot are mentioned in the 1st paragraph, but if you do not laugh during the 3rd and 4th paragraphs, then you are in a coma.
There are many different proofs that confirm the Bible is God's Word. This hub focuses on one of the major proofs: consistently predicting the future, and amazingly you can see it played out right now.