diff.cpp

#include <iostream>
#include <cmath>
#include <vector>

using namespace std;

int main() {
    vector<pair<double, double>> f;
    f.push_back(pair<double, double>(1.0, 0.0));
    f.push_back(pair<double, double>(1.5, 0.40547));
    f.push_back(pair<double, double>(2.0, 0.69315));
    f.push_back(pair<double, double>(2.5, 0.91629));
    f.push_back(pair<double, double>(3.0, 1.0986));

    for (auto & p : f) {
        cout << p.first << "\t" << p.second << endl;
    }

    double x1 = f[2].first;
    double y1 = f[2].second;

    double x0 = f[1].first;
    double y0 = f[1].second;

    double x2 = f[3].first;
    double y2 = f[3].second;

    cout << "first order:" << endl;
    cout << "\tleft:\t y'(t) = "    << (y1 - y0) / (x1 - x0) << endl;
    cout << "\tright:\t y'(t) = "   << (y2 - y1) / (x2 - x1) << endl;
    cout << "\tcenter:\t y'(t) = "  << (y2 - y0) / 2 / (x2 - x0) << endl;

    cout << "second order:" << endl;
    // cout << "\tleft:\t y'(t) = "    << (y1 - y0) / (x1 - x0);
    // cout << "\tright:\t y'(t) = "   << (y2 - y1) / (x2 - x1);
    cout << "\tcenter:\t y''(t) = "  << (y2 - 2*y1 + y0) / pow((x2 - x0), 2) << endl;
    return 0;
}