GE 611 - Numerical Methods

3 lecture hours 0 lab hours 3 credits

• Model engineering systems using first and second order differential equations, and solve the equations both analytically and numerically
• Employ the Taylor Series for approximation and error analysis
• Formulate and apply numerical techniques for root finding, curve fitting, differentiation, and integration
• Write computer programs to solve engineering problems

• Computer programming
• Differential equations and Laplace Transform

• Taylor series, error propagation, numerical differentiation, forward-backward-central difference formulations of First and Second derivatives, Richardson’s Extrapolation
• Numerical Integration: Newton-Gregory forward formula for interpolation, trapezoidal rule, Simpson’s rules, Boole’s rule, Romberg Integration
• Root finding methods: bisection, false position, fixed-point iteration, Newton-Raphson, secant, modified secant
• Ordinary differential equations: initial value problems, Euler’s method, Heun’s method, Runge-Kutta methods, third order and fourth order, stiff equations: implicit Euler’s method, Adam’s solvers: explicit and implicit methods, Milne’s predictor-corrector methods