Ordinary differential equations | Differential equations

Exponential response formula

In mathematics, the exponential response formula (ERF), also known as exponential response and complex replacement, is a method used to find a particular solution of a non-homogeneous linear ordinary differential equation of any order. The exponential response formula is applicable to non-homogeneous linear ordinary differential equations with constant coefficients if the function is polynomial, sinusoidal, exponential or the combination of the three. The general solution of a non-homogeneous linear ordinary differential equation is a superposition of the general solution of the associated homogeneous ODE and a particular solution to the non-homogeneous ODE. Alternative methods for solving ordinary differential equations of higher order are method of undetermined coefficients and method of variation of parameters. (Wikipedia).

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Determine if Equations Are Linear or Exponential and Increasing or Decreasing

This video explains how to identify linear and exponential equation as well as determine if the behavior is increasing or decreasing. http://mathispower4u.com

From playlist Introduction to Exponential Functions

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Exponential Growth Models

Introduces notation and formulas for exponential growth models, with solutions to guided problems.

From playlist Discrete Math

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Compare Linear and Exponential Functions

This video compares linear and exponential functions. http://mathispower4u.com

From playlist Introduction to Exponential Functions

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Determine the Initial Value and Percent Rate of Change from an Exponential Equation

This video explains how to determine the initial value and growth or decay rate from an exponential equation. http://mathispower4u.com

From playlist Introduction to Exponential Functions

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Solving an exponential equation using the one to one property 16^x + 2 = 6

👉 Learn how to solve exponential equations. An exponential equation is an equation in which a variable occurs as an exponent. To solve an exponential equation, we isolate the exponential part of the equation. Then we take the log of both sides. Note that the base of the log should correspo

From playlist Solve Exponential Equations with Logarithms

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Learn basics for solving an exponential equation by using one to one property

👉 Learn how to solve exponential equations. An exponential equation is an equation in which a variable occurs as an exponent. To solve an exponential equation, we isolate the exponential part of the equation. Then we take the log of both sides. Note that the base of the log should correspo

From playlist Solve Exponential Equations with Logarithms

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Second order systems and complex poles

Second order systems can have complex poles. This video explores the link between first orders in series, second orders and complex poles

From playlist Laplace

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5. Second-Order Equations (continued)

MIT 2.087 Engineering Mathematics: Linear Algebra and ODEs, Fall 2014 View the complete course: http://ocw.mit.edu/2-087F14 Instructor: Gilbert Strang In this lecture, Prof. Strang explains second-order equations. License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/

From playlist MIT 2.087 Engineering Mathematics: Linear Algebra and ODEs, Fall 2014

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Pure Resonance | MIT 18.03SC Differential Equations, Fall 2011

Pure Resonance Instructor: Lydia Bourouiba View the complete course: http://ocw.mit.edu/18-03SCF11 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT 18.03SC Differential Equations, Fall 2011

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13. Frequency response of LTI systems

MIT 6.02 Introduction to EECS II: Digital Communication Systems, Fall 2012 View the complete course: http://ocw.mit.edu/6-02F12 Instructor: George Verghese This lecture continues the discussion of properties of the frequency response and the shift from time to frequency domain. Examples o

From playlist MIT 6.02 Introduction to EECS II: Digital Communication Systems, Fall 2012

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Learn the basics for solve an exponential equation using a calculator

👉 Learn how to solve exponential equations. An exponential equation is an equation in which a variable occurs as an exponent. To solve an exponential equation, we isolate the exponential part of the equation. Then we take the log of both sides. Note that the base of the log should correspo

From playlist Solve Exponential Equations with Logarithms

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Frequency linked to Laplace

How can the response of a system to sinusoidal inputs be useful? I explore the links between Fourier series and the Laplace transform in this video

From playlist Frequency domain

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Solve an exponential equation using one to one property and isolating the exponent

👉 Learn how to solve exponential equations. An exponential equation is an equation in which a variable occurs as an exponent. To solve an exponential equation, we isolate the exponential part of the equation. Then we take the log of both sides. Note that the base of the log should correspo

From playlist Solve Exponential Equations with Logarithms

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Write Exponential Equations Given Initial Values and Growth or Decay Rate

This video explains how to write exponential equations given the initial value and the percent of change. http://mathispower4u.com

From playlist Introduction to Exponential Functions

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Lec 33 | MIT 18.085 Computational Science and Engineering I, Fall 2008

Lecture 33: Filters; Fourier integral transform (part 1) License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT 18.085 Computational Science & Engineering I, Fall 2008

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14. Spectral representation of signals

MIT 6.02 Introduction to EECS II: Digital Communication Systems, Fall 2012 View the complete course: http://ocw.mit.edu/6-02F12 Instructor: George Verghese This lecture starts with a demonstration of echo cancelation using deconvolution, and then continues to cover the spectral content of

From playlist MIT 6.02 Introduction to EECS II: Digital Communication Systems, Fall 2012

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4. Second-Order Equations

MIT 2.087 Engineering Mathematics: Linear Algebra and ODEs, Fall 2014 View the complete course: http://ocw.mit.edu/2-087F14 Instructor: Gilbert Strang In this lecture, Prof. Strang explains second-order equations. License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/

From playlist MIT 2.087 Engineering Mathematics: Linear Algebra and ODEs, Fall 2014

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Laplace Transform an intuitive approach

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From playlist Fourier and Laplace

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Using inverse properties to solve an exponential equation

👉 Learn how to solve exponential equations. An exponential equation is an equation in which a variable occurs as an exponent. To solve an exponential equation, we isolate the exponential part of the equation. Then we take the log of both sides. Note that the base of the log should correspo

From playlist Solve Exponential Equations with Logarithms

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2. First-Order Equations

MIT 2.087 Engineering Mathematics: Linear Algebra and ODEs, Fall 2014 View the complete course: http://ocw.mit.edu/2-087F14 Instructor: Gilbert Strang In this lecture, Prof. Strang explains first-order equations. License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/t

From playlist MIT 2.087 Engineering Mathematics: Linear Algebra and ODEs, Fall 2014

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Equilibrium point | Method of undetermined coefficients | Signal processing | Characteristic polynomial | Deflection (engineering) | Kirchhoff's circuit laws | Polynomial | Exponential function | Resonance | Linearity | Euler's formula | Control theory | Mathematics | Ordinary differential equation | Real number | Time-invariant system | Harmonic oscillator | Sine wave | Eigenvalues and eigenvectors | Complex number | Variation of parameters | Linear differential equation