Numerical Methods for Engineers

# Numerical Methods for Engineers

This course is part of Mathematics for Engineers Specialization

Taught in English

Some content may not be translated

Instructor: Jeffrey R. Chasnov

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Included with

## Course

Gain insight into a topic and learn the fundamentals

4.9

(314 reviews)

|

92%

Intermediate level

Recommended experience

41 hours (approximately)
Flexible schedule

## What you'll learn

• MATLAB and Scientific Computing

• Root Finding and Numerical Matrix Algebra

• Numerical Solution of Ordinary and Partial Differential Equations

## Details to know

Shareable certificate

Assessments

14 quizzes

## Course

Gain insight into a topic and learn the fundamentals

4.9

(314 reviews)

|

92%

Intermediate level

Recommended experience

41 hours (approximately)
Flexible schedule

# See how employees at top companies are mastering in-demand skills

This course is part of the Mathematics for Engineers Specialization
When you enroll in this course, you'll also be enrolled in this Specialization.
• Learn new concepts from industry experts
• Gain a foundational understanding of a subject or tool
• Develop job-relevant skills with hands-on projects
• Earn a shareable career certificate

## Earn a career certificate

Share it on social media and in your performance review

## There are 6 modules in this course

MATLAB is a high-level programming language extensively utilized by engineers for numerical computation and visualization. We will learn the basics of MATLAB: how real numbers are represented in double precision; how to perform arithmetic with MATLAB; how to use scripts and functions; how to represent vectors and matrices; how to draw line plots; and how to use logical variables, conditional statements, for loops and while loops. For your programming project, you will write a MATLAB code to compute the bifurcation diagram for the logistic map.

#### What's included

14 videos16 readings3 quizzes10 app items

Root finding is a numerical technique used to determine the roots, or zeros, of a given function. We will explore several root-finding methods, including the Bisection method, Newton's method, and the Secant method. We will also derive the order of convergence for these methods. Additionally, we will demonstrate how to compute the Newton fractal using Newton's method in MATLAB, and discuss MATLAB functions that can be used to find roots. For your programming project, you will write a MATLAB code using Newton's method to compute the Feigenbaum delta from the bifurcation diagram for the logistic map.

#### What's included

12 videos9 readings2 quizzes4 app items1 plugin

Numerical linear algebra is the term used for matrix algebra performed on a computer. When conducting Gaussian elimination with large matrices, round-off errors may compromise the computation. These errors can be mitigated using the method of partial pivoting, which involves row interchanges before each elimination step. The LU decomposition algorithm must then incorporate permutation matrices. We will also discuss operation counts and the big-Oh notation for predicting the increase in computational time with larger problem sizes. We will show how to count the number of required operations for Gaussian elimination, forward substitution, and backward substitution. We will explain the power method for computing the largest eigenvalue of a matrix. Finally, we will show how to use Gaussian elimination to solve a system of nonlinear differential equations using Newton's method. For your programming project, you will write a MATLAB code that applies Newton's method to the Lorenz equations.

#### What's included

13 videos11 readings2 quizzes5 app items

#### What's included

13 videos12 readings2 quizzes4 app items

We will learn about the numerical integration of ordinary differential equations (ODEs). We will introduce the Euler method, a single-step, first-order method, and the Runge-Kutta methods, which extend the Euler method to multiple steps and higher order, allowing for larger time steps. We will show how to construct a family of second-order Runge-Kutta methods, discuss the widely-used fourth-order Runge-Kutta method, and adopt these methods for solving systems of ODEs. We will show how to use the MATLAB function ode45.m, and how to solve a two-point boundary value ODE using the shooting method. For your programming project, you will conduct a numerical simulation of the gravitational two-body problem.

#### What's included

13 videos10 readings2 quizzes4 app items

We will learn how to solve partial differential equations (PDEs). While this is a vast topic with various specialized solution methods, such as those found in computational fluid dynamics, we will provide a basic introduction to the subject. We will categorize PDE solutions into boundary value problems and initial value problems. We will then apply the finite difference method for solving PDEs. We will solve the Laplace equation, a boundary value problem, using two methods: a direct method via Gaussian elimination; and an iterative method, where the solution is approached asymptotically. We will next solve the one-dimensional diffusion equation, an initial value problem, using the Crank-Nicolson method. We will also employ the Von Neumann stability analysis to determine the stability of time-integration schemes. For your programming project, you will solve the two-dimensional diffusion equation using the Crank-Nicolson method.

#### What's included

17 videos16 readings3 quizzes5 app items

### Instructor

Instructor ratings
4.9 (125 ratings)

Top Instructor

The Hong Kong University of Science and Technology
16 Courses204,041 learners

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