I’m not posting any math equations this week!
What I’ve been working on:
As suggested by the title of this post, it’s been nine weeks since I started exploring differential equations. My learning experience has generally been smooth yet challenging. I remember that during my first meeting with T. Margaret, my independent project coordinator, she said, “Differential Equations is where you would find out if you are a true math person.” From what I’ve learned so far, I can see why that is. It requires a thorough understanding of high school calculus, as well as some specific ideas in linear algebra.
Learning how to solve first-order linear ODEs (ordinary differential equations) is very important. Much like calculus, only mastering one-variable calculus can one make sense of multivariable calculus. Essentially, the key to solve any first-orders is to find a way in which the equation can be easily integrated . When it comes to second order, however, this rule doesn’t quite apply. Just like one-variable and multivariable calculus, things become a little different when the order goes up in differential equations. Higher-order means that the terms are differentiated more times. Solutions to higher-order ODEs are much more complex, given that even for a first-order, there is usually not just one single solution, but instead a set of solutions. Linear algebra here becomes very useful. In a linear system, solutions for higher-order ODEs can be seen as a linear combination of several distinct linearly independent solutions.
Problems I’ve encountered:
Of course, I had some trouble understanding certain concepts – it’s diff eq anyways! Beyond that, putting everything in order has been a big challenge. At first, I had to figure out when I was going to watch lecture videos and when I had to do homework problems. The course itself requires a lot more time than the limited time frame I have on my schedule for this independent seminar. Right after I had my timing figured out, college application messed it all up. I already passed a checkpoint where I should have taken a test, yet because of my scheduling, that is yet to take place. Figuring out about my senior project also took a lot of time.
Of course, I’m going to watch more lecture videos, do more problems, and post more math equations. I definitely need to figure out in advance how I am going to do major assessments, such as quizzes or tests, as well the final exam. I also need to look into my future calendar for this course and adjust my pace. With a high-speed constant input of math, I don’t think that I have mastered everything I’ve learned. Since there are only a few assessments throughout the course, I feel that I should insert some time just for reviewing things I’ve learned.
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- Edwards, C. Henry, David E. Penney, and David Calvis. Elementary Differential Equations with Boundary Value Problems. Upper Saddle River, NJ: Pearson/Prentice Hall, 2008. Print.