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 propogation, Numerical Differentiation, Forward-Backward-Central difference formulations of First and Second derivatives, Richardson’s Extrpolation
• 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