What textbooks should I consider for my upcoming birthday?

[alexhenderson]

Hello Physicsforums,

Some of you may know me from my previous thread "how to thrive at an early age" and I have made much progress. Techniques of integration, differentiation, Newtonian dynamics, functions and limits, energy physics. I am also working on a system of trying to theoretically develop an orbit using the real values of the Earth's mass, sun's mass, and the gravitational constant. Updating acceleration, velocity, x and y positions, for each time delta of one day. And using vectors, force equations, and equations to update the x and y comps of : position, velocity, and acceleration. Thank you for the advice.

My birthday is coming up, and I am looking at getting some new textbooks. I have University Physics 13th Addition with Modern Physics, and Calculus 4th edition by Spivak. I was interested in getting a DE's textbook, linear algebra textbook, or maybe a trig textbook might be helpful. Suggestions are pleased.

Thanks,
Alex.

 

[demonelite123]

hi there. for DE you might have heard of boyce and diprima. while it is not the most rigorous book, it does give you a pretty good grounding in the techniques for solving DEs. if you do want a treatment that focuses more on understanding then i suggest vladimir arnold's ordinary differential equations. although i have not read arnold's book, i heard it provides a great exposition on the theoretical aspects of DE. to fully understand it, you may need to be acquainted with some analysis and modern algebra.

for linear algebra, i have heard that axler's linear algebra done right is a good choice. hoffman and kunze is also a standard pick although it may be a bit dry. both are formal and rigorous in their presentation.