Since we want a specific potential function, we will choose K = 0, and so 1x3 3 Dy3. We know that if the curve C is given by r(t) with a sts b, the + F. dr = f(r(b)) – f(r(a)).

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Topic Video
Question
Use part (a) to evaluate
Vf • dr along the given curve C.
Step 1
Since we want a specific potential function, we will choose K = 0, and so
f(x, y) = x
1x3 +
3
3. We know that if the curve C is given by r(t) with a <t s b, then
F• dr = f(r(b)) – f(r(a)).
Transcribed Image Text:Use part (a) to evaluate Vf • dr along the given curve C. Step 1 Since we want a specific potential function, we will choose K = 0, and so f(x, y) = x 1x3 + 3 3. We know that if the curve C is given by r(t) with a <t s b, then F• dr = f(r(b)) – f(r(a)).
Consider F and C below.
F(x, y) = x2 i + y2 j
C is the arc of the parabola y = 3x2 from (-2, 12) to (-1, 3)
Exercise (a)
Find a function f such that F = Vf.
Step 1
If Vf(x, y) = F(x, y) = x²i + y²j, then
fx(x, y) =
and
fy(x, y) =
Transcribed Image Text:Consider F and C below. F(x, y) = x2 i + y2 j C is the arc of the parabola y = 3x2 from (-2, 12) to (-1, 3) Exercise (a) Find a function f such that F = Vf. Step 1 If Vf(x, y) = F(x, y) = x²i + y²j, then fx(x, y) = and fy(x, y) =
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Knowledge Booster
Chain Rule
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,