Section 6.1 - Slope Fields and Euler's Method
Essential Question(s):
What do slope fields illustrate?
What is the difference between a general solution and a particular solution?
What do slope fields illustrate?
What is the difference between a general solution and a particular solution?
Follow these three steps to complete this "flip" lesson.
STEP 1: Preparation
Title your spiral with the heading above and copy the essential question(s).
Title your spiral with the heading above and copy the essential question(s).
STEP 2: Vocabulary & Examples
Answer the follow questions. They address examples, vocabulary, rules, theorems, corollaries, procedures, and/or postulates. Following a Cornell notes format, the questions should be written in the left-hand column and with the answers to the right of the question. Make sure to write enough to answer the question.
Answer the follow questions. They address examples, vocabulary, rules, theorems, corollaries, procedures, and/or postulates. Following a Cornell notes format, the questions should be written in the left-hand column and with the answers to the right of the question. Make sure to write enough to answer the question.
Differential Equations
Slope Fields
Euler's Method
- Where do differential equations stem from?
- What is a differential equation and its order?
- What are the different types of solutions for a differential equation?
- What is different between solutions for a continuous or discontinuous curve?
- How can the FTC help with initial value problem?
- Why does the graph of a general solution consist of parallel curves or lines?
Slope Fields
- What is a slope field? (
Euler's Method
- What does Euler's Method do?
- What is Euler's Method?
- A note about movies and math. (sidebar)
- How would we know if the approximation is an over- or under-estimate?
- How can Euler's Method do a better job of approximating a curve?