Practice Introduction (8.1.1) - Picard’s Method - Mathematics - iii (Differential Calculus) - Vol 4

Practice: Introduction

Lesson 8.1.1Picard’s Method

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6 sample questions

Question 1.
What is the first step in Picard's Iteration Method?
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Think about what value you have at x = 0.
Question 2.
Define what ODE stands for.
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It involves derivatives and describes change.
3Question 3.
What does Picard's Iteration Method primarily solve?
- Algebraic equations
- Ordinary differential equations
- Matrix equations
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Remember what type of equations are often difficult to solve.
4Question 4.
True or False: The integral form is the basis for Picard’s Method.
- True
- False
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Consider the transformation mentioned in the introduction.
Question 5.
For a nonlinear ODE like dy/dx = y^2 + x, use Picard's method to find at least three iterations starting with y(0) = 1. Discuss the observed convergence or lack thereof.
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Be cautious about how y changes your f(t, y) as it may alter your approximations significantly.
Question 6.
Consider dy/dx = e^(-y), y(0) = 0. Show at least two iterations using Picard’s method and highlight any difficulties in convergence.
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Look out for how exponential growth affects iterations.

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