Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
An exercise on the gradient of a vector field Consider a potential function of the form • U(x, y) = Ax² + Bxy + Cy² + Dx + Ey+F Compute the gradient vector VU (x, y). Answer: U(x, y) = (2Ax+By+D,Bx+2C y +E) ⚫ Pick some values for A, B, C, D, E, F out of a hat (keep it simple!) • Ask yourself: does there exist a point (x, y) at which the gradient vector VU(x, y) is the zero vector? If so, is that point unique? • Repeat as necessary. • What conditions on A, B, C, D, E, F are necessary and sufficient for the existence of a point (x, y) at which VU (x, y) is the zero vector? If that point exists, is it unique?

An exercise on the gradient of a vector field Consider a potential function of the form • U(x, y) = Ax² + Bxy + Cy² + Dx + Ey+F Compute the gradient vector VU (x, y). Answer: U(x, y) = (2Ax+By+D,Bx+2C y +E) ⚫ Pick some values for A, B, C, D, E, F out of a hat (keep it simple!) • Ask yourself: does there exist a point (x, y) at which the gradient vector VU(x, y) is the zero vector? If so, is that point unique? • Repeat as necessary. • What conditions on A, B, C, D, E, F are necessary and sufficient for the existence of a point (x, y) at which VU (x, y) is the zero vector? If that point exists, is it unique?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
An exercise on the gradient of a vector field Consider a potential function of the form • U(x, y) = Ax² + Bxy + Cy² + Dx + Ey+F Compute the gradient vector VU (x, y). Answer: U(x, y) = (2Ax+By+D,Bx+2C y +E) ⚫ Pick some values for A, B, C, D, E, F out of a hat (keep it simple!) • Ask yourself: does there exist a point (x, y) at which the gradient vector VU(x, y) is the zero vector? If so, is that point unique? • Repeat as necessary. • What conditions on A, B, C, D, E, F are necessary and sufficient for the existence of a point (x, y) at which VU (x, y) is the zero vector? If that point exists, is it unique?
Transcribed Image Text:An exercise on the gradient of a vector field Consider a potential function of the form • U(x, y) = Ax² + Bxy + Cy² + Dx + Ey+F Compute the gradient vector VU (x, y). Answer: U(x, y) = (2Ax+By+D,Bx+2C y +E) ⚫ Pick some values for A, B, C, D, E, F out of a hat (keep it simple!) • Ask yourself: does there exist a point (x, y) at which the gradient vector VU(x, y) is the zero vector? If so, is that point unique? • Repeat as necessary. • What conditions on A, B, C, D, E, F are necessary and sufficient for the existence of a point (x, y) at which VU (x, y) is the zero vector? If that point exists, is it unique?
Expert Solution
steps

Step by step

Solved in 2 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
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,
SEE MORE TEXTBOOKS