# UTPA STEM/CBI Courses/Graduate Seminar (combined with BVP-MATH 4318)/How to use Maxwell Model to Reconstruct Radar Image

Course Title: How to use Maxwell Model to Reconstruct Radar Image
Lecture Topic:
Instructor: Zhijun Qiao
Institution: UTPA - Math Dept

## Backwards Design

Course Objectives
* Primary Objectives- By the next class period students will be able to:
** Understand the model and how to solve the Maxwell equation
* Sub Objectives- The objectives will require that students be able to:
** What basic concepts
** What approach/method used
* Difficulties- Students may have difficulty:
** How to apply the boundary values to get solution
** students may encounter the problems how to solve the ODE reduced from the Maxwell equation
* Real-World Contexts- There are many ways that students can use this material in the real-world, such as:
** Radar Wave
** Water Wave
Model of Knowledge
* Concept Map
** Boundary Condition
** Domain for Solution
** Equations nature (describe magnetic-wave)
* Content Priorities
** Enduring Understanding
*** Derivatives
*** Origin of Maxwell equation
** Important to Do and Know
*** Separation of Variabls
** Worth Being Familiar with
*** Calculus III
*** ODEs
Assessment of Learning
* Formative Assessment
** In Class (groups)
*** Discussion of Separation of Variabls
*** Discussion of solving ODEs
** Homework (individual)
*** Get familiar with ODEs and solve them
*** Calculus III
* Summative Assessment
** Discussion in group's conclusion

## Legacy Cycle

OBJECTIVE
By the next class period, students will be able to:
* understand the math model -- PDEs (each term in model)
* understand boundary conditions
* understand initial conditions and scource signal function
The objectives will require that students be able to:
* explain model by themself
* try to replated the system to the radar signal process
* figure out source function to match the initial or boundary conditions.
THE CHALLENGE
How to use Maxwell euqations to reconstruct the radar image for real targets
GENERATE IDEAS
This seminar is to mentor the graduate students participating in my DoD research project on PDE Analysis and Radar Image Reconstruction to enhance achievement level and retention rate here at UTPA. The program students are anticipated to apply mathematical and engeneering methodology to deal with radar imaging problems appearing in military, air force and naval affairs. I deliver PDEs lectures to my DoD program students and direct them to do preliminary work for my DoD research project on Radar Image Reconstruction.
Ideas: solving model using fundamental solutions; point spread functions; delta functions; Solutions for Inverse Problems based on radar data; and numeric simulations.
MULTIPLE PERSPECTIVES
Handle the method of separation of variables and wave front set, and delta function/point spread function skills.
RESEARCH & REVISE
This is my DoD research project on PDE Analysis and Radar Image Reconstruction. The program students are anticipated to apply mathematical and engeneering methodology to deal with radar imaging problems appearing in military, air force and naval affairs. I will give special PDEs lectures to my DoD program students and direct them to do preliminary work for my DoD research project on Radar Image Reconstruction.
TEST YOUR METTLE
Verify every step works fine. We plan to use radar data to test our procedure and solution of inverse problem as well as numeric simulations.
GO PUBLIC
Finally, our students will attend national and international conferences to show their work done through the project. Also, we plan to publish our work in some refereed journal or proceedings.

## Pre-Lesson Quiz

* Linear PDEs
* Initial Conditions
* Boundary Conditions
* Separation of Variables
* Transformation through some variables
* Integrals formulas
* Partial Derivatives
* Electro-magnetic wave model
* Range Image
* Crossing Range Image
* Delta function
* Point Spread Function
* Sinc function
* Time sampling
* Fourier integrals
* Fourier series
* Fourier Integral Operators

## Test Your Mettle Quiz

* Scattering Data
* Incidental Data
* Electro-magnetic wave
* Slow time image
* Fast time image
* Fundamental solutions
* Fourier Integral Operators
* Time sampling
* Inverse problem
* Sinc function and refectivity function
* Numeric Simulations
129.113.150.41 21:06, 19 January 2010 (UTC)It would be useful to include the actual questions for the pre-lesson quiz and test your mettle quiz