No, linear algebra is not more useful than calculus or differential equations for any branch of engineering other than computer engineering. Computers engineering is the only discrete engineering discipline.

Calculus is useful roughly to the degree it's able to turn non-linear problems into problems of linear algebra.

In what field?

Every branch of science and engineering. e.g. optimizing distribution networks, predicting the weather, designing structures that won’t fall down, setting the orbits of rockets, controlling robots, simulating materials for 3d animation, designing new pharmaceutical molecules, analyzing data from high-energy physics experiments, ...

If you look at how people solve differential equations in practice, it’s all matrix algebra.

Linear algebra is also pervasive throughout pure mathematics.

Edit: I think everyone should also learn calculus though, and differential equations are the heart of calculus. Here’s an introductory calculus book http://www.math.smith.edu/~callahan/intromine.html and here’s an introductory linear algebra book https://web.stanford.edu/~boyd/vmls/ which try to get students closer to the way these tools get used in practice.

Linear algebra has many uses beyond computers:

http://aix1.uottawa.ca/~jkhoury/app.htm

https://math.stackexchange.com/questions/256682/why-study-li...

Yes, and all of them outside of computer science/engineering are using linear algebra on top of calculus.

Computer software/engineering is the only field of science that can use naive linear algebra directly to solve hard problems in the field.

Ummm, what about say quantum mechanics as the first huge example off the top of my head..

How many school graduates will end up studying quantum mechanics?