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The book I used in college, and still use when needed, is A First Course in Differential Equations, by Dennis Zill. It's very clearly written with tons of problems and examples.

The book Mathematics From the Birth of Numbers, by Jan Gullberg, is a cool book in general and also has a short and sweet introduction to ordinary differential equations (ODEs) at the end. He derives the general theories of ODEs pretty much entirely through the use of applications.

Gradshteyn and Ryzhik's Table of Integrals, Series, and Products, which is a must-own book for mathematicians and scientists anyways, also has a rather short, but surprisingly detailed section on ODEs toward the end. I wouldn't recommend this for a novice, but it's a great reference to have once you've become familiar with differential equations.

Mathematical Methods in the Physical Sciences, by Mary Boas, is a classic text covering many topics, including ODEs and PDEs (partial differential equations). I'd get this book simply for the immense amount of very useful topics it introduces in all the fields of mathematics, including the calculus of variations, tensor analysis, and functional analysis.

Eventually, you'll need or want to learn about PDEs, and the most intuitive and comprehensible book I've seen regarding them is Partial Differential Equations for Scientists and Engineers, by Stanley Farlow. It's almost (if such a thing can be said about a rigorous math book) entertaining.

Q: What are good books on differential equations for novices?

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You take algebra, and trigonometry, and calculus, and then differential equations, and then you just do it. Until you've taken those classes, no explanation I could give would do you much good; after you've taken them, you won't need it.

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Eh.... it really depends on how well you can handle word problems actually. Think of most physics problems as the word problems in algebra you have tried. The math should be okay for you to handle, as long as all the equations you will learn are in discrete form rather than differential form, which requires calculus. But really, being good at math is definitely a hand up in learning physics, if not a requirement. Whenever you've heard the term "mechanics" associated with some level of physics, they are referring to the mathematics. Everything is explained using equations and then interpreting those equations based on the problem you are trying to solve. Eventually, if you stick in long enough, everything boils down to differential equations and must be solved using calculus. But EVEN THEN, alegrba is paramount in reducing equations and solving for unknown variables. I think you'll do just fine. Just imagine how the students are going to feel that hate math lol

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