Topics include:

a.     Taylor polynomial and the error in Taylor polynomial.

b.    The binary number system, floating-point number.

c.     Error: definitions, sources, and examples.

d.    Finding roots of nonlinear equations: bisection method, Newton’s method, Secant method, and their error and convergence rate.

e.     Interpolation: Polynomial interpolation and the error in polynomial interpolation.

f.      Numerical Integration: Trapezoidal and Simpson rules, and the error formulas.

g.     Numerical Differentiation: Forward difference, Backward difference, central difference, undetermined Coefficients method, their error and effects of error in function values.

Numerical method for Initial Value Problems: Euler, Taylor, and Runge-Kutta Methods, their error and stability.