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Calculus can be described at times as mathematics in motion. Differential calculus is how one usually begins the study of calculus. In differential calculus, you begin by studying limits, and you then apply methods of determining limits to the difference quotient. The limit of the difference quotient is what we call the derivative. The derivative has many applications, including the ability to determine the velocity and accelerations of an object when the position of the object is known with respect to time. From differential calculus we proceed to integral calculus. It basically involves calculations in the opposite direction compared to differential calculus; so in applications, we can begin with knowledge of acceleration and obtain the velocity of an object. Courses also sometimes cover series and sequences.
Precalculus covers the mathematical knowledge necessary to prepare for calculus. It covers algebra, functions, linear and higher order equations, logarithms, trigonometry, linear algebra, and sometimes more.
MATLAB is a common software and interpreted language used for analysis in engineering and scientific disciplines. It is used for things like numerical methods, statistics, plotting, and more; it has toolboxes for greater utility, like control systems applications. It provides an easier way to be introduced into programming. As a graduate in mechanical engineering, I successfully used MATLAB to write code to solve problems in heat transfer, mechanics, and numerical methods. I can also use it to interact with electronics, like Arduino boards. Whether a simple calculation is required, or a complex calculation with thousands of iterations, I can guide the student to write code that produces the desired results.