# Newton Forward Interpolation-Numerical Methods in Engineering-Lecture 7 Slides-Civil Engineering and Geological Sciences

Newton Forward Interpolation, Forward Difference Tables, Zeroth Order Forward Difference, First Order Forward Difference, Second Order Forward Difference, Third Order Forward Difference, Kth Order Forward Difference, Newton Forward Interpolation,...

# Numerical Differentiation-Numerical Methods in Engineering-Lecture 11 Slides-Civil Engineering and Geological Sciences

Numerical Differentiation, Taylor Series Expansion, Taylor Series, Approximating Derivatives, Actual Slope, Approximate Slope, Forward Difference Approximations, Backward Difference Approximations, First Derivative Approximations, Central Differen...

# Numerical Integration-Numerical Methods in Engineering-Lecture 17 Slides-Civil Engineering and Geological Sciences

Trapezoidal rule is simply applying linear interpolation between two points and integrating the approximating polynomial. Numerical Integration, Trapezoidal Rule, Error, Extended Trapezoidal Rule, Romberg Integration, Interpolating Polynomials, T...

# Lagrange Interpolation-Numerical Methods in Engineering-Lecture 6 Slides-Civil Engineering and Geological Sciences

Each Lagrange polynomial or basis function is set up such that it equals unity at the data point with which it is associated, zero at all other data points and nonzero inbetween. Lagrange Interpolation, Interpolation Points, Power Series, Fitting,...

# Roots of Nonlinear Equations-Numerical Methods in Engineering-Lecture 10 Slides-Civil Engineering and Geological Sciences

Newton-Raphson is based on using an initial guess for the root and finding the intersection with the axis of the straight line which represents the slope at the initial guess. It works very fast and converges assuming the initial guess was good. R...

# Review of Numerical Methods-Numerical Methods in Engineering-review3-Civil Engineering and Geological Sciences

Describe a function by passing a polynomial through a set of functional values and/or functional derivative values. Review of Numerical Methods, ODE Classification, Runge Kutta Formulae, Deriving Runge Kutta Methods, Multi Step Methods, Open Formu...

# Review of Numerical Methods-Numerical Methods in Engineering-review2-Civil Engineering and Geological Sciences

Review of Numerical Methods, Numerical Differentiation, Errors, Partial Differentiation, Numerical Integration, Newton Cotes, Closed Formulae, Open Formulae, Gauss Legendre, Integration Formulae, Extended Integration Methods, Romberg Integration

# Review of Numerical Methods-Numerical Methods in Engineering-review1-Civil Engineering and Geological Sciences

Review of Numerical Methods, Taylor Series, System of Linear Equations, Numerical Solution, Direct Methods, Gauss Elimination, LU Decomposition, Cholesky, Decomposition, Factor Method, Matrix Conditioning, Matrix Storage, Iterative Methods, Interp...

# System of Ordinary Differential Equations-Numerical Methods in Engineering-Lecture 23 Slides-Civil Engineering and Geological Sciences

However for both R.K. type methods and multi-step methods we must complete the computation for the entire vector before moving on to the next step of the procedure due to the coupling inherent to the system. System of Ordinary Differential Equatio...

# Multi Step Methods-Numerical Methods in Engineering-Lecture 22 Slides-Civil Engineering and Geological Sciences

Multi step methods use information from several previous or known time levels. Multi Step Methods, Open Formulae, Adam, Bashforth, Closed Formulae, Adams Moulton, Predictor Corrector Methods, PC Methods, Starters, Modifier