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Numerical Methods for Engineers
  • Level Professional
  • Duration 42 hours
  • Course by The Hong Kong University of Science and Technology
  • Offered by

About

This course covers the most important numerical methods that an engineer should know, including root finding, matrix algebra, integration and interpolation, ordinary and partial differential equations. We learn how to use MATLAB to solve numerical problems, and access to MATLAB online and the MATLAB grader is given to all students who enroll. We assume students are already familiar with the basics of matrix algebra, differential equations, and vector calculus. They should have a working knowledge of a programming language, and be willing to learn MATLAB. The course contains 74 short lecture videos and MATLAB demonstrations. After each lecture or demonstration, there are problems to solve or programs to write. The course is organized into six weeks, and at the end of each week, there is an assessed quiz and a longer programming project. Download the lecture notes from the link https://www.math.hkust.edu.hk/~machas/numerical-methods-for-engineers.pdf And watch the promotional video from the link https://youtu.be/qFJGMBDfFMY

Modules

Welcome to Numerical Methods for Engineers

    • 1 Videos
    • 4 Readings
    • 1 Assignment
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1 Assignment

  • Diagnostic Quiz

1 Videos

  • Course Overview

4 Readings

  • Welcome and Course Information
  • Certificate or Audit?
  • How to Write Math in the Discussions Using MathJax
  • MATLAB Online

Introduction to Week One

    • 1 Videos
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1 Videos

  • Week One Introduction

Representation of Computer Numbers

    • 2 Videos
    • 5 Readings
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2 Videos

  • Binary Numbers | Lecture 1
  • Double Precision | Lecture 2

5 Readings

  • Rounding Binary Numbers
  • Computer Numbers
  • REALMAX
  • REALMIN
  • EPS

MATLAB Fundamentals

    • 8 Videos
    • 3 Readings
    • 8 ExternalTool
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8 External Tool

  • MATLAB as a Calculator
  • Binet's Formula for the Fibonacci Numbers
  • Table of Sines and Cosines
  • Logarithmic Spiral
  • Lemniscate
  • Manipulating Matrices
  • Banded Matrices
  • Recursion Definition for the Fibonacci Numbers

8 Videos

  • MATLAB as a Calculator | Lecture 3
  • Scripts and Functions | Lecture 4
  • Vectors | Lecture 5
  • Line Plots | Lecture 6
  • Matrices | Lecture 7
  • Logicals | Lecture 8
  • Conditionals | Lecture 9
  • Loops | Lecture 10

3 Readings

  • Logical Expressions
  • Logical Vectors
  • Quadratic Equation

Quiz

    • 2 Assignment
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2 Assignment

  • Week One Assessment (audit)
  • Week One Assessment

Programming Assignment: Bifurcation Diagram for the Logistic Map

    • 2 Videos
    • 4 Readings
    • 2 ExternalTool
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2 External Tool

  • Bifurcation Diagram for the Logistic Map (audit)
  • Bifurcation Diagram for the Logistic Map

2 Videos

  • Logistic Map (Part A) | Lecture 11
  • Logistic Map (Part B) | Lecture 12

4 Readings

  • Background for the Logistic Map
  • Period-2
  • Reference Solution to "Bifurcation Diagram for the Logistic Map (audit)"
  • Reference Solution to "Bifurcation Diagram for the Logistic Map"

Introduction to Week Two

    • 1 Videos
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1 Videos

  • Week Two Introduction

Root-Finding Methods

    • 3 Videos
    • 3 Readings
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3 Videos

  • Bisection Method | Lecture 13
  • Newton's Method | Lecture 14
  • Secant Method | Lecture 15

3 Readings

  • Estimate the Square-root of Three Using the Bisection Method
  • Estimate the Square-root of Three Using Newton's Method
  • Estimate the Square-Root of Three Using the Secant Method

Order of Convergence

    • 2 Videos
    • 2 Readings
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2 Videos

  • Order of Convergence| Lecture 16
  • Convergence of Newton's Method | Lecture 17

2 Readings

  • Rates of Convergence
  • Order of Convergence of the Secant Method

Root Finding in MATLAB

    • 3 Videos
    • 1 Readings
    • 2 ExternalTool
    • 1 Plugin
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2 External Tool

  • Fractals from the Four Fourth Roots of Unity
  • Elliptical Planetary Orbits

3 Videos

  • Fractals from Newton's Method | Lecture 18
  • Coding the Newton Fractal | Lecture 19
  • Root-Finding in MATLAB | Lecture 20

1 Readings

  • The Four Fourth Roots of Unity

Quiz

    • 2 Assignment
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2 Assignment

  • Week Two Assessment (audit)
  • Week Two Assessment

Programming Assignment: Computation of the Feigenbaum Delta

    • 3 Videos
    • 3 Readings
    • 2 ExternalTool
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2 External Tool

  • Computation of the Feigenbaum Delta (audit)
  • Computation of the Feigenbaum Delta

3 Videos

  • Feigenbaum Delta (Part A) | Lecture 21
  • Feigenbaum Delta (Part B) | Lecture 22
  • Feigenbaum Delta (Part C) | Lecture 23

3 Readings

  • Compute the Value of m in the Period-Two Cycle
  • Reference Solution to "Computation of the Feigenbaum Delta (audit)"
  • Reference Solution to "Computation of the Feigenbaum Delta"

Introduction to Week Three

    • 1 Videos
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1 Videos

  • Week Three Introduction

Gaussian Elimination

    • 3 Videos
    • 3 Readings
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3 Videos

  • Gaussian Elimination without Pivoting | Lecture 24
  • Gaussian Elimination with Partial Pivoting | Lecture 25
  • LU Decomposition with Partial Pivoting | Lecture 26

3 Readings

  • Round-off Errors in Gaussian Elimination
  • Reduced Round-off Errors in Gaussian Elimination with Partial Pivoting
  • The (PL)U Decomposition of A

Operation Counts

    • 3 Videos
    • 3 Readings
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3 Videos

  • Operation Counts | Lecture 27
  • Operation Counts for Gaussian Elimination | Lecture 28
  • Operation Counts for Forward and Backward Substitution | Lecture 29

3 Readings

  • Estimating Computational Time using Operation Counts
  • Summation Identities
  • Operation Counts for a Lower Triangular System

Eigenvalues and Eigenvectors

    • 2 Videos
    • 2 Readings
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2 Videos

  • Eigenvalue Power Method | Lecture 30
  • Eigenvalue Power Method (Example) |Lecture 31

2 Readings

  • Convergence of the Eigenvalue Power Method
  • Determine the Dominant Eigenvalue

Matrix Algebra in MATLAB

    • 1 Videos
    • 2 ExternalTool
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2 External Tool

  • The LU Decomposition of a Matrix
  • Eigenvalues and Eigenvectors

1 Videos

  • Matrix Algebra in MATLAB | Lecture 32

Systems of Nonlinear Equations

    • 2 Videos
    • 1 Readings
    • 1 ExternalTool
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1 External Tool

  • Fixed-Point Solutions of the Lorenz Equations

2 Videos

  • Systems of Nonlinear Equations | Lecture 33
  • Systems of Nonlinear Equations (Example) | Lecture 34

1 Readings

  • How to Solve Three Nonlinear equations

Quiz

    • 2 Assignment
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2 Assignment

  • Week Three Assessment (audit)
  • Week Three Assessment

Programming Assignment: Fractals from the Lorenz Equations

    • 1 Videos
    • 2 Readings
    • 2 ExternalTool
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2 External Tool

  • Fractals from the Lorenz Equations (audit)
  • Fractals from the Lorenz Equations

1 Videos

  • Fractals from the Lorenz Equations | Lecture 35

2 Readings

  • Reference Solution to "Fractals from the Lorenz Equations (audit)"
  • Reference Solution to "Fractals from the Lorenz Equations"

Introduction to Week Four

    • 1 Videos
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1 Videos

  • Week Four Introduction

Elementary Integration Formulas

    • 3 Videos
    • 4 Readings
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3 Videos

  • Midpoint Rule | Lecture 36
  • Trapezoidal Rule | Lecture 37
  • Simpson's Rule | Lecture 38

4 Readings

  • The Midpoint Rule is the Area of a Rectangle
  • Midpoint Rule for a Quadratic Function
  • Derive the Trapezoidal Rule
  • Derive Simpson's Rule

Composite Integration Formulas

    • 3 Videos
    • 3 Readings
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3 Videos

  • Composite Quadrature Rules | Lecture 39
  • Gaussian Quadrature | Lecture 40
  • Adaptive Quadrature | Lecture 41

3 Readings

  • Simpson's 3/8 Rule
  • Three-point Legendre-Gauss Quadrature
  • Computing the Error in an Adaptive Quadrature

Quadrature in MATLAB

    • 1 Videos
    • 1 ExternalTool
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1 External Tool

  • Cornu Spiral

1 Videos

  • Quadrature in MATLAB | Lecture 42

Interpolation

    • 3 Videos
    • 3 Readings
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3 Videos

  • Interpolation | Lecture 43
  • Cubic Spline Interpolation (Part A) | Lecture 44
  • Cubic Spline Interpolation (Part B) | Lecture 45

3 Readings

  • Linear and Quadratic Interpolation
  • Cubic Spline Interpolation with Endpoint Slopes Known
  • Cubic Spline Interpolation with the Not-a-Knot Condition

Interpolation in MATLAB

    • 1 Videos
    • 1 ExternalTool
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1 External Tool

  • Interpolate Two Data Files

1 Videos

  • Interpolation in MATLAB | Lecture 46

Quiz

    • 2 Assignment
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2 Assignment

  • Week Four Assessment (audit)
  • Week Four Assessment

Programming Assignment: Bessel Function Zeros

    • 1 Videos
    • 2 Readings
    • 2 ExternalTool
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2 External Tool

  • Bessel Function Zeros (audit)
  • Bessel Function Zeros

1 Videos

  • Bessel Functions and their Zeros | Lecture 47

2 Readings

  • Reference Solution to "Bessel Function Zeros (audit)"
  • Reference Solution to "Bessel Function Zeros"

Introduction to Week Five

    • 1 Videos
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1 Videos

  • Week Five Introduction

Initial Value Problems

    • 5 Videos
    • 5 Readings
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5 Videos

  • Euler Method | Lecture 48
  • Modified Euler Method | Lecture 49
  • Runge-Kutta Methods | Lecture 50
  • Second-Order Runge-Kutta Methods | Lecture 51
  • Higher-Order Runge-Kutta Methods | Lecture 52

5 Readings

  • When the Euler Method is Exact
  • When the Modified Euler Method is Exact
  • Ralston's Method
  • Runge-Kutta Methods and Quadrature Formulas
  • Fourth-Order Runge-Kutta Method and Simpson's Rule

Systems of Differential Equations

    • 1 Videos
    • 1 Readings
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1 Videos

  • Higher-Order ODEs and Systems | Lecture 53

1 Readings

  • Systems of ODEs

Initial Value Problems in MATLAB

    • 3 Videos
    • 1 Readings
    • 1 ExternalTool
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1 External Tool

  • The Lorenz Equations

3 Videos

  • Adaptive Runge-Kutta Method | Lecture 54
  • Integrating ODEs in MATLAB (Part A) | Lecture 55
  • Integrating ODEs in MATLAB (Part B) | Lecture 56

1 Readings

  • Example of Adaptive Integration

Boundary Value Problems

    • 1 Videos
    • 1 ExternalTool
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1 External Tool

  • Swing a Pendulum to the Top

1 Videos

  • Shooting Method for Boundary Value Problems | Lecture 57

Quiz

    • 2 Assignment
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2 Assignment

  • Week Five Assessment (audit)
  • Week Five Assessment

Programming Assignment: The Two-Body Problem

    • 2 Videos
    • 3 Readings
    • 2 ExternalTool
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2 External Tool

  • Two-Body Problem (audit)
  • Two-Body Problem

2 Videos

  • The Two-Body Problem (Part A) | Lecture 58
  • The Two-Body Problem (Part B) | Lecture 59

3 Readings

  • Circular orbits
  • Reference Solution to "Two-Body Problem (audit)"
  • Reference Solution to "Two-Body Problem"

Introduction to Week Six

    • 1 Videos
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1 Videos

  • Week Six Introduction

Numerical Solutions of PDEs

    • 2 Videos
    • 1 Readings
    • 1 Assignment
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1 Assignment

  • Classify Partial Differential Equations

2 Videos

  • Boundary and Initial Value Problems | Lecture 60
  • Central Difference Approximation | Lecture 61

1 Readings

  • Higher-order Central Difference Approximation

Direct Solution of Boundary Value Problems

    • 4 Videos
    • 4 Readings
    • 1 ExternalTool
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1 External Tool

  • Direct Solution of the Laplace Equation

4 Videos

  • Discrete Laplace Equation | Lecture 62
  • Natural Ordering | Lecture 63
  • Matrix Formulation | Lecture 64
  • MATLAB Solution of the Laplace Equation (Direct Method) | Lecture 65

4 Readings

  • Mean Value Property of the Laplace Equation
  • Coordinates of the four corners
  • The Discrete Laplace Equation on a Four-by-Four Grid
  • Number of Interior and Boundary Points

Iterative Solution of Boundary Value Problems

    • 3 Videos
    • 1 Readings
    • 1 ExternalTool
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1 External Tool

  • Iterative Solution of the Laplace Equation

3 Videos

  • Jacobi, Gauss-Seidel and SOR Methods | Lecture 66
  • Red-Black Ordering | Lecture 67
  • MATLAB Solution of the Laplace Equation (Iterative Method) | Lecture 68

1 Readings

  • Iterative Solution of a System of Linear Equations

Time-stepping Methods for Initial Value Problems

    • 5 Videos
    • 6 Readings
    • 1 ExternalTool
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1 External Tool

  • The Diffusion Equation with No-Flux Boundary Conditions

5 Videos

  • Explicit Methods for Solving the Diffusion Equation | Lecture 69
  • Von Neumann Stability Analysis of the FTCS Scheme | Lecture 70
  • Implicit Methods for Solving the Diffusion Equation | Lecture 71
  • Crank-Nicolson Method for the Diffusion Equation | Lecture 72
  • MATLAB Solution of the Diffusion Equation | Lecture 73

6 Readings

  • Using a Second-Order Time-Stepping Method
  • FTCS Scheme for the Advection Equation
  • Von Neumann Stability Analysis of the FTCS Scheme for the Advection Equation
  • Implicit Discrete Advection Equation
  • Lax Scheme for the Advection Equation
  • Difference Approximations for the Derivative at Boundary Points

Quiz

    • 2 Assignment
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2 Assignment

  • Week Six Assessment (audit)
  • Week Six Assessment

Programming Assignment: Two-dimensional Diffusion Equation

    • 1 Videos
    • 2 Readings
    • 2 ExternalTool
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2 External Tool

  • Two-Dimensional Diffusion Equation (audit)
  • Two-Dimensional Diffusion Equation

1 Videos

  • Two-Dimensional Diffusion Equation | Lecture 74

2 Readings

  • Reference Solution to "Two-Dimensional Diffusion Equation (audit)"
  • Reference Solution to "Two-Dimensional Diffusion Equation"

Farewell

    • 1 Videos
    • 2 Readings
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1 Videos

  • Concluding Remarks

2 Readings

  • Please Rate this Course
  • Acknowledgements

Auto Summary

"Numerical Methods for Engineers" is a professional-level course in Maths & Statistics, designed by Coursera. Taught by expert instructors, it covers essential numerical methods like root finding, matrix algebra, and differential equations using MATLAB. The course spans six weeks with 74 short lectures, practical problems, quizzes, and programming projects. Ideal for engineers familiar with matrix algebra, differential equations, and programming, it offers access to MATLAB tools for hands-on learning. Subscriptions start at the Starter level.

Jeffrey R. Chasnov
Instructor

Jeffrey R. Chasnov