Saturday, October 22, 2011

Kindle and Math

    I am married to the most amazing wife ever! Sarah got me a Kindle for an early birthday present. I am reading Thomas Hobbes's Laviathan on it. Hobbes has some interesting ideas on law and order (not referring to the TV show which had yet to be filmed in Hobbes's day). I also just finished reading the Hunger series by Suzanne Collins on the Kindle. The first book was really good (the Hunger Games) but the other two sucked. I also downloaded a few other philosophy books: Immanuel Kant's The Critique of Practical Reason, Bertrand Russell's The Problems of Philosophy, and Jean-Jacques's A Discourse Upon the Origin and the Foundation Of The Inequality Among Mankind. So I have lots of fun stuff to read now.

    Speaking of fun reading material I have also had the chance to read Advanced Engineering Mathematics by Erwin Kreyszig 8th edition. I skipped all of chapter 1 and it's section because it was only focused on first order differential equations which are very simple. Chapter two is on Linear Differential Equations , while looking over this section I fondly remembered my differential equations (DE) class. The one part I read in-depth was 2.9 Solution by Undetermined Coefficients. I loved this section in  my DE class because this is where you learn how to solve for linear differential equations of any size homogeneous AND non-homogeneous. I went through this prescribed procedure and solved a number of problems from this section. I should have tried this years ago, I forgot how much fun math is! I will next try using this analytic approach to solve problems like these using a visual basic program and display my results in excel. Solving problems like these numerically is going to be even more fun. Part 2.15 is basically using the method for 2.9 and expanding it to higher orders, so I solved a lot of these problems for fun as well.
    Chapter 3 covers the basics of vectors and matrices which I covered already in my Linear Algebra class. Chapter 4 covers Series Solutions of Differential Equations, which I have not really learned except what was covered in my Calculus course. I finished reading through the Power Series Method covered in 4.1 and 4.2 and solved many of the these section's problems. The rest of the sections in this chapter seem to cover specialty problems involving derivatives of multiple variables. I didn't cover this much as I haven't seen many problems come up involving equations of this nature. But if do in the future I will know where to go. Chapter 5 was on Laplace Transforms - I covered this subject extensively in my DE class but read through most of these sections in this chapter for fun anyway and solved many of the example problems. I skipped over 5.5 and 5.7. I skipped over chapters 6 and 7 because I covered most all of this in my Linear Algebra course. Chapter 8 covered Vector Differential Calculus and chapter 9 covered Vector Integral Calculus. I covered both of these chapters in Calculus 3 and didn't read them now because there applications are more theoretical than practical (at least for what I do). Chapter 10 is on Fourier Series, Integrals, and Transforms which I am reading in-depth and loving every minute of it. This chapter reminds me a lot of Series Solutions of Differential Equations. Any periodic function can be broken down into a series of sines and cosines (taking the derivative of sines and cosines is fairly easy).
   Once I am finished reading Chapter 10 I will skip over chapters 11, 12, and 13 and go straight to chapter 14 Power Series and Taylor Series. Chapter 15 looks pretty interesting so I may read it as well. I will skip over chapter 16 and go to read through chapters 17, 18, and 19 Numerical Methods. Chapters 20 and 21 also look interesting.