2011 | OriginalPaper | Chapter

# Numerical solutions of equations and interpolation

Appreciate the Fundamental Theorem of Algebra Find the two roots of a quadratic equation and recognise that for polynomial equations with real coefficients complex roots exist in complex conjugate pairs Use the relationships between the coefficients and the roots of a polynomial equation to find the roots of the polynomial Transform a cubic equation to its reduced form Use Tartaglia solution to find the roots of a cubic equation Find the solution of the equation the method of bisection Solve equations involving a single real variable by iteration and use a spreadsheet for efficiency Solve equations using the Newton-Raphson iterative method Use the modified Newton-Raphson method to find the first approximation when the derivative is small Understand the meaning of interpolation and use simple linear and graphical interpolation Use the Gregory-Newton interpolation formula with forward and backward differences for equally spaced domain points Use the Gauss interpolation formulas using central differences for equally spaced domain points Use Lagrange interpolation when the domain points are not equally spaced