contents computing integrals basic ideas of numerical integration the composite trapezoidal rule the general formula implementation making module alternative flat special-purpose implementation the composite midpoint method the general formula implementation comparing the trapezoidal and the midpoint methods testing problems with brief testing procedures proper test procedures finite precision of floating-point numbers constructing unit tests and writing test functions vectorization measuring computational speed double and triple integrals the midpoint rule for double integral the midpoint rule for triple integral monte carlo integration for complex-shaped domains exercises solving ordinary differential equations population growth derivation of the model numerical solution programming the forward euler schemethe special case understanding the forward euler method programming the forward euler schemethe general case making the population growth model more realistic verificationexact linear solution of the discrete equations spreading of diseases spreading of flu forward euler method for the differential equation system programming the numerical methodthe special case outbreak or not abstract problem and notation programming the numerical methodthe general case time-restricted immunity incorporating vaccination discontinuous coefficientsa vaccination campaign oscillating one-dimensional systems derivation of simple model numerical solution programming the numerical methodthe special case