Learning Objectives
Upon successful completion of this module, you will be able to:
1) Define an ordinary differential equation.
2) Differentiate between an ordinary and partial differential equation.
3) Solve first-order linear ordinary differential equations with fixed constants by using classical solution techniques.
4) Solve second-order linear ordinary differential equations with fixed constants by using classical solution techniques.
Videos
Title: Exact Solution of First-Order Ordinary Differential Equation with Fixed Constants: Example
Summary: Learn how to find the exact solution of a first-order ordinary differential equation with fixed constants by using the classical solution technique by finding the homogeneous and particular parts.
Learning Objectives: After watching this video, you will refresh your pre-requisite knowledge of how to solve a first-order ordinary differential equation with fixed constants by using classical solution techniques. This is required to find the true error in the numerical solution of ordinary differential equations.
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Title: Exact Solution of first-Order Ordinary Differential Equation with Fixed Constants: Another Example
Summary: Learn how you can find the exact solution of a first-order ordinary differential equation with fixed constants by using the classical solution technique by finding the homogeneous and particular parts. In this case, the form of the forcing functions and their derivatives matches the homogeneous solution.
Learning Objectives: After watching this video, you will refresh your pre-requisite knowledge of how to solve a first-order ordinary differential equation with fixed constants by using classical solution techniques. In this case, the forcing function and/or its derivatives match the homogeneous part of the solution. This is required to find the true error in the numerical solution of ordinary differential equations.
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Title: Exact Solution of 2nd order ODE with Fixed Constants: Distinct Real Roots of Characteristic Equation
Summary: Learn how you can find the exact solution of a second-order ordinary differential equation with fixed constants by using the classical solution technique by finding the homogeneous and particular parts. In this example, the roots of the characteristic equation are distinct real roots.
Learning Objectives: After watching this video, you will refresh your pre-requisite knowledge of how to solve a second-order ordinary differential equation with fixed constants by using classical solution techniques. This is required to find the true error in the numerical solution of ordinary differential equations.
Transcript: Read the transcript
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Title: Exact Solution of 2nd order ODE with Fixed Constants: Repeated Real Roots of Characteristic Equation
Summary: Learn how you can find the exact solution of a 2nd order ODE (with Fixed Constants) by using the classical solution technique by finding the homogeneous and particular parts. In this example, the roots of the characteristic equation are real and repeated.
Learning Objectives: After watching this video, you will refresh your pre-requisite knowledge of how to solve a second-order ordinary differential equation with fixed constants by using classical solution techniques. In this case, the characteristic equation of the homogeneous part of the solution has repeated roots. This is required to find the true error in the numerical solution of ordinary differential equations.
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Title: Fundamental Theorem of Calculus Used to Finding an Integral as an Ordinary Differential Equation
Summary: Learn how we use the Fundamental Theorem of Calculus to find an integral by posing it as an ordinary differential equation. This will later allow hence then to use the numerical solution of ordinary differential equations as a method to numerically solve definite integrals.
Learning Objectives: After watching this video, you will learn the fundamental theorem of calculus, and be able to pose a definite integral as an ordinary differential equation.
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