Mathematics courses useful in engineering, data analysis and modeling

[moyam01]

Hello,

I am currently pursuing my degree in Mechanical Engineering, and was wondering what math courses were good to take after the basic math sequence has been completed (Calculus 1-3, Differential Eq & Linear Algebra.).

I have an interest in mathematical modeling and data analysis, as well as having enouph math to cover some advanced topics in engineering, as well as physics. My school offers a concurrent degree in Engineering mathematics, where you take an additional 14 credits in math of your choosing from the following subjects:

Applied Combinatorics (3 credits)
Computing with Mathematica (3 credits)
Topics in Mathematics (1-3 credits)
Dynamical Systems (3 credits)
Integral Equations (3 credits)
First Course in Modern Algebra (3 credits)
Linear Algebra (3 credits)
Stochastic Processes (3 credits)
Mathematical Statistics II (3 credits)
Advanced Calculus I (3 credits)
Advanced Calculus II (3 credits)
Fourier Series and Boundary Value Problems (3 credits)
Introduction to Wavelets (3 credits)
Mathematical Modeling (3 credits)
Introduction to Numerical Analysis (3 credits)
Matrix Computation (3 credits)
Numerical Solutions of Partial Differential Equations (3 credits)
Approximations of Functions (3 credits)
Partial Differential Equations (3 credits)
Linear Algebra with Applications (3 credits)
Functions of a Complex Variable with Applications (3 credits)
Computer Algebra Systems (3 credits)
Discrete Systems (3 credits)
Applied and Algorithmic Graph Theory (3 credits)
Topics in Mathematics and Statistics (3 credits)

Doing some research I read that partial differential equations is good to take, so ile probably be taking that, as well as mathematical modeling (the name matches the interest). I am wondering about Advanced Calculus 1& 2. I also heard for physics it is good to take Forier and Boundary problems.

In your opinion given my interests what sould i take?

EDIT:

Please give second/third choice in case it is not being offered this semseter.

 

[yungman]

PDE will be the next logical one. PDE should cover Fourier series, Fourier Transform and Laplace Transform. I know the PDE class in San Jose State does.

 

[moyam01]

Thank you for the response, I just found out my University is not giving PDE this semester :(

 

[PhanthomJay]

A good engineer stays away from calculus whenever possible. I have met many from all disciplines, and none have ever used it directly. Oddly enough, however, Calc 1 thru 3 anfd Diffy Q are essential to becoming an engineer of quality. Beyond that, higher math is not a huge necessity, unless you want to become a prof.
I took Theory of Elasticity in Grad school with 4 blackboards full of PDE's wall to wall (if you know what a blackboard is) required to determine the stress concentration factor at a hole in the center of a flat plate subject to tensile forces. The answer was 3. I memorized it. The PDE's nearly made me quit going into Engineering. Fortunately, it's not like that.

 

[Matrix0]

I can say that all of the courses listed can be useful in some way for engineering, data analysis, and modeling. However, based on your interests, I would recommend prioritizing the following courses:

1. Mathematical Modeling - This course will specifically focus on applying mathematical concepts and techniques to real-world problems, which aligns with your interests in data analysis and modeling.

2. Partial Differential Equations - This course is important for understanding and solving complex engineering problems, as well as for modeling physical systems. It is also a prerequisite for some of the other courses on the list, such as Numerical Solutions of Partial Differential Equations and Approximations of Functions.

3. Fourier Series and Boundary Value Problems - This course will provide a foundation for understanding and solving problems involving waves and vibrations, which are common in engineering and physics. It also aligns with your interest in Fourier and Boundary problems.

For your second and third choices, I would recommend considering Advanced Calculus I and II, and Linear Algebra. These courses will build upon your existing knowledge of calculus and linear algebra, and provide a strong mathematical foundation for your studies in engineering and physics. Additionally, they are often prerequisites for more advanced courses in these fields.

Overall, I would suggest speaking with your academic advisor or professors to determine which courses would be best suited to your specific interests and academic goals. It is also important to keep in mind that the courses offered may vary from semester to semester, so it may be helpful to have a backup plan in case your top choices are not available. Good luck with your studies!