Topics for the Second Midterm

• Lagrange interpolating polynomial with error term
• Neville's method
• Newton Forward difference formula
• Hermite interpolation
• How to derive derivative formulas
• Error terms for derivative formulas
• Richardson's extrapolation
• How to derive integral formulas
• Error terms for integral formulas
• Romberg integration
• Gaussian Quadrature
• Taylor methods for initial value problems
• How Runge-Kutta methods are derived
• Ideas behind the Runge-Kutta-Fehlberg method
• How to solve systems and higher order differential equations