If you’re taking MATH 1080 – Elements of Calculus, chances are you’re in your first semester of university and taking this as a required course—and not as a math major! Even the word calculus seems extremely daunting, especially if you’d never been introduced to it in high school. To ease your transition into the university world of mathematics, here’s a list of 4 core concepts you should—ahem, need—to understand to succeed at MATH 1080. Each concept is touched on in class, of course, but the pace of the course may seem overwhelming; therefore, practicing the following concepts beforehand will guarantee you a smooth ride on the roller coaster that is calculus.
1. Mental arithmetic
This may either come across as obvious, futile, or both. If you can add 10 and 9 together, that’s great! A calculator can solve the rest of your problems, right?
Wrong. MATH 1080 is designed to make you channel your mental fortitude and do essential arithmetic entirely by yourself, i.e. no calculators allowed! This includes long division (with unknown variables), cross-multiplication, and basic addition and subtraction. You also have to know your fractions. The majority of high school math classes most likely allowed the use of calculators, so relearn the above skills if you need to!
2. Factoring and simplifying algebraic expressions
Again, this one may seem like a given, but its importance cannot be understated. Factoring includes simple and complex trinomial factoring, difference of squares, and common factoring (which you should have learned a billion times by now). Simplifying is when things get a bit messy, ironically. Skills like rationalizing the numerator (which can be tricky), finding a common denominator, and utilizing the exponential and logarithmic rules are all basics in simplifying algebraic expressions.
3. Exponential and Logarithmic Properties
A huge portion of this course involves dealing with functions using exponential and logarithmic properties. You’ll receive a decent refresher on these rules, but it’s not long before you’re determining maximum drug level and eventual maximum residual drug level using a combination of these rules—and yes, they are different! Practicing different applications of these rules will help solidify them for heavy usage in this course.
4. Derivatives! And…integrals…
Perhaps the most important yet least liked concept among many students are derivatives. If you were introduced to these in high school, you should know that derivatives are essentially what calculus is all about—that is, the rate of change of one variable with respect to another. The absolute key to derivatives is practice! Although the term practice may seem saturated here, it is by no means an understatement. You will be thrown a ton of practice examples, fortunately, but the thing about derivatives is that they lead to, arguably, a much more difficult but very similar concept… Integrals! That is to say that if you don’t understand derivatives, you won’t understand integrals—and these topics make up at least a third of the final exam.
Work on these 4 core concepts and calculus won’t seem so daunting. In fact, the core concepts are simply extensions of what you’ve already learned in high school, all with one common strategy and goal: to practice enough to become comfortable and relaxed. After all, what gives you more bragging rights than to say calculus was a breeze once all is said and done?