advanced mathematical methods for civil engineering applications
TRANSCRIPT
![Page 1: Advanced Mathematical Methods for Civil Engineering Applications](https://reader033.vdocuments.us/reader033/viewer/2022042522/55cf9c00550346d033a832eb/html5/thumbnails/1.jpg)
Advanced Mathematical Methods for Civil Engineering Applications
Ordinary Differential Equations (ODEs) (Section I)(Section I)
Wonsiri Punurai, PhDWonsiri Punurai, PhD
Department of Civil EngineeringRoom 6391, EG Building 3Faculty of Engineering, Mahidol UniversityClass Web: www.egmu.net/~civil/wonsiri
![Page 2: Advanced Mathematical Methods for Civil Engineering Applications](https://reader033.vdocuments.us/reader033/viewer/2022042522/55cf9c00550346d033a832eb/html5/thumbnails/2.jpg)
Outline
Basic IdeasApproximations and Errors ReviewTaylor Series and Order Notation ReviewEuler’s MethodPredictor-Corrector ApproachRunge-Kutta MethodAdaptive step size Algorithm
Basic IdeasApproximations and Errors ReviewTaylor Series and Order Notation ReviewEuler’s MethodPredictor-Corrector ApproachRunge-Kutta MethodAdaptive step size Algorithm
![Page 3: Advanced Mathematical Methods for Civil Engineering Applications](https://reader033.vdocuments.us/reader033/viewer/2022042522/55cf9c00550346d033a832eb/html5/thumbnails/3.jpg)
Basic ideas - ODEs in Civil Engineering
![Page 4: Advanced Mathematical Methods for Civil Engineering Applications](https://reader033.vdocuments.us/reader033/viewer/2022042522/55cf9c00550346d033a832eb/html5/thumbnails/4.jpg)
Basic ideas - ODEs in Civil Engineering
![Page 5: Advanced Mathematical Methods for Civil Engineering Applications](https://reader033.vdocuments.us/reader033/viewer/2022042522/55cf9c00550346d033a832eb/html5/thumbnails/5.jpg)
Approximations and Errors Review
![Page 6: Advanced Mathematical Methods for Civil Engineering Applications](https://reader033.vdocuments.us/reader033/viewer/2022042522/55cf9c00550346d033a832eb/html5/thumbnails/6.jpg)
Outline
Basic IdeasApproximations and Errors ReviewTaylor Series and Order Notation ReviewEuler’s MethodPredictor-Corrector ApproachRunge-Kutta MethodAdaptive step size Algorithm
Basic IdeasApproximations and Errors ReviewTaylor Series and Order Notation ReviewEuler’s MethodPredictor-Corrector ApproachRunge-Kutta MethodAdaptive step size Algorithm
![Page 7: Advanced Mathematical Methods for Civil Engineering Applications](https://reader033.vdocuments.us/reader033/viewer/2022042522/55cf9c00550346d033a832eb/html5/thumbnails/7.jpg)
Use of significant figures
![Page 8: Advanced Mathematical Methods for Civil Engineering Applications](https://reader033.vdocuments.us/reader033/viewer/2022042522/55cf9c00550346d033a832eb/html5/thumbnails/8.jpg)
Round-off errors
![Page 9: Advanced Mathematical Methods for Civil Engineering Applications](https://reader033.vdocuments.us/reader033/viewer/2022042522/55cf9c00550346d033a832eb/html5/thumbnails/9.jpg)
Approximations and Errors Review
![Page 10: Advanced Mathematical Methods for Civil Engineering Applications](https://reader033.vdocuments.us/reader033/viewer/2022042522/55cf9c00550346d033a832eb/html5/thumbnails/10.jpg)
Error Definition
![Page 11: Advanced Mathematical Methods for Civil Engineering Applications](https://reader033.vdocuments.us/reader033/viewer/2022042522/55cf9c00550346d033a832eb/html5/thumbnails/11.jpg)
Example – error estimates for iterative methods
See more in later
![Page 12: Advanced Mathematical Methods for Civil Engineering Applications](https://reader033.vdocuments.us/reader033/viewer/2022042522/55cf9c00550346d033a832eb/html5/thumbnails/12.jpg)
Example – error estimates for iterative methods
![Page 13: Advanced Mathematical Methods for Civil Engineering Applications](https://reader033.vdocuments.us/reader033/viewer/2022042522/55cf9c00550346d033a832eb/html5/thumbnails/13.jpg)
Effect of order of operations
![Page 14: Advanced Mathematical Methods for Civil Engineering Applications](https://reader033.vdocuments.us/reader033/viewer/2022042522/55cf9c00550346d033a832eb/html5/thumbnails/14.jpg)
Taylor Series
![Page 15: Advanced Mathematical Methods for Civil Engineering Applications](https://reader033.vdocuments.us/reader033/viewer/2022042522/55cf9c00550346d033a832eb/html5/thumbnails/15.jpg)
Outline
Basic IdeasApproximations and Errors ReviewTaylor Series and Order Notation ReviewEuler’s MethodPredictor-Corrector ApproachRunge-Kutta MethodAdaptive step size Algorithm
Basic IdeasApproximations and Errors ReviewTaylor Series and Order Notation ReviewEuler’s MethodPredictor-Corrector ApproachRunge-Kutta MethodAdaptive step size Algorithm
![Page 16: Advanced Mathematical Methods for Civil Engineering Applications](https://reader033.vdocuments.us/reader033/viewer/2022042522/55cf9c00550346d033a832eb/html5/thumbnails/16.jpg)
Taylor Series
![Page 17: Advanced Mathematical Methods for Civil Engineering Applications](https://reader033.vdocuments.us/reader033/viewer/2022042522/55cf9c00550346d033a832eb/html5/thumbnails/17.jpg)
Taylor series of a function
![Page 18: Advanced Mathematical Methods for Civil Engineering Applications](https://reader033.vdocuments.us/reader033/viewer/2022042522/55cf9c00550346d033a832eb/html5/thumbnails/18.jpg)
Taylor series expansions for some common functions
![Page 19: Advanced Mathematical Methods for Civil Engineering Applications](https://reader033.vdocuments.us/reader033/viewer/2022042522/55cf9c00550346d033a832eb/html5/thumbnails/19.jpg)
MATLAB example – evaluating the series for sin(x)
![Page 20: Advanced Mathematical Methods for Civil Engineering Applications](https://reader033.vdocuments.us/reader033/viewer/2022042522/55cf9c00550346d033a832eb/html5/thumbnails/20.jpg)
Order Notation
![Page 21: Advanced Mathematical Methods for Civil Engineering Applications](https://reader033.vdocuments.us/reader033/viewer/2022042522/55cf9c00550346d033a832eb/html5/thumbnails/21.jpg)
Outline
Basic IdeasApproximations and Errors ReviewTaylor Series and Order Notation ReviewEuler’s MethodPredictor-Corrector ApproachRunge-Kutta MethodAdaptive step size Algorithm
Basic IdeasApproximations and Errors ReviewTaylor Series and Order Notation ReviewEuler’s MethodPredictor-Corrector ApproachRunge-Kutta MethodAdaptive step size Algorithm
![Page 22: Advanced Mathematical Methods for Civil Engineering Applications](https://reader033.vdocuments.us/reader033/viewer/2022042522/55cf9c00550346d033a832eb/html5/thumbnails/22.jpg)
Euler’s Method
![Page 23: Advanced Mathematical Methods for Civil Engineering Applications](https://reader033.vdocuments.us/reader033/viewer/2022042522/55cf9c00550346d033a832eb/html5/thumbnails/23.jpg)
Example - Hand Calculation with Euler’s Method
![Page 24: Advanced Mathematical Methods for Civil Engineering Applications](https://reader033.vdocuments.us/reader033/viewer/2022042522/55cf9c00550346d033a832eb/html5/thumbnails/24.jpg)
Implementing Euler’s Method in MATLAB
![Page 25: Advanced Mathematical Methods for Civil Engineering Applications](https://reader033.vdocuments.us/reader033/viewer/2022042522/55cf9c00550346d033a832eb/html5/thumbnails/25.jpg)
Solving Previous Example using MATLAB