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    Applied Numerical Methods For Engineering & Science Students

    Posted By: ELK1nG
    Applied Numerical Methods For Engineering & Science Students

    Applied Numerical Methods For Engineering & Science Students
    Last updated 5/2022
    MP4 | Video: h264, 1280x720 | Audio: AAC, 44.1 KHz
    Language: English | Size: 726.98 MB | Duration: 2h 37m

    Engineering, Science, Finance, Economics

    What you'll learn

    Develop an understanding of numerical Root Finding techniques.

    Develop an understanding of Linear and Nonlinear Equation Solvers.

    Develop an understanding of Numerical Integration and Differentiation.

    Develop an understanding of Curve Fitting.

    Develop an understanding of errors inherent in numerical methods and the use of Taylor Series Expansions.

    Improved computer programming skills.

    Requirements

    Knowledge of basic calculus, a programming language, and access to a computer.

    Description

    Motivation:Many, if not most, mathematical formulations resulting from the application of physical laws in science and engineering are not amenable to analytic solutions.  This leads to a numerical approach which generally involves the formulation of problems so that they may be solved using what is typically a large number of arithmetic operations, ideally suited for programming on a computer.  Numerical methods are also widely employed in fields of finance and economics.This Course:This is a first course in applied numerical methods for engineering and science university students, or those interested in a refresher course in numerical methods.  It may also be of interest to students with interests in the fields of finance and economics.  Course content is aimed toward students at the sophomore or junior level who have a basic knowledge of calculus and computer programming.  Topics covered include errors and Taylor series expansions, root finding, solution of systems of linear and nonlinear equations, numerical differentiation and integration, and curve fitting.  The subject of numerical solutions to ordinary and partial differential equations is covered in a separate course as is the subject of optimization.  To receive the most benefit from this course, students should have completed a basic calculus class and have access to a computer with a programming language installed.  Several programs are made available for download with Fortran being used for the algorithms, while Octave is used for graphics.  All PowerPoint slides used in the lectures are also available for download.

    Overview

    Section 1: Introduction

    Lecture 1 Introduction

    Section 2: Errors and Taylor Series Expansions

    Lecture 2 Numerical Errors

    Lecture 3 Taylor Series Expansions

    Section 3: Root Finding

    Lecture 4 Introduction and Example Problem

    Lecture 5 Interval Halving

    Lecture 6 Interval Halving Error Analysis

    Lecture 7 Linear Interpolation

    Lecture 8 Fixed Point Iteration

    Lecture 9 Fixed Point Example

    Lecture 10 Newton's Method

    Lecture 11 Newton's Method Example

    Lecture 12 Secant Method

    Lecture 13 Nonlinear System of Equations

    Section 4: Simultaneous Equation Solvers

    Lecture 14 Introduction

    Lecture 15 Matrix Notation and Operations

    Lecture 16 Basic Elimination Methods

    Lecture 17 Partial Pivoting

    Lecture 18 LU Decomposition

    Lecture 19 Matrix Inverse

    Lecture 20 Matrix Norms and Condition Number

    Lecture 21 Iterative Solvers

    Lecture 22 Iterative Convergence

    Lecture 23 Spectral Radius Example

    Lecture 24 SOR/Spectral Radius Example

    Section 5: Numerical Differentiation and Integration

    Lecture 25 Finite Difference Approximations I

    Lecture 26 Finite DIfference Approximations II

    Lecture 27 Finite Difference Example

    Lecture 28 Numerical Integration: Trapezoidal Rule

    Lecture 29 Trapezoidal Rule Error

    Lecture 30 Simpson's Rules

    Lecture 31 Numerical Integration Example

    Lecture 32 Richardson Extrapolation

    Section 6: Curve Fitting

    Lecture 33 Least Squares Fit Introduction

    Lecture 34 Linear Least Squares Fit

    Lecture 35 Quantification of Least Squares Fit Errors

    Lecture 36 Quadratic Least Squares Fit and Example

    Lecture 37 Exponential Least Squares Fits

    Lecture 38 Lagrange Polynomials

    Lecture 39 Linear Spline Interpolation

    Lecture 40 Quadratic and Cubic Splines with Example

    Advanced high school and college-level students in mathematics, engineering, and the sciences.