Python Programming
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Python for Science and Maths › Solving EquationsChapter 2Maths by Computer
Let the computer do the heavy maths: find roots, solve systems of equations, and work out derivatives and integrals.
Part of Python Programming · Science and Maths (chapter 2)
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Solving Equations
Many equations in science have no formula for their solution. In this course the computer solves them. You find a bracket with a change of sign, write the bisection method, and then Newton's method, which doubles the number of correct digits at every step, and learn when each of them fails. You work with polynomials in NumPy, with polyval, roots and polyfit, fit a straight line to measurements and judge the fit, and solve systems of linear equations with matrices, including a circuit with three unknowns. A project uses brentq and curve_fit from SciPy to fit the decay of a radioactive sample, and finds its half-life with an uncertainty. The practice runs your code and tells you which results are wrong.
Calculus by Computer
Calculus asks how fast something changes and how much it has added up to. In this course the computer answers both from numbers. You find slopes with the forward and the central difference and with np.gradient, and learn why the best step is not the smallest. You find areas with rectangles and trapezoids, integrate with SciPy, including functions with no antiderivative and infinite limits, and find the work of a changing force. You follow a motion in small steps with Euler's method, see that it is first order, and use solve_ivp. A project follows a ball through the air with drag, stops it at the ground with an event, and finds that the best angle is lower than 45 degrees. The practice runs your code and tells you which results are wrong.