- How is the value of $\\pi$ ( Pi ) actually calculated?
When I was a child I was taught $\\pi$ (Circumference Diameter) is an irrational number and can be approximated to $22 7$ but $= 3 (142857)(\\ldots)$ But where does this value comes from? In
- How to prove Eulers formula: $e^{it}=\\cos t +i\\sin t$?
A basic idea is this: note that 1 00001x ≈ 1 + 00001x, when x is small (For example, 1 000015 ≈ 1 00005; check this!) Now, assume this is sill true when x is complex! This helps give us a way to define complex exponentiation Of course, this is far from rigorous, but it's something And it works: 1 00001i = 99999999995… + 00000999995…i, whereas our approximation says that it should be
- How to prove the divisibility rule for $3\\, $ [casting out threes]
The divisibility rule for 3 is well-known: if you add up the digits of n and the sum is divisible by 3, then n is divisible by three This is quite helpful for determining if really large numbers are multiples of three, because we can recursively apply this rule: 1212582439 → 37 → 10 → 1 3 ∤ 1212582439
- Explanation and proof of the 4th order Runge-Kutta method
There are many Runge–Kutta methods The one you have described is (probably) the most popular and widely used one I am not going to show you how to derive this particular method – instead I will derive the general formula for the explicit second-order Runge–Kutta methods and you can generalise the ideas In what follows we will need the following Taylor series expansions
- Thì quá khứ tiếp diễn (Past continuous tense) - Công thức, ví dụ và bài tập
Thì quá khứ tiếp diễn (Past continuous tense) – Công thức, cách dùng, dấu hiệu và bài tập Ngữ pháp luôn là một trong khó khăn ban đầu đối với những người bắt đầu học tiếng Anh Thì quá khứ tiếp diễn là một trong những chủ điểm ngữ pháp bạn không thể bỏ qua nếu muốn học giỏi ngôn ngữ này Hiểu
- Formula for the simple sequence 1, 2, 2, 3, 3, 4, 4, 5, 5,
Is it possible to create a simple formula without piecewise it into odd and even? Sorry for my bad English
- What does the dx mean in an integral? [duplicate]
I know dy dx for example means "derivative of y with respect to x," but there's another context that confuses me You will generally just see a dx term sitting at the end of an integral equation an
- linear algebra - Determine if vectors are linearly independent . . .
Firstly, you are to arrange the vectors in a matrix form the reduce them to a row-reduced echelon form (If the last row becomes all zeros then it is linearly dependent, but if the last row isn't all zeros then it is linearly independent) Let's get to it now Arranging the vectors in matrix form we have :
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