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Numerical Methods for Engineers · LearnSpace
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Numerical Methods for Engineers

Курс от The Hong Kong University of Science and Technology
Средний≈ 40.4 чАнглийский
О курсеНавыкиПрограммаПреподаватели

О курсе

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

Навыки, которые вы освоите

Numerical AnalysisMatlabDifferential EquationsLinear AlgebraApplied MathematicsScriptingAlgorithmsPlot (Graphics)CalculusComputational ThinkingSimulation and Simulation SoftwareMathematical SoftwareIntegral CalculusSimulations

Программа курса

6 модулей · 184 учебных материалов

01Scientific Computing39 материалов

Welcome to Numerical Methods for Engineers

Welcome and Course InformationЧтениеCourse OverviewВидеоDiagnostic QuizЗаданиеHow to Write Math in the Discussions Using MathJaxЧтение

Учитесь у экспертов

Jeffrey R. Chasnov

Professor

Numerical Methods for Engineers
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Обучение на Coursera

≈ 40.4 ч

6 модулей

Язык: Английский

Субтитры: Арабский, Французский, Бенгальский, Узбекский, Украинский, Китайский (Китай), Греческий, Итальянский, Бразильский португальский, Нидерландский, Корейский, Немецкий, Пушту, Урду, Русский, Тайский, Индонезийский, Шведский, Турецкий, Азербайджанский, Испанский, Дари, Хинди, Японский, Казахский, Венгерский, Польский

Часть программы вашего университета
MATLAB OnlineЧтение

Introduction to Week One

Week One IntroductionВидео

Representation of Computer Numbers

Binary Numbers | Lecture 1ВидеоRounding Binary NumbersЧтениеDouble Precision | Lecture 2ВидеоComputer NumbersЧтениеREALMAXЧтениеREALMINЧтениеEPSЧтение

MATLAB Fundamentals

MATLAB as a Calculator | Lecture 3ВидеоMATLAB as a CalculatorВнешний инструментScripts and Functions | Lecture 4ВидеоBinet's Formula for the Fibonacci NumbersВнешний инструментVectors | Lecture 5ВидеоTable of Sines and CosinesВнешний инструментLine Plots | Lecture 6ВидеоLogarithmic SpiralВнешний инструментLemniscateВнешний инструментMatrices | Lecture 7ВидеоManipulating MatricesВнешний инструментBanded MatricesВнешний инструментLogicals | Lecture 8ВидеоLogical ExpressionsЧтениеLogical VectorsЧтениеConditionals | Lecture 9ВидеоQuadratic EquationЧтениеLoops | Lecture 10ВидеоRecursion Definition for the Fibonacci NumbersВнешний инструмент

Quiz

Week One AssessmentЗадание

Programming Assignment: Bifurcation Diagram for the Logistic Map

Background for the Logistic MapЧтениеLogistic Map (Part A) | Lecture 11ВидеоPeriod-2ЧтениеLogistic Map (Part B) | Lecture 12ВидеоBifurcation Diagram for the Logistic MapВнешний инструментReference Solution to "Bifurcation Diagram for the Logistic Map"Чтение
02Root Finding25 материалов

Introduction to Week Two

Week Two Introduction Видео

Root-Finding Methods

Bisection Method | Lecture 13ВидеоEstimate the Square-root of Three Using the Bisection MethodЧтениеNewton's Method | Lecture 14ВидеоEstimate the Square-root of Three Using Newton's MethodЧтениеSecant Method | Lecture 15ВидеоEstimate the Square-Root of Three Using the Secant MethodЧтение

Order of Convergence

Order of Convergence| Lecture 16ВидеоRates of ConvergenceЧтениеConvergence of Newton's Method | Lecture 17ВидеоOrder of Convergence of the Secant MethodЧтение

Root Finding in MATLAB

Fractals from Newton's Method | Lecture 18ВидеоThe Four Fourth Roots of UnityЧтениеCoding the Newton Fractal | Lecture 19 ВидеоFractals from the Four Fourth Roots of UnityВнешний инструментDeep Dive into The Newton FractalPLUGINRoot-Finding in MATLAB | Lecture 20Видео

Quiz

Week Two AssessmentЗадание

Programming Assignment: Computation of the Feigenbaum Delta

Feigenbaum Delta (Part A) | Lecture 21ВидеоCompute the Value of m in the Period-Two CycleЧтениеFeigenbaum Delta (Part B) | Lecture 22ВидеоFeigenbaum Delta (Part C) | Lecture 23ВидеоComputation of the Feigenbaum DeltaВнешний инструментReference Solution to "Computation of the Feigenbaum Delta"Чтение
03Matrix Algebra28 материалов

Introduction to Week Three

Week Three Introduction Видео

Gaussian Elimination

Gaussian Elimination without Pivoting | Lecture 24ВидеоRound-off Errors in Gaussian EliminationЧтениеGaussian Elimination with Partial Pivoting | Lecture 25ВидеоReduced Round-off Errors in Gaussian Elimination with Partial PivotingЧтениеLU Decomposition with Partial Pivoting | Lecture 26ВидеоThe (PL)U Decomposition of AЧтение

Operation Counts

Operation Counts | Lecture 27ВидеоEstimating Computational Time using Operation CountsЧтениеOperation Counts for Gaussian Elimination | Lecture 28ВидеоSummation IdentitiesЧтениеOperation Counts for Forward and Backward Substitution | Lecture 29ВидеоOperation Counts for a Lower Triangular SystemЧтение

Eigenvalues and Eigenvectors

Eigenvalue Power Method | Lecture 30ВидеоConvergence of the Eigenvalue Power MethodЧтениеEigenvalue Power Method (Example) |Lecture 31ВидеоDetermine the Dominant EigenvalueЧтение

Matrix Algebra in MATLAB

Matrix Algebra in MATLAB | Lecture 32ВидеоThe LU Decomposition of a MatrixВнешний инструментEigenvalues and EigenvectorsВнешний инструмент

Systems of Nonlinear Equations

Systems of Nonlinear Equations | Lecture 33ВидеоHow to Solve Three Nonlinear equationsЧтениеSystems of Nonlinear Equations (Example) | Lecture 34ВидеоFixed-Point Solutions of the Lorenz EquationsВнешний инструмент

Quiz

Week Three AssessmentЗадание

Programming Assignment: Fractals from the Lorenz Equations

Fractals from the Lorenz Equations | Lecture 35ВидеоFractals from the Lorenz EquationsВнешний инструментReference Solution to "Fractals from the Lorenz Equations"Чтение
04Quadrature and Interpolation28 материалов

Introduction to Week Four

Week Four Introduction Видео

Elementary Integration Formulas

Midpoint Rule | Lecture 36ВидеоThe Midpoint Rule is the Area of a RectangleЧтениеMidpoint Rule for a Quadratic FunctionЧтениеTrapezoidal Rule | Lecture 37ВидеоDerive the Trapezoidal RuleЧтениеSimpson's Rule | Lecture 38ВидеоDerive Simpson's RuleЧтение

Composite Integration Formulas

Composite Quadrature Rules | Lecture 39ВидеоSimpson's 3/8 RuleЧтениеGaussian Quadrature | Lecture 40ВидеоThree-point Legendre-Gauss QuadratureЧтениеAdaptive Quadrature | Lecture 41ВидеоComputing the Error in an Adaptive QuadratureЧтение

Quadrature in MATLAB

Quadrature in MATLAB | Lecture 42ВидеоCornu SpiralВнешний инструмент

Interpolation

Interpolation | Lecture 43ВидеоLinear and Quadratic InterpolationЧтениеCubic Spline Interpolation (Part A) | Lecture 44ВидеоCubic Spline Interpolation with Endpoint Slopes KnownЧтениеCubic Spline Interpolation (Part B) | Lecture 45ВидеоCubic Spline Interpolation with the Not-a-Knot ConditionЧтение

Interpolation in MATLAB

Interpolation in MATLAB | Lecture 46ВидеоInterpolate Two Data FilesВнешний инструмент

Quiz

Week Four AssessmentЗадание

Programming Assignment: Bessel Function Zeros

Bessel Functions and their Zeros | Lecture 47ВидеоBessel Function ZerosВнешний инструментReference Solution to "Bessel Function Zeros"Чтение
05Ordinary Differential Equations26 материалов

Introduction to Week Five

Week Five Introduction Видео

Initial Value Problems

Euler Method | Lecture 48ВидеоWhen the Euler Method is ExactЧтениеModified Euler Method | Lecture 49ВидеоWhen the Modified Euler Method is ExactЧтениеRunge-Kutta Methods | Lecture 50ВидеоSecond-Order Runge-Kutta Methods | Lecture 51ВидеоRalston's MethodЧтениеRunge-Kutta Methods and Quadrature FormulasЧтениеHigher-Order Runge-Kutta Methods | Lecture 52ВидеоFourth-Order Runge-Kutta Method and Simpson's RuleЧтение

Systems of Differential Equations

Higher-Order ODEs and Systems | Lecture 53ВидеоSystems of ODEsЧтение

Initial Value Problems in MATLAB

Adaptive Runge-Kutta Method | Lecture 54ВидеоExample of Adaptive IntegrationЧтениеIntegrating ODEs in MATLAB (Part A) | Lecture 55ВидеоIntegrating ODEs in MATLAB (Part B) | Lecture 56ВидеоThe Lorenz EquationsВнешний инструмент

Boundary Value Problems

Shooting Method for Boundary Value Problems | Lecture 57ВидеоSwing a Pendulum to the TopВнешний инструмент

Quiz

Week Five AssessmentЗадание

Programming Assignment: The Two-Body Problem

The Two-Body Problem (Part A) | Lecture 58ВидеоCircular orbitsЧтениеThe Two-Body Problem (Part B) | Lecture 59ВидеоTwo-Body ProblemВнешний инструментReference Solution to "Two-Body Problem"Чтение
06Partial Differential Equations38 материалов

Introduction to Week Six

Week Six Introduction Видео

Numerical Solutions of PDEs

Boundary and Initial Value Problems | Lecture 60ВидеоClassify Partial Differential EquationsЗаданиеCentral Difference Approximation | Lecture 61ВидеоHigher-order Central Difference ApproximationЧтение

Direct Solution of Boundary Value Problems

Discrete Laplace Equation | Lecture 62ВидеоMean Value Property of the Laplace EquationЧтениеNatural Ordering | Lecture 63ВидеоCoordinates of the four cornersЧтениеMatrix Formulation | Lecture 64ВидеоThe Discrete Laplace Equation on a Four-by-Four GridЧтениеNumber of Interior and Boundary PointsЧтениеMATLAB Solution of the Laplace Equation (Direct Method) | Lecture 65ВидеоDirect Solution of the Laplace EquationВнешний инструмент

Iterative Solution of Boundary Value Problems

Jacobi, Gauss-Seidel and SOR Methods | Lecture 66ВидеоIterative Solution of a System of Linear EquationsЧтениеRed-Black Ordering | Lecture 67ВидеоMATLAB Solution of the Laplace Equation (Iterative Method) | Lecture 68ВидеоIterative Solution of the Laplace EquationВнешний инструмент

Time-stepping Methods for Initial Value Problems

Explicit Methods for Solving the Diffusion Equation | Lecture 69ВидеоUsing a Second-Order Time-Stepping MethodЧтениеFTCS Scheme for the Advection EquationЧтениеVon Neumann Stability Analysis of the FTCS Scheme | Lecture 70ВидеоVon Neumann Stability Analysis of the FTCS Scheme for the Advection EquationЧтениеImplicit Methods for Solving the Diffusion Equation | Lecture 71Видео

Quiz

Week Six AssessmentЗадание

Programming Assignment: Two-dimensional Diffusion Equation

Two-Dimensional Diffusion Equation | Lecture 74ВидеоTwo-Dimensional Diffusion EquationВнешний инструментReference Solution to "Two-Dimensional Diffusion Equation"Чтение

Farewell

Concluding Remarks ВидеоPlease Rate this CourseЧтениеAcknowledgementsЧтение
Elliptical Planetary OrbitsВнешний инструмент
Implicit Discrete Advection EquationЧтение
Crank-Nicolson Method for the Diffusion Equation | Lecture 72Видео
Lax Scheme for the Advection EquationЧтение
MATLAB Solution of the Diffusion Equation | Lecture 73Видео
Difference Approximations for the Derivative at Boundary PointsЧтение
The Diffusion Equation with No-Flux Boundary ConditionsВнешний инструмент