Calculus is one of the most rigorous yet rewarding courses I've taken; I started learning Precalculus in Spring 2021 before I took Calculus because Precalculus was a prerequisite two-part course before I could advance towards Calculus since I didn't take precalculus during high school. Precalculus I was hard, even though I followed the instructions and watched videos on how to solve certain problems; I still failed the course and had to retake it in the next semester. The experience created a new outlook on improving my study habits, as well as working with tutors from the mathematics learning center for PGCC because the Knewton homework was very confusing since it was a new feature my second precalculus professor introduced. The habits I frequently used the most was consulting with tutors and forming a study group with a couple of my peers; focusing on the hardest parts of the assignments like quadratic equations, inequalities, and formulas. The group and myself watched countless videos for instructions because whenever we solved a problem for the Knewton assignments, a box titled "Correct Answer" appears and explains the correct step-by-step solution; sometimes with formulas our professor never taught. After earning a 75 for my final grade in Precalculus I, I advanced to Precalculus II where I had a much better grasp on the subjects; particularly studying the Unit Circle, learning the trigonometric functions of angles like Sine, Cosine, Tangent, Cotangent, Cosecant, and Secant. I found the concepts of Trigonometry for angles, Length times Width, and logistics more interesting and understandable than the concepts from Precalculus I.
The duration of studying Precalculus and Calculus was extremely difficult yet rewarding because the greatest tool I used to gain a better understanding was practicing the concepts of the problems with not only formulas; but with structure and different perspectives when approaching a problem. Upon entering Calculus I, I repeated the same outcome like my first attempt at Precalculus I and became disappointed at the final results. The concepts from my first Calculus I course used for the exams; most of the problems were completely unrelated to what I studied constantly from practice exams and the textbook, even though one of my peers who had the same professor, strongly recommended to ignore using the textbook because she considered it useless. When the Fall 2022 semester finally came to a close; I was very disappointed initially with the final outcome, however I knew this was another wall in my path and similar to Precalculus I; I'll pass the course on the second attempt. course on the second attempt. The second attempt for Calculus, it almost felt like a spiritual successor to my second attempt at Precalculus I, though the process was better by comparison from the lessons I engraved inside my mind when approaching the same concepts from the past attempt.
All things considered, Calculus has been a hardship yet rewarding because being able to correct any bad habits from understanding formulas, the concept of using PEMDAS for derivatives and integrals, and reading the questions before knowing which route or formula to utilize first. The abundance of tutorials, instructors, and peers that help better develop your skills in mathematics, which can be used in daily life, work, or planning to send your child to college with proper tools and resources. The college path has broadened my perspective on both my career and personal life, however remembering how to form solutions and visualize an everyday scenario as a derivative is something eternal.