Resource recommendation for undergraduate-level wave mechanics?

Question

I'd like a resource---preferably a book---to learn wave mechanics at the undergraduate level without a particular application in mind. I don't have a PDEs background and my ODE knowledge is rusty.

Answer 1

If you are new to wave mechanics then I'll suggest some easy to read books that introduce the abstract ideas little bit pedagogically to the reader, and gives many physical insights. The first book might be:
Introduction to Quantum Mechanics (David J Griffiths). This is one of the easy to read books. If you like to dig a little deeper in the concepts, then you can start with Quantum physics (Stephen Gasiorowicz) This book is a little harder than the former one but will be of help in the long run.

Answer 2

For a book that develops the notion of a physical wave from the ground up and does a very comprehensive job of describing the modeling of wave-like phenomena in physics, I highly recommend Howard Georgi's "The Physics of Waves".

I took a wave mechanics course in my undergraduate studies using this textbook, and don't feel that the reader needs too much background for it other than understanding ODE's/linear algebra.