# 1st

1. ### GÃ¶delâ€™s 1st theorem is meaningless

GÃ¶delâ€™s 1st theorem is meaningless http://gamahucherpress.yellowgum.com/wp-content/uploads/GODEL5.pdf GÃ¶delâ€™s 1st theorem a) â€œAny effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. In particular, for any consistent...
2. ### 1st order system of ODEs - don't understand intro

The chapter I'm reading is actually about numerics but this introductory material is calculus I think: http://i.imgur.com/HhFhhqF.png I don't understand how/why they obtain (2).. Okay, it is possible to say y_1 = y', y_2 = y'', etc., but why would you? Doesn't that result in a different...
3. ### Ordered set (1,2)<<(3,4). But how to write if 1st set contains a single object only?

To denote the relation between sets, I can write (1,2)<<(3,4) to say that each object in the first set is smaller than each object in the second set. Or does it only mean that 1<3 and 2<4? Now my questions: How do I write the relation between set {1} and set (3,4)? How do I write the...
4. ### Rewriting second order to 1st order diff eqn

Hi I need to apply the ralston 2nd order method to find an approximate value for y(2) of the following differential equation: xy'' - y' = x^2 + x With initial conditions y(1) = 1 and y'(1) = 5 So far I have done z1=y, z2=y' and z3=y'', resulting in the equation xz2' = x^2 + x + z2...
5. ### Thermodynamics 1st law

13. A can filled with a high-pressure gas has a balloon attached over the top. What happens to the temperature of the gas inside the can as you allow the gas to expand into the balloon? For this it needs to be explained in terms of Q, W, and (delta)U Q = heat applied. W = work...
6. ### 1st Century Calendar.

Is it possible to trace the 1st Century Calendar mathematically?. I.e Year 1 to Year 100 Example Year 1 ---------- 01-01-0001- Jan 1,Year 1 02-01-0001- Jan 2, Year 1 Jan 1, Year 1 was a Sunday or Monday?. Thanks & Regards, Prashant S Akerkar
7. ### 1st Century Calendar.

Is it possible to trace the 1st Century Calendar mathematically?. i.e. Year 1 to Year 100. Thanks & Regards, Prashant S Akerkar
8. ### Fractions & smart pirates - Fun Educational Math Game for kids

Virtual Space is proud to announce the release of Fractions & Smart Pirates 1.3 for iOS and Android devices, offering a fun and easy way to learn fractions with the Caribbean Pirates. Recognizing and Comparing Fractions, Equivalent fractions, adding fractions - If you're struggling with fraction...
9. ### Parametric Equations 1st & 2nd derivative.

The instructions are to find dy/dx and d^2y/dx^2, and find the slope of concavity at the given value of the parameter. Leibniz notation confuses me so I won't use that. x=4cos(Î¸), y=4sin(Î¸) and Î¸=Ï€/4 1. First derivative. x'=-4sin(Î¸) y'=4cos(Î¸) 2. The ratio. y'/x'=...
10. ### H&B's 2nd axiom for successor function contradicts 1st?

Hi all, I'm reading Charles Petzold's "The Annotated Turing" for fun, and I'm no mathematician, so this might be a silly question. I have a question about page 226, where Hilbert and Bernay's axioms for the successor function are defined. Specifically, the second axiom: (ÆŽx)(y)-S(y,x) I...
11. ### 1st order theories

Can we have a 1st order theory in physics,give an example
12. ### 1st year math - Riemann zeta function & series

the riemann zeta function is defined for p > 1 as \zeta(p) : = \displaystyle \sum_{n=1}^\infty \dfrac{1}{n^p} prove \displaystyle \sum_{p=2}^\infty [\zeta(p) - 1] = 1 by considering \displaystyle \right | 1 - \sum_{p=2}^P \sum_{n=2}^N\dfrac{1}{n^p} \left | < \epsilon so my thoughts: as...
13. ### Differentiating Trigonometric Functions from 1st Principles

With this question I have arrived at the correct answers provided in the text book, as shown in the attempt. However, when I subbed \pi into the solution, without converting to 180^{\circ}, I arrived at the answers shown at the bottom of the post. As you can see, (i) & (iii) are very close to...
14. ### 1st Fund. Theorem of Calc. Misunderstanding.

I'm trying to apply the first fundamental theorem of calculus to a couple problems but it's not quite working. I'm using the same method on both and only getting one right. The other is off by a factor of -1. Perhaps my problem is in misunderstanding the question? I'll post the questions...
15. ### this is the 1st limit problem from my collection

evaluate \lim_{x\to\infty}x[(1+\frac{1}{x})^x-e] To clarify, in this limit as \{x\to\infty}, we have a product of x and (1+\frac{1}{x})^x-e where e is the irrational number 2.718281828....
16. ### a new member posting very 1st integral problem

Hi everyone, I am a new member,kevinrhsp, on this forum. My friend, davedave, recommends me to get on this forum now. I heard from him that it didn't take you guys long to solve his challenging integral. It's good to have so many bright math people gathering up on this forum. So, we can share...
17. ### here comes the 1st challenging integral

I posted this challenging integral on another forum two years ago. It captured a lot of people's attention and discussion. They came up with different ways of analyzing it. I hope that it will spark the same level of interest on this forum. Here is the challenging integral. evaluate...
18. ### 1st derivative test

For the following function, fill in the table to find where the function is increasing or decreasing. y = f(x) = x^(2) + 6x + 10 f ' (x) = 2x + 6 open interval -infinity<x<0 0<x<+infinity Test # -2 1 sign of f '(x)...
19. ### 1st order diff equations

The Standard form of a 1st order linear differential equation is dy/dx + P(X)Y = Q(X) Put each of the following 1st order linear differential equations into Standard Form and determine P(X) and Q(X) (a) dy/dx + x^2 y = 3 sin (x) P(X) = ? Q(X) = ? (b) 5dy/dx + x^2 = x...
20. ### Transform 2nd order ODE to two 1st order ODE using matrices

Hey guys, got a homework problem: Transform the given 2nd order initial value problem into an initial value problem of two 1st order equations by letting x_1 = u and x_2 = u' and write it in matrix form: x' = Ax + b, x(t_0) = x_0. (No need to solve!) u'' + 0.25u' + 4u = 2cos(3t) , u(0) = 1...