# euler

1. ### Matlab Plotting Euler Iteration Against Exact Solution how to Set Initial Condition

Hi I have the following code to plot an approximation using Euler's iteration against the exact value of the function. I have used x and y for time and population when coding the Euler iterations and t and m for time and population when plotting the exact function. I can't work out how to...
2. ### Integral 1/sqrt(x^2+1) dx using Euler substitution

So I've seen some options on the internet, but I have this substitution x^2 + 1 = t^2-2tx+x^2 and you get x = (t^2-1)/2t, x + 1 = (t^2-1)/2t + 1 and if we call this function e(t) for example, dx is now equal to e(t) derivative. But how to proceed from here?
3. ### clothoid (euler spiral) between 2 arcs

Hello I need to calculate coordinates along a polyline made up of lines, arcs (of circles) and transition spirals (clothoids). The general case is line-clothoid-arc-clothoid-line (see attachment A1). The coordinates of the start and end points of each entity are known, the radius R of the...
4. ### Clothoid (Euler Sprial) between 2 arcs

Hello I need to calculate coordinates along a polyline made up of lines, arcs (of circles) and transition spirals (clothoids). The general case is line-clothoid-arc-clothoid-line (see attachment A1). The coordinates of the start and end points of each entity are known, the radius R of the...
5. ### Euler's Iteration Scheme

Euler's Iteration I understand the idea of plotting points at very small intervals to approximate the function however don't understand how to use the formula. I have been given an ODE of the form dy/dx and had to solve for an exact solution. I can see that my lecturer is getting us to show...
6. ### Euler's Method

I have come across the following question in my study for the exam, and I was wondering if I was on the right track. The question is : "Use Euler's method with three steps of size h = 1 to approximately solve the differential equation dy/dx=x(1+y^2) on the interval 1 less than or equal to x less...
7. ### Finding approximation using Euler's method

The answer for Question #1 is solved. I just need to know wether I did Question #2 right, specifically the "Compare y2 with the exact value of y you found in a". This is how I got the exact values. I plugged in dx=0.03 inside the solution that I found in Question #1. To find the second exact...
8. ### Euler's Method. Finding exact solution

How can I isolate y on the left side?
9. ### Euler's method

Why is it that when you take the integral of y'/y it equals to ln(y)?
10. ### Improved Euler's Method

Hello, I am practicing an Improved Euler's question, and I don't have the solution. I looked online for a calculator but I couldn't find any. If you are bored or looking for some fun, can you (someone) please check my work ;D? I really do question my ability to use a calculator. As...
11. ### Euler Lagrange equation of motion

Hi I have the Lagrangian where H(r) is the height \mathcal{L}=\frac{1}{2}m\left(\left(1+\left(\frac{\partial H}{\partial r} \right)^{2} \right)\dot{r}^{2}+r^{2}\dot{\theta} \right)-mgH and \frac{\partial\mathcal{L}}{\partial\dot{r}}=m\dot{r}+m\dot{r}\left(\frac{\partial H}{\partial...
12. ### Leonhard Euler

I must write an essay on the mathematical work of Leonhard Euler for an exam that lasts for one hour. The main content of the essay must be mathematical discoveries or mathematical works. I would appreciate suggestions, e.g. appropriate internet research websites, suggested word count, etc.
13. ### Finding Critical Numbers for a derivative with euler's number

This is a problem I came across in my Calculus textbook: g(x)=e^(-x)+e^(3x) I am asked to find the open intervals over which this function increases and decreases. The original function isn't undefined for any value of x so I proceeded to find the derivative: g'(x)=3e^(3x)-e^(-x) For the...
14. ### Euler's Identity problem

Euler's Identity problem (Solved) My problem goes as follows: Use Euler's Identity to find A and B so that (cos(x))^3 = A*cos(3x) + B*cos(x) Any help would be greatly appreciated!! I have no clue where to start.
15. ### Manipulating Derivatives: Euler's Chain Rule / Cycle Rule

Hi, I am just starting a physical chemistry course and I have never done multivariable calculus (although I understand derivatives and integrals for single variable calculus well and understand partial derivatives). The course requires very basic MV calculus and my professor introduced the...
16. ### Does a Euler Circuit have to be a connected graph?

I'm thinking the answer is yes, but not really getting much clarification on the net. My assumption is that it would have to be, otherwise you can't really make your way around the 'whole' thing once if it is disconnected - then you would be going around 'two' different circuits. Is this...
17. ### Implicit Euler Scheme and stability

Find the fixed points of the implicit Euler scheme $$y_{n+1}-y_{n}= hf(t_{n+1},y_{n+1})$$ when applied to the differential equation $y'=y(1-y)$ and investigate their stability? => implicit Euler scheme $$y_{n+1}-y_{n}= hf(t_{n+1},y_{n+1})$$...
18. ### Euler Car Depreciation Calculus

Say a car's value drops 20% annually. In ﬁve years estimate the percentage of the original vehicle value that is retained. Assume you bought this vehicle at the time t = 0 (assume the mileage of x = 0 km) for \$ 20,000. Assume you drive about 15,000 km annualy (assume uniform driving habits...