Upper Level Math for Optical Physics/Engineering

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In summary, the individual is a double major undergrad in physics and math and is interested in pursuing a PhD in optics research. They prefer experimental work and are looking to take one upper level math class that will help them in this field. They have narrowed down their options to Advanced Differential Equations and Dynamical Systems Theory. The latter is preferred, especially if they will be developing codes to integrate the differential equations.
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mandarino31
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I am entering my final year as a physics/math double major undergrad and have hopes to continue onto a PhD program where I can do optics research, either through a physics or ECE department. That being said, my interests lie in experimental work rather than computational or theoretical, but I have one upper level math class left required for my degree and I'm looking to take the one that will help me most to carry on with optics. I've narrowed my choices down to the two following courses.

Advanced Differential Equations (w/ ODE's as a prereq):
"Development and application of advanced topics in differential equations. Topics may include foundational theories of differential equations, partial differential equations, perturbation theory, calculus of variations, distribution theory, transform theory, or other advanced topics"

and Dynamical Systems Theory:
"Development and application of the theory of dynamical systems. Topics include phase plane analysis, bifurcation theory, and chaos theory. Basic applications relevant to each topic are included. Additional topics may include fractional dimensions, differential equations, and cellular automata."
 
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Dynamical Systems Theory, especially if you will be developing codes to integrate the diff eqs.
 

Related to Upper Level Math for Optical Physics/Engineering

1. What is the importance of upper level math in optical physics/engineering?

Upper level math is crucial in optical physics/engineering because it provides the necessary tools for analyzing and solving complex problems in this field. It allows scientists and engineers to understand the fundamental principles behind optical phenomena and develop advanced technologies such as lasers, fiber optics, and imaging systems.

2. What are some examples of upper level math concepts used in optical physics/engineering?

Some examples of upper level math concepts used in optical physics/engineering include vector calculus, differential equations, complex analysis, linear algebra, and Fourier analysis. These concepts are applied in the development of mathematical models for light propagation, reflection, refraction, and diffraction, among others.

3. How does upper level math improve optical designs and systems?

Upper level math allows for more accurate modeling and prediction of optical systems, leading to improved designs and performance. By using mathematical tools to analyze and optimize different parameters such as light intensity, polarization, and wavelength, engineers can create more efficient and precise optical systems.

4. Can upper level math be challenging for those without a strong math background?

Yes, upper level math can be challenging for those without a strong math background. It requires a solid foundation in basic math concepts and a strong understanding of algebra, geometry, and trigonometry. However, with dedication and practice, anyone can develop the necessary skills to understand and apply upper level math in optical physics/engineering.

5. How can someone prepare for studying upper level math for optical physics/engineering?

To prepare for studying upper level math for optical physics/engineering, it is recommended to have a strong understanding of basic math concepts and to review topics such as calculus, differential equations, and linear algebra. It can also be helpful to familiarize oneself with the properties of light and basic optical principles. Additionally, practicing problem-solving and critical thinking skills can also aid in understanding and applying upper level math in this field.

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