Content Skill: This semester was focused around how to solve integrals. This becomes complicated because there are many different kinds of equations that have to be solved using different techniques.
One of the coolest proofs of the year was finding the integral of inverse trig functions. Below is the proof for acrsin(x). Similar proofs can be used to figure out the other inverse trig functions.
AsWhen Kyle first introduced this proof I was fairly mind blown by the answer of the integral. It initially didn't make logical sense to me. After I looked into the proof though, the ideas are actually very simple. By practicing lots problems with inverse trig functions, I felt like I mastered this skill fairly easily. What I struggled with after that was recognizing these problems when we were not specifically working on inverse trig problems. These function have continually come up throughout the semester and sometimes it is hard to remember the unique answer. Every time I recognize these function, it helps to master the skill.
Problem-Solving Skill: Generating Ideas - Formulate a plan - anticipate major intermediate steps - Generate multiple means of approaching a problem; brainstorm plans - Identify and apply appropriate mathematical tools (formulate, equations, diagrams, graphs)
This semester I think I really grew in this area. As a junior, I would freak out when I saw a problem that I wasn't immediately sure how to solve. I think by working all semester on some really hard problems, I have learned how to be more confident and determined to find an answer. Even now, I sometimes find myself stumped with a problem and end up giving up. My classmate's determination and creativity to solve problems helps me remember that I should be more persistent. I predict that by continuing to do hard problems, as I will be doing as an engineering major in college, I will improve with this skill.