Author: Saim Khalid

Concepts Demonstrated Use of the Clapeyron and Antoine equations for vapor pressure correlation and estimation of latent heat of vaporization from the Clapeyron equation. Numerical Methods Utilized Linear regressions after proper transformations to a linear expression. Problem Statement The Clapeyron equation is commonly used to correlate vapor pressure (Pv) with absolute temperature (T) in °C…

A system of linear algebraic equations can be represented by the equation: Equation 1-2.  where A is an n × n matrix of coefficients, x is an n × 1 vector of unknowns and b an n × 1 vector of constants. Note that the number of equations is equal to the number of the unknowns. A detailed description of the various aspects of the solution of systems of linear…

The problem solving tools on the desktop that were used by engineers prior to the introduction of the handheld calculators (i.e., before 1970) are shown in Figure 1-1. Most calculations were carried out using the slide rule. This required carrying out each arithmetic operation separately and writing down the results of such operations. The highest precision…

As an engineering student or professional, you are almost always involved in numerical problem solving on a personal computer. The objective of this book is to enable you to solve numerical problems that you may encounter in your student or professional career in a most effective and efficient manner. The tools that are typically used…

Suppose that in a spreadsheet the following formula is entered into cell B1: Since cell reference B1 is in the formula of the same cell, this is called a “circular reference.” Normally, Excel will complain about this. However, if the Enable Iterative Calculations (see File/Options/Formulas) box is checked, Excel will immediately do the following: 1. It will automatically use an initial…

If it is (somehow) known that a root lies in the interval [a, b], then by simply halving the interval in which the root lies, the interval can be reduced to an acceptable level. This idea is at the heart of the bisection method as shown in Figure 1.2. The restriction is that f(a) and f(b) must have opposite signs—one…

Excel has very good plotting capabilities. Unfortunately, it is not possible in Excel to simply give a command such as plot(f(x)). It is necessary to produce a list or table of x and f(x) values and to graph the resulting data. This is best illustrated by an example. Example 1.1: Plotting the Equation A table of data and…

In Chapter 4, methods for approximating the derivative of a function using finite differences are presented. The secant method uses the idea of finite differences to approximate the derivative in the Newton method formula. Starting with two initial guesses x0 and x1, which need not bracket the root of interest, the approximation to f΄(x) can be written as follows: Or, in general, after k steps or iterations,…

Many engineering problems require the solution of a single nonlinear equation. Such an equation can always be cast into the form The objective of this chapter is to study methods and learn of Excel® tools for finding the root(s) of a nonlinear equation, that is, for finding x such that f(x) = 0. Simple algebra provides the root for…