CHAPTER 01.01: INTRODUCTION TO NUMERICAL METHODS

Why Do We Use Numerical Methods

Hello, my name is Autar Kaw. I am a professor of Mechanical Engineering at University of South Florida. I have taught the Numerical Methods course close to about 50 times. The main goal of this course is to learn methods that solve mathematical models approximately, also what we call as numerically. Hence, the name of the course – Introduction to Numerical Methods. So why problems approximately one may ask? Well, most times, the exact solution does not exist. Look at this normal probability density function, which is an important tool used in quality control in manufacturing. The integral of this function cannot be found exactly except for the value of x approaching infinity. For any other value, we need to find this integral approximately yes, what we call as numerically. Other times an exact solution may be available but the solution would take a long-long time. For example, one can solve a set of 1000 simultaneous linear equations by hand but it would take a long-long time to do so. That is why we solve such problems numerically by using a computer. At the end of this course, you will learn how to approximately do the following: Find Derivatives of Continuous and Discrete Functions Solve Nonlinear Equations Solve Simultaneous Linear Equations Curve Fit Discrete Data using Interpolation Curve Fit Discrete Data using Regression Find Integrals of Continuous and Discrete Functions, and Solve Ordinary Differential Equations All these will become tools for you to solve many-many engineering and science problems. The course is taught at the beginning of a 3rd year level of a 4-year undergraduate degree. The pre-requisites for the course are: High School Algebra Differential Calculus Integral Calculus Ordinary Differential Equations The audience is any 3rd year level or above undergraduate who is STEM major. STEM standing for Science, Technology, Engineering and Mathematics. There are several other sources which are available to you free of charge. So I would think you would use them. So what are you waiting for - let's get started! ;