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 ^{[1]}. 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.

**Looking forward:**

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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Works Cited:

- 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.

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Sophie XiI found it rather interesting that many seniors of this seminar share concerns about their college application as it does really affect our working progress. I am looking forward to your future blog posts and will try my best to understand them!

tkbarnetHave you thought any specifics on your plan or idea on how to review what you’ve learned so that the concepts really stick?