In the beginning, Calculus may seem misleadingly easy especially when the
student begins learning about limits and rates of change which both build on concepts learned previously in Precalculus. Unfortunately, this moment of bliss is short-lived as the student soon dives headfirst into the world of derivatives which leads to the first reason why Calculus sucks.
Students usually learn about derivatives immediately after limits and rates of change. Again here, derivatives may seem easy at first but once the differentiation formulas and concepts including those for trigonometric functions, the chain rule, implicit differentiation, and related rates are introduced, they add to the student’s general feeling of impending doom! This does not have to be so! The student should resort to keeping extensive class notes and trying to genuinely understand the concept of differentiation as well as its associated rules and theorems.
Integrals
The next stop on the journey of Calculus leads to the world of integrals. As with derivatives, there is no love lost for most students when dealing with integrals. Why? Well it’s probably because there are a seemingly infinite number of topics and subtopics that fall under the banner of integrals. Again here, it’s crucial for the student to take extensive notes, seek clarification on difficult topics from the teacher or a tutor, and try to master the fundamental theorem of Calculus. In addition, the student should work on as many problems as possible related to the substitution rule, area, volume (using either the washer or shell method), integration by parts, partial fractions, as well as exponential, logarithmic, and trigonometric functions.
Sequences and Series
Finally, many students will end the course by looking at infinite sequences and series. Though some may remember working on these topics in Precalculus, they will soon discover that they are covered far more extensively in Calculus. There is no other way to say that practice makes perfect in mastering the definitions and rules needed to work on this part of the course. The student needs to devote a lot of time to not only working on homework problems but also working on problems not assigned in class so that a more comprehensive view of series and sequences can be achieved. This may go against the average student’s intuition, but in short, he or she should ask the teacher for more homework to work on!
In conclusion, the student should try to incrementally master differentiation, integration, sequences, and series as the course progresses so that the individual pieces better fit together. This leads to the student learning the subject matter at a comfortable pace, fully understanding the material, and realizing that Calculus doesn’t suck at all!
If you enjoyed this post, make sure you subscribe to my RSS feed!
