# 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,...

# 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,...

# Interpolation-Numerical Methods in Engineering-Lecture 5 Slides-Civil Engineering and Geological Sciences

In numerical methods, like tables, the values of the function are only specified at a discrete number of points! Using interpolation, we can describe or at least approximate the function at every point in space. Interpolation, Linear Interpolation...

# 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...

# 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...

# 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...

# 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

# Ordinary Differential Equations-Numerical Methods in Engineering-Lecture 21 Slides-Civil Engineering and Geological Sciences

Qualitative basis for verifying accuracy of solutions ® use 2 different time steps (similar to Romberg integration). Ordinary Differential Equations, 2nd Order, Runge Kutta, Improved Euler Method, Modified Euler Cauchy, 4th Order, Runge Kutta Meth...

# Ordinary Differential Equations-Numerical Methods in Engineering-Lecture 20 Slides-Civil Engineering and Geological Sciences

In general the total solution has an error which can be defined by examining the difference between the Euler formula, Equation (3) and our Taylor Series expansion, Equation (5). Ordinary Differential Equations, Iinitial Value Problems, IVP, Runge...

# Gauss Quadrature-Numerical Methods in Engineering-Lecture 19 Slides-Civil Engineering and Geological Sciences

Concept: Let’s allow the placement of the integration points to vary such that we further increase the degree of the polynomial we can integrate exactly for a given number of integration points. Gauss Quadrature, Gauss Legendre Formulae, Hermite I...