📘 numerical analysis

1. **State the problem:** We are given values of a function $f(x)$ at points $x = 0.12, 0.16, 0.20, 0.24, 0.28, 0.32$ and corresponding function values $f(x) = 0.6144, 0.6256, 0.64

1. **State the problem:** We are given values of a function $f(x)$ at points $x = 0.12, 0.16, 0.20, 0.24, 0.28, 0.32$ and corresponding $f(x)$ values. We need to find $f(0.14)$ usi

1. **State the problem:** We are given values of a function $f(x)$ at points $x = 3, 3.2, 3.4, 3.6, 3.8, 4.0$ and need to find the first derivative $f'(3)$ and the second derivativ

1. The problem is to find the Lagrange polynomial that interpolates a given set of points. 2. The formula for the Lagrange polynomial of degree $n$ given points $(x_0,y_0), (x_1,y_

1. **State the problem:** We want to find the Lagrange interpolation polynomial for the points $(0,3)$, $(1,3.19)$, $(2,3.16)$, and $(2.57,2.95)$. This polynomial will pass exactly

1. Zadatak je da odredimo Njutnov interpolacioni polinom za funkciju zadatu tabelarno tačkama (1,1), (2,5), (3,17) i (5,89). 2. Njutnov interpolacioni polinom koristi formulu:

1. Zadatak je da odredimo Njutnov interpolacioni polinom za funkciju zadatu tabelarno tačkama (1,1), (2,5), (3,17) i (5,89). 2. Njutnov interpolacioni polinom se gradi pomoću difer

1. The problem is to verify the correctness of the given proof showing stability estimates for the bilinear form $a(v,v)$ in three cases: SIPG ($\theta=-1$), IIPG ($\theta=0$), and

1. **Problem Statement:** Verify if the given proof establishes the stability of the Interior Penalty Discontinuous Galerkin (IPDG) bilinear form $a(\cdot,\cdot)$ defined on a disc

1. **Problem:** Solve the system of equations using two iterations of Jacobi's iteration method: $$\begin{cases} 10x + y + z = 12 \\ x + 10y + z = 13 \\ x + y + 10z = 14 \end{cases

1. **Problem Statement:** We are given height data of a road at distances 0, 2, 4, and 6 km and need to:

1. **Problem Statement:** We are given population data of a town for the years 1980, 1990, 2000, 2010, and 2020 (in thousands): 15, 30, 47, 53, and 65 respectively. We need to find

1. **Problem Statement:** Find the population of the town in the year 2003 using the Gauss backward difference formula given the population data for years 1980, 1990, 2000, 2010, a

1. **State the problem:** Given data points $(1,1)$, $(2,5)$, $(7,5)$, and $(8,4)$, find the Newton's divided difference interpolation polynomial $f(x)$ and evaluate $f(6)$. 2. **F

1. **Problem Statement:** Explain the finite differences method with an example. 2. **What is the Finite Differences Method?**

1. **Problem Statement:** Use Newton's Backward Interpolation formula to find $f(45095)$ given the data points: $(45000, 9.648583)$, $(45020, 9.648696)$, $(45040, 9.648810)$, $(450

1. **Problem Statement:** Find the value of $y$ at $x=1.75$ using Gauss's forward interpolation formula given the data points:

1. **Énoncé du problème :** Nous avons une méthode de Runge–Kutta définie par le tableau de Butcher donné. Il faut décrire les méthodes intermédiaires (M_2) et (M_3), déterminer le

1. **Énoncé du problème :** Nous avons une méthode de Runge–Kutta définie par le tableau de Butcher donné. Il faut décrire les méthodes intermédiaires (M_2) et (M_3), déterminer le

1. **Problem Statement:** Given the values of $x$ and $y$, construct the forward difference table and find the values of $\Delta^2 f(5)$ and $\Delta^3 f(10)$.\n\n2. **Given Data:**

1. **Problem Statement:** Find $f(22)$ using the Gauss forward interpolation formula given the data points: $x$: 20, 25, 30, 35, 40, 45