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Numerical Methods for Engineers

Approx. 40 hours to complete

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Course Summary

Learn how to solve engineering problems using numerical methods such as linear algebra, optimization, and differential equations.

Key Learning Points

Gain practical skills in solving complex engineering problems
Learn to use MATLAB for numerical analysis
Understand numerical methods for optimization, interpolation, and integration

Learning Outcomes

Ability to solve complex engineering problems using numerical methods
Proficiency in using MATLAB for numerical analysis
Understanding of numerical methods for optimization, interpolation, and integration

Prerequisites or good to have knowledge before taking this course

Familiarity with calculus
Basic knowledge of linear algebra

Course Difficulty Level

Intermediate

Course Format

Online
Self-paced
Video lectures
Assignments

Similar Courses

Numerical Methods for Engineers
Applied Numerical Methods
Numerical Methods for Differential Equations

Related Education Paths

Notable People in This Field

Cleve Moler
Gilbert Strang

Related Books

Description

Numerical Methods for Engineers covers the most important numerical methods that an engineer should know. We derive basic algorithms in root finding, matrix algebra, integration and interpolation, ordinary and partial differential equations. We learn how to use MATLAB to solve numerical problems. 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. Students should have already studied 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: http://www.math.ust.hk/~machas/numerical-methods-for-engineers.pdf Watch the promotional video: https://youtu.be/qFJGMBDfFMY

Knowledge

MATLAB and Scientific Computing
Root Finding and Numerical Matrix Algebra
Quadrature and Interpolation
Numerical Solution of Ordinary and Partial Differential Equations

Outline

Scientific Computing
Promotional Video
Course Overview
Week One Introduction
Binary Numbers | Lecture 1
Double Precision | Lecture 2
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
Logistic Map (Part A) | Lecture 11
Logistic Map (Part B) | Lecture 12
Welcome and Course Information
How to Write Math in the Discussions Using MathJax
MATLAB Online
Rounding Binary Numbers
Computer numbers
REALMAX
REALMIN
EPS
Logical Expressions
Logical Vectors
Quadratic Equation
Background for the Logistic Map
Period-2
Diagnostic Quiz
Week One Assessment

Root Finding
Week Two Introduction
Bisection Method | Lecture 13
Newton's Method | Lecture 14
Secant Method | Lecture 15
Order of Convergence| Lecture 16
Convergence of Newton's Method | Lecture 17
Fractals from Newton's Method | Lecture 18
Coding the Newton Fractal | Lecture 19
Root-Finding in MATLAB | Lecture 20
Feigenbaum Delta (Part A) | Lecture 21
Feigenbaum Delta (Part B) | Lecture 22
Feigenbaum Delta (Part C) | Lecture 23
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
Rates of Convergence
Order of Convergence of the Secant Method
The Four Fourth Roots of Unity
Deep Dive into The Newton Fractal
Compute the Value of m in the Period-Two Cycle
Week Two Assessment

Matrix Algebra
Week Three Introduction
Gaussian Elimination without Pivoting | Lecture 24
Gaussian Elimination with Partial Pivoting | Lecture 25
LU Decomposition with Partial Pivoting | Lecture 26
Operation Counts | Lecture 27
Operation Counts for Gaussian Elimination | Lecture 28
Operation Counts for Forward and Backward Substitution | Lecture 29
Eigenvalue Power Method | Lecture 30
Eigenvalue Power Method (Example) |Lecture 31
Matrix Algebra in MATLAB | Lecture 32
Systems of Nonlinear Equations | Lecture 33
Systems of Nonlinear Equations (Example) | Lecture 34
Fractals from the Lorenz Equations | Lecture 35
Round-off Errors in Gaussian Elimination
Reduced Round-off Errors in Gaussian Elimination with Partial Pivoting
The (PL)U Decomposition of A
Estimating Computational Time using Operation Counts
Summation Identities
Operation Counts for a Lower Triangular System
Convergence of the Eigenvalue Power Method
Determine the Dominant Eigenvalue
How to Solve Three Nonlinear equations
Week Three Assessment

Quadrature and Interpolation
Week Four Introduction
Midpoint Rule | Lecture 36
Trapezoidal Rule | Lecture 37
Simpson's Rule | Lecture 38
Composite Quadrature Rules | Lecture 39
Gaussian Quadrature | Lecture 40
Adaptive Quadrature | Lecture 41
Quadrature in MATLAB | Lecture 42
Interpolation | Lecture 43
Cubic Spline Interpolation (Part A) | Lecture 44
Cubic Spline Interpolation (Part B) | Lecture 45
Interpolation in MATLAB | Lecture 46
Bessel Functions and their Zeros | Lecture 47
The Midpoint Rule is the Area of a Rectangle
Midpoint Rule for a Quadratic Function
Derive the Trapezoidal Rule
Derive Simpson's Rule
Simpson's 3/8 Rule
Three-point Legendre-Gauss Quadrature
Computing the Error in an Adaptive Quadrature
Linear and Quadratic Interpolation
Cubic Spline Interpolation with Endpoint Slopes Known
Cubic Spline Interpolation with the Not-a-Knot Condition
Week Four Assessment

Ordinary Differential Equations
Week Five Introduction
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
Higher-Order ODEs and Systems | Lecture 53
Adaptive Runge-Kutta Method | Lecture 54
Integrating ODEs in MATLAB (Part A) | Lecture 55
Integrating ODEs in MATLAB (Part B) | Lecture 56
Shooting Method for Boundary Value Problems | Lecture 57
The Two-Body Problem (Part A) | Lecture 58
The Two-Body Problem (Part B) | Lecture 59
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 ODEs
Example of Adaptive Integration
Circular orbits
Week Five Assessment

Partial Differential Equations
Week Six Introduction
Boundary and Initial Value Problems | Lecture 60
Central Difference Approximation | Lecture 61
Discrete Laplace Equation | Lecture 62
Natural Ordering | Lecture 63
Matrix Formulation | Lecture 64
MATLAB Solution of the Laplace Equation (Direct Method) | Lecture 65
Jacobi, Gauss-Seidel and SOR Methods | Lecture 66
Red-Black Ordering | Lecture 67
MATLAB Solution of the Laplace Equation (Iterative Method) | Lecture 68
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
Two-Dimensional Diffusion Equation | Lecture 74
Concluding Remarks
Higher-order Central Difference Approximation
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 a System of Linear Equations
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
Classify Partial Differential Equations
Week Six Assessment

Summary of User Reviews

The Numerical Methods for Engineers course on Coursera has received positive reviews from users. It has been praised for its comprehensive coverage of numerical methods and their applications. Users have found the course to be engaging and informative, with valuable insights and practical examples provided throughout the course.

Key Aspect Users Liked About This Course

Many users have appreciated the practical approach taken by the course, which allows them to apply the concepts they learn to real-world problems and projects.

Pros from User Reviews

Comprehensive coverage of numerical methods and their applications
Engaging and informative content
Valuable insights and practical examples provided throughout the course
Practical approach allows for application of concepts to real-world problems and projects
High-quality video lectures and course materials

Cons from User Reviews

Some users have found the course to be too advanced for beginners
The course can be challenging and time-consuming
Limited interaction with instructors and other students
Some users have reported technical issues with the course platform
The course may not be suitable for those who prefer a more traditional classroom setting

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