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Calculus is the field of mathematics dealing with determining derivatives and integrals of various functions as well as studying their properties through methods originally based on summating infinitesimal differences. A much shorter definition goes like this: “calculus is the mathematical study of continuous change”.
Calculus is indispensable for many branches of human activity where quantitative analysis, mathematical methods, and mathematical modelling is commonly employed: physics, engineering, computer science, chemistry, economy, business, statistics, life sciences. Among very famous application are Newton’s 2nd law of motion, Einstein’s general relativity theory, Maxwell’s electromagnetism theory – in general, physics abounds in examples of calculus use.
Being such an important instrument in understanding the mathematical reasoning, calculus should be learned by virtually all students that have or will have anything to do with sciences and in particular, with complex quantitative analysis. However, it may result in various difficulties with this subject and calculus help becomes a necessity.
Due to their complexity, calculus exercises and application of calculus methods are frequently the kind of challenges that make students give up on their mathematics course. It’s unfortunate since all calculus material can be mastered in time-efficient manner if approached patiently, gradually, and following a correct order, starting from the basics.
College or school students might often have the problem that certain concepts are not explained to them properly or simply insufficient individual attention is given to help them understand this challenging field. Hence, it could be enormously beneficial for students to have someone provide clear demonstrations of solved model exercises from the beginning till the end. In other words, they would benefit greatly from having a personal calculus tutor or from receiving online assistance.
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Below is a list of basic topics and concepts expected at a beginner level or of college calculus course:
Continuous function – is a function without undefined points, gaps, or jumps. In other words, its plot is continuous – between any two points on this plot, there would be an infinity of others.
Discontinuity – discontinuous function, as opposed to a continuous one, has points at which it’s either undefined, jumps in value, or has no value.
Critical point – located in function’s graph where its derivative equals zero or is undefined.
Extreme Value Theorem – states that continuous functions on closed intervals have both maximum and minimum.
First Derivative Test – method of identifying a function’s minimum and maximum using its first derivative. It is set equal to zero and the roots of the equation are identified, rafter which the values of the function for these points are determined).
Inflection point – is on a function’s plot where concavity changes, in other words, a point where the function either becomes convex or concave.
Second Derivative Test – it’s a method for determining inflection points by using second derivatives. Again, it’s set as zero, solutions are identified, and function values are determined at these points.
Definite integral – this is an integral which has upper and lower limits.
Limit – the value a dependent variable approaches as the independent variable approaches a particular value.
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