https://cienciaprogramada.com/series/from-symbol-to-number/ Recent content in From Symbol to Number on Ciência Programada Hugo -- gohugo.io en contato[@]cienciaprogramada.com.br (Francisco Bustamante) contato[@]cienciaprogramada.com.br (Francisco Bustamante) © 2026 Francisco Bustamante Wed, 28 Oct 2026 00:00:00 +0000 https://cienciaprogramada.com/2026/10/optimization-scipy/ Wed, 28 Oct 2026 00:00:00 +0000 contato[@]cienciaprogramada.com.br (Francisco Bustamante) https://cienciaprogramada.com/2026/10/optimization-scipy/ Differentiating and setting the result to zero solves textbook optimization. With several variables, constraints, or a function without a tractable derivative, that calculation breaks down. We will see minimize, SLSQP and bounds from scipy.optimize, local minima, and global search with differential_evolution. https://cienciaprogramada.com/2026/10/differential-equations-scipy/ Wed, 21 Oct 2026 00:00:00 +0000 contato[@]cienciaprogramada.com.br (Francisco Bustamante) https://cienciaprogramada.com/2026/10/differential-equations-scipy/ The classic pendulum period formula only holds for small oscillations, and the exact equation has no closed-form solution. With SciPy’s solve_ivp, we measure the real period and solve stiff systems, Lotka-Volterra, falling with drag, and consecutive reactions. https://cienciaprogramada.com/2026/10/numerical-integration-scipy/ Wed, 14 Oct 2026 00:00:00 +0000 contato[@]cienciaprogramada.com.br (Francisco Bustamante) https://cienciaprogramada.com/2026/10/numerical-integration-scipy/ The Gaussian function has no elementary antiderivative, and that is a theorem of Liouville. When the antiderivative does not exist, or all you have is a table of measurements, the way forward is numerical: quad, trapezoid and Simpson, from scipy.integrate, with the care each one demands. https://cienciaprogramada.com/2026/10/numerical-derivatives-scipy/ Wed, 07 Oct 2026 00:00:00 +0000 contato[@]cienciaprogramada.com.br (Francisco Bustamante) https://cienciaprogramada.com/2026/10/numerical-derivatives-scipy/ Is the reactor temperature rising too fast? The question is a derivative, but all we have are numbers in a table. We will see finite differences, numpy.gradient and scipy.differentiate, and why shrinking the step does not always improve the derivative, because of rounding and noise. https://cienciaprogramada.com/2026/09/curve-fitting-numpy/ Wed, 30 Sep 2026 00:00:00 +0000 contato[@]cienciaprogramada.com.br (Francisco Bustamante) https://cienciaprogramada.com/2026/09/curve-fitting-numpy/ Experimental data rarely falls on a curve. We will see how NumPy fits polynomials to noisy data, what SymPy cannot do, why extrapolating is dangerous, and why Runge’s phenomenon comes from equally spaced nodes, not from high degree. https://cienciaprogramada.com/2026/09/polynomials-numpy/ Wed, 23 Sep 2026 00:00:00 +0000 contato[@]cienciaprogramada.com.br (Francisco Bustamante) https://cienciaprogramada.com/2026/09/polynomials-numpy/ Stored in float64, the coefficients of Wilkinson’s polynomial no longer return the roots 1 to 20: two of them become a complex pair. Before getting there, we look at roots, derivatives, integrals and division with numpy.polynomial, and at the coefficient-order trap. https://cienciaprogramada.com/2026/09/chemistry-engineering-numerical-equations/ Wed, 16 Sep 2026 00:00:00 +0000 contato[@]cienciaprogramada.com.br (Francisco Bustamante) https://cienciaprogramada.com/2026/09/chemistry-engineering-numerical-equations/ From the pH of a weak acid to the volume of a real gas and the friction factor of a pipe: three equations that chemistry and engineering use every day and that only have a useful numerical solution. We solve all three with brentq and numpy.roots and rebuild the Moody chart. https://cienciaprogramada.com/2026/09/orbits-trajectories-physics/ Wed, 09 Sep 2026 00:00:00 +0000 contato[@]cienciaprogramada.com.br (Francisco Bustamante) https://cienciaprogramada.com/2026/09/orbits-trajectories-physics/ Where is Halley’s Comet on any given date? The answer requires solving Kepler’s equation, which has no closed form. With SciPy’s newton and brentq, we locate the comet, make the law of areas visible, and compute the range of a projectile with air resistance. https://cienciaprogramada.com/2026/09/numerical-equations-scipy/ Wed, 02 Sep 2026 00:00:00 +0000 contato[@]cienciaprogramada.com.br (Francisco Bustamante) https://cienciaprogramada.com/2026/09/numerical-equations-scipy/ In Kepler’s equation, the unknown appears both inside and outside a sine, and no algebra isolates it. For cases like this, SciPy approximates the root. We will see bisection and brentq, Newton’s method and why it can fail, and nonlinear systems with fsolve and root. https://cienciaprogramada.com/2026/09/from-symbol-to-number/ Tue, 01 Sep 2026 00:00:00 +0000 contato[@]cienciaprogramada.com.br (Francisco Bustamante) https://cienciaprogramada.com/2026/09/from-symbol-to-number/ Most equations, integrals, and differential equations in real problems have no closed-form solution, and SymPy can’t solve them. This 13-article series shows how NumPy and SciPy tackle these problems: roots, polynomials, numerical calculus, optimization, and FFT.