I am attending a course about differential equations hoping to be able to use and solve them in the right way. I am Actually doing research in engineering and it is highly mathematically involved. I Like math too much and i wish i can get the right mathematical model and solve it for the problems i am dealing with. Anyways, the lecturer started the lectures by introducing the set theory, and then he assessed on that we have to understand the theories of uniqueness and existence of IVp. he tried to prove each Lemma and theory used for that. I found that the book " principles of differential equations" by Nelson G Markley is the best match to the lectures, as the lecturer did not provide any references. However, the way the topic is dealt with in this book is difficult for me to grasp. i used to use "Advanced engineering mathematics" by KREYSZIG as my general math reference but it doesn't deal with the topic the same way as the lecturer.
So the point is that as an engineer/not a mathematician who tries to use the math tolls to solve his problems , it is difficult for me to use the right tool and get the basics behind when i try to solve an engineering problem. I tried to teach my self without taking more courses but when it comes to apply the pure math we learn to an engineering problem here comes the troubles.Also learning from books doesn't help much, as you can misunderstand what you read.
Any suggestions for an engineer who try to use math topics to solve his problems?