Programs Which of these courses is best for an ME major?

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For an undergraduate Mechanical Engineering (ME) major at the University of Texas at Austin, the most beneficial courses from the listed natural science and math electives include Advanced Calculus for Applications I, Partial Differential Equations and Applications, Fourier and Laplace Transformations, and Theory of Functions of a Complex Variable. These courses provide essential mathematical tools and concepts that are directly applicable to engineering problems, particularly in areas such as fluid dynamics, heat transfer, and system dynamics. While the suggestion to take upper-level ME classes or audit graduate courses is valid, the requirement to select from the specified electives necessitates a focus on those that enhance analytical and problem-solving skills critical for an ME career.
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Advanced Calculus for Applications I
Matrices and Matrics Calculations
Theory of Functions of a Complex Variable
Vector and Tensor Analysis I
Partial Differential Equations and Applications
Fourier and Laplace Transformations
Fourier and Laplace Transformations
Introductory Biology I
Principles of Chemistry II
Physical Geology
Introduction to Geology
Geologic Engineering
Modern Physics for Engineers


These are all the natural science/math electives required of the ME undergrad program at Univeristy of Texas at Austin. I'm trying to figure out which classes would benefit me the most in my studies and future career, NOT just "broaden my horizon."

Could someone rank his top 4 picks out of these courses for an ME major?
 
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matrices, PDE's, Fourier transforms, advanced calculus.

but if you really want to benefit yourself, why not just take more upper level ME classes? or audit a grad course?
 
I MUST select classes from one of those choices. It's a requirement.

Thanks BTW!
 
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