Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
How do I parameterize the portion from Rei pi/4 to 0?

How do I parameterize the portion from Rei pi/4 to 0?

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
100%

How do I parameterize the portion from Rei pi/4 to 0?  

The image above displays a graph depicting the path of a contour in the complex plane. The contour starts at the origin (0, 0), moves linearly to the point represented by \(Re^{i\frac{\pi}{4}}\), and then follows a curved path back to the point \(R\) on the real axis. ### Graph Explanation: 1. **Axes**: - The horizontal axis is labeled \(R\) and represents the real part of the complex plane. - The vertical axis is not labeled but typically represents the imaginary part of the complex plane. 2. **Path Description**: - The contour begins at the origin, indicated by the point \(0\) at the intersection of the two axes. - It then proceeds linearly to the point labeled \(Re^{i\frac{\pi}{4}}\). This point is at a distance \(R\) from the origin and makes an angle of \( \frac{\pi}{4}\) (or 45 degrees) with the positive real axis. - The path then follows a curved line back to the point \(R\) on the real axis. This curved part is an arc, indicating a transition from the angular position \(Re^{i\frac{\pi}{4}}\) to \(R\) along a radial path. 3. **Arrows**: - The arrows on the graph indicate the direction of the contour. It moves from the origin along a straight line to \(Re^{i\frac{\pi}{4}}\) and then follows an arc back to \(R\). This graph is typically used in the context of complex analysis to illustrate contour integration, a crucial concept for evaluating integrals over complex functions using paths in the complex plane.
Transcribed Image Text:The image above displays a graph depicting the path of a contour in the complex plane. The contour starts at the origin (0, 0), moves linearly to the point represented by \(Re^{i\frac{\pi}{4}}\), and then follows a curved path back to the point \(R\) on the real axis. ### Graph Explanation: 1. **Axes**: - The horizontal axis is labeled \(R\) and represents the real part of the complex plane. - The vertical axis is not labeled but typically represents the imaginary part of the complex plane. 2. **Path Description**: - The contour begins at the origin, indicated by the point \(0\) at the intersection of the two axes. - It then proceeds linearly to the point labeled \(Re^{i\frac{\pi}{4}}\). This point is at a distance \(R\) from the origin and makes an angle of \( \frac{\pi}{4}\) (or 45 degrees) with the positive real axis. - The path then follows a curved line back to the point \(R\) on the real axis. This curved part is an arc, indicating a transition from the angular position \(Re^{i\frac{\pi}{4}}\) to \(R\) along a radial path. 3. **Arrows**: - The arrows on the graph indicate the direction of the contour. It moves from the origin along a straight line to \(Re^{i\frac{\pi}{4}}\) and then follows an arc back to \(R\). This graph is typically used in the context of complex analysis to illustrate contour integration, a crucial concept for evaluating integrals over complex functions using paths in the complex plane.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
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