major bottlenecks CT1

0.0(0)
Studied by 0 people
call kaiCall Kai
Locked
learnLearn
examPractice Test
spaced repetitionSpaced Repetition
heart puzzleMatch
flashcardsFlashcards
GameKnowt Play
Card Sorting

1/4

flashcard set

Earn XP

Description and Tags

first iteration

Last updated 8:58 AM on 12/25/25
Name
Mastery
Learn
Test
Matching
Spaced
Call with Kai
Chat

No analytics yet

Send a link to your students to track their progress

5 Terms

1
New cards
<p>Power series method for ODEs</p>

Power series method for ODEs

  1. Assume a series

  1. Differentiate

  2. Substitute

  3. reindex so all terms are x^n

  4. collect coefficients

  5. Isolate the the highest index

  6. apply initial conditions if given

  7. write the amount of non zero terms asked


<ol><li><p>Assume a series</p></li></ol><ol start="2"><li><p>Differentiate</p></li><li><p>Substitute</p></li><li><p>reindex so all terms are x^n</p></li><li><p>collect coefficients</p></li><li><p>Isolate the the highest index</p></li><li><p>apply initial conditions if given</p></li><li><p>write the amount of non zero terms asked</p></li></ol><p></p>
2
New cards
<p>LINEAR SYSTEMS</p>

LINEAR SYSTEMS

p = a + d

detA = ad - bc = q
delta = p² - 4q


<p>p = a + d</p><p>detA = ad - bc = q<br>delta = p² - 4q <br><br></p>
3
New cards
<p>VARIATION OF PARAMETERS</p>

VARIATION OF PARAMETERS

  1. solve the homogenous equation
    yh = c1y1 + c2y2

  2. Assume a particular solution
    yp = mu1(x)y1 + mu2(x)y2

  3. (u1’y1 + u2’y2 = 0
    (u1’y1’ + u2’y2’ = g(x)

  4. compute the wronskian
    W = y1y2’ - y1’y2

  5. solve for mu1’ and mu2’

  6. Integrate the mu’s


<ol><li><p>solve the homogenous equation<br>yh = c1y1 + c2y2</p></li><li><p>Assume a particular solution <br>yp = mu1(x)y1 + mu2(x)y2</p></li><li><p>(u1’y1 + u2’y2 = 0<br>(u1’y1’ + u2’y2’ = g(x)</p></li><li><p>compute the wronskian<br>W = y1y2’ - y1’y2</p></li><li><p>solve for mu1’ and mu2’</p></li><li><p>Integrate the mu’s<br></p></li></ol><p></p>
4
New cards
<p>FIRST-ORDER ODEs (1)</p>

FIRST-ORDER ODEs (1)

  1. Rearrange all y;s on one side, all x’s on the other.

  2. Integrate both sides.

  3. Combine constant into one C

  4. Apply IC immediately if given

  5. Solve for y if required


<ol><li><p>Rearrange all y;s on one side, all x’s on the other.</p></li><li><p>Integrate both sides.</p></li><li><p>Combine constant into one C</p></li><li><p>Apply IC immediately if given</p></li><li><p>Solve for y if required </p></li></ol><p></p>
5
New cards
<p>FIRST-ORDER ODEs (2)</p>

FIRST-ORDER ODEs (2)

  1. Write in standard form

  2. compute integrating factor

  3. multiply entire equation by mu(x)

  4. left side is product rule

  5. integrate both sides

  6. solve for y

  7. apply IC


<ol><li><p>Write in standard form</p></li><li><p>compute integrating factor</p></li><li><p>multiply entire equation by mu(x)</p></li><li><p>left side is product rule</p></li><li><p>integrate both sides</p></li><li><p>solve for y</p></li><li><p>apply IC</p></li></ol><p></p>