18.03 Differential Equations, Spring 2006
Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which c...
| Main Authors: | , |
|---|---|
| Other Authors: | |
| Format: | Learning Object |
| Language: | en-US |
| Published: |
2006
|
| Subjects: | |
| Online Access: | http://hdl.handle.net/1721.1/70961 |
| _version_ | 1826194311317815296 |
|---|---|
| author | Miller, Haynes Mattuck, Arthur |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Miller, Haynes Mattuck, Arthur |
| author_sort | Miller, Haynes |
| collection | MIT |
| description | Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time. Topics include: Solution of first-order ODE's by analytical, graphical and numerical methods; Linear ODE's, especially second order with constant coefficients; Undetermined coefficients and variation of parameters; Sinusoidal and exponential signals: oscillations, damping, resonance; Complex numbers and exponentials; Fourier series, periodic solutions; Delta functions, convolution, and Laplace transform methods; Matrix and first order linear systems: eigenvalues and eigenvectors; and Non-linear autonomous systems: critical point analysis and phase plane diagrams. |
| first_indexed | 2024-09-23T09:54:05Z |
| format | Learning Object |
| id | mit-1721.1/70961 |
| institution | Massachusetts Institute of Technology |
| language | en-US |
| last_indexed | 2025-03-10T08:16:51Z |
| publishDate | 2006 |
| record_format | dspace |
| spelling | mit-1721.1/709612025-02-24T15:06:48Z 18.03 Differential Equations, Spring 2006 Differential Equations Miller, Haynes Mattuck, Arthur Massachusetts Institute of Technology. Department of Mathematics Ordinary Differential Equations ODE modeling physical systems first-order ODE's Linear ODE's second order ODE's second order ODE's with constant coefficients Undetermined coefficients variation of parameters Sinusoidal signals exponential signals oscillations damping resonance Complex numbers and exponentials Fourier series periodic solutions Delta functions convolution Laplace transform methods Matrix systems first order linear systems eigenvalues and eigenvectors Non-linear autonomous systems critical point analysis phase plane diagrams Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time. Topics include: Solution of first-order ODE's by analytical, graphical and numerical methods; Linear ODE's, especially second order with constant coefficients; Undetermined coefficients and variation of parameters; Sinusoidal and exponential signals: oscillations, damping, resonance; Complex numbers and exponentials; Fourier series, periodic solutions; Delta functions, convolution, and Laplace transform methods; Matrix and first order linear systems: eigenvalues and eigenvectors; and Non-linear autonomous systems: critical point analysis and phase plane diagrams. 2006-06 Learning Object 18.03-Spring2006 local: 18.03 local: IMSCP-MD5-ac47dc8c6f52190dcbcf3983c01a04cf http://hdl.handle.net/1721.1/70961 en-US Usage Restrictions: This site (c) Massachusetts Institute of Technology 2012. Content within individual courses is (c) by the individual authors unless otherwise noted. The Massachusetts Institute of Technology is providing this Work (as defined below) under the terms of this Creative Commons public license ("CCPL" or "license") unless otherwise noted. The Work is protected by copyright and/or other applicable law. Any use of the work other than as authorized under this license is prohibited. By exercising any of the rights to the Work provided here, You (as defined below) accept and agree to be bound by the terms of this license. The Licensor, the Massachusetts Institute of Technology, grants You the rights contained here in consideration of Your acceptance of such terms and conditions. text/html Spring 2006 |
| spellingShingle | Ordinary Differential Equations ODE modeling physical systems first-order ODE's Linear ODE's second order ODE's second order ODE's with constant coefficients Undetermined coefficients variation of parameters Sinusoidal signals exponential signals oscillations damping resonance Complex numbers and exponentials Fourier series periodic solutions Delta functions convolution Laplace transform methods Matrix systems first order linear systems eigenvalues and eigenvectors Non-linear autonomous systems critical point analysis phase plane diagrams Miller, Haynes Mattuck, Arthur 18.03 Differential Equations, Spring 2006 |
| title | 18.03 Differential Equations, Spring 2006 |
| title_full | 18.03 Differential Equations, Spring 2006 |
| title_fullStr | 18.03 Differential Equations, Spring 2006 |
| title_full_unstemmed | 18.03 Differential Equations, Spring 2006 |
| title_short | 18.03 Differential Equations, Spring 2006 |
| title_sort | 18 03 differential equations spring 2006 |
| topic | Ordinary Differential Equations ODE modeling physical systems first-order ODE's Linear ODE's second order ODE's second order ODE's with constant coefficients Undetermined coefficients variation of parameters Sinusoidal signals exponential signals oscillations damping resonance Complex numbers and exponentials Fourier series periodic solutions Delta functions convolution Laplace transform methods Matrix systems first order linear systems eigenvalues and eigenvectors Non-linear autonomous systems critical point analysis phase plane diagrams |
| url | http://hdl.handle.net/1721.1/70961 |
| work_keys_str_mv | AT millerhaynes 1803differentialequationsspring2006 AT mattuckarthur 1803differentialequationsspring2006 AT millerhaynes differentialequations AT mattuckarthur differentialequations |