Practice Introduction To Ordinary Differential Equations (odes) (4.1) - Numerical Solutions of Ordinary Differential Equations

Practice: Introduction to Ordinary Differential Equations (ODEs)

Lesson 4.1Numerical Solutions of Ordinary Differential Equations

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9 questions

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6 sample questions

Question 1.
Define what an ordinary differential equation (ODE) is.
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Think about the equations that involve derivatives.
Question 2.
What is an initial value problem (IVP)?
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What do we need to specify to begin solving an ODE?
3Question 3.
What is an ordinary differential equation (ODE)?
- An equation involving functions of a single variable.
- An equation with multiple variables.
- A type of algebraic equation.
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Remember the definition of ODE—think about the derivatives!
4Question 4.
True or False: Numerical methods are only useful if an analytical solution exists.
- True
- False
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Consider the purpose of numerical methods.
Question 5.
Consider the ODE dy/dt = y with the initial condition y(0) = 2. Use Euler’s method with a step size of 0.5 to approximate y at t = 1.
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Remember to take small steps and adjust for each calculated slope.
Question 6.
Using the initial value problem dy/dt = -2y with y(0) = 1, outline why a numerical method may be preferred for large time intervals.
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Think about the characteristics of the differential equation and its behavior over time.

5 more questions in this section. Enroll free to practise them all.