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Now I'm learning about Laplace Transforms and we derived a couple easy ones but now we're gonna use a table to figure out the more complicated solutions.. My goal is not rigor but strong intuition in math and physics. I don't mind using a table for quick reference but I'd rather like to at least feel the correct solution from a intuitive geometrical sense. What can help me bring back my intuition of math?

This semester I'm taking a math class on perturbation theory, transforms, and special functions and my hopes are it will help my math thinking but I'm not sure it will yet. I think I learned more about calculus and intuition from my physics classes than math classes. Has anyone else ever felt this way?