Not to say that students including math and physics guys don’t already use the internet to get help in their studies but we are talking about some key specifics here. These could be helpful for those students who are unaware of them and not reaping the benefits. We are discussing key mathematical concepts here that are frequently used by math and physics students to solve mathematical problems. However, the manual calculations of these functions and operators is like reinventing the wheel. Not worth the valuable time a future mathematician or physicist can spend solving problems with the help of these functions, formulas and operators.These students generally carry scientific calculators along with their limitations, unsurprisingly! A scientific calculator would provide you a lot of functions that don’t exist in a basic calculator. However, even this is not enough, since there are innumerable things that need calculations that aren’t included in these calculators and students generally have to waste a lot of time figuring them out manually. Even smartphones and laptops don’t include these applications in default. This is a big problem, but when all else disappoints, the internet wont! So we outline the information of some great mathematical applications that you can use to help in your math stuff. Here goes! 1: Factor Calculator You can think of factor as a number which is divisible by an integer (excluding decimal numbers). Correspondingly, factoring is to find the factors of a given number.Not to say you can’t factor an expression using a calculator but it’s still pointless, it would be time consuming, you’d have to work out the numbers yourself. However, with an online tool such as an online Factor calculator, you can simply input the expression and factorize it. And rather than reinvent the wheel, you can use the same time to work on other problems. 2: Permutation CalculatorPermutation refers to the number of order-based configurations you can make out of a set of population. Permutations are orderly and non-repeatable. Calculation of permutations are crucial in statistical mechanics and some domains of mathematics. And again, We are presented with a limitation when it comes to scientific calculators, they don’t include the formula for permutation and you have to work out all the math and the formula yourself to be able to calculate it with a scientific calculator and again, that takes time which we don’t want to waste, do we!To make our case, the formula for permutation is given below and how calculating it manually or with a scientific calculator takes more time than faster alternatives.nCr = n!/(n-r)!Where,n = the populationr = the size of permutation sample! = factorial If the population and the permutation sample size is large enough, working them out with their factorial becomes extraordinarily time consuming even with a scientific calculator. However, you can simply circumvent this situation by using a typical online permutation calculator where you just input the population size, the permutation sample size and voila! It would save you plenty of time. 3: Covariance calculatorCovariance is the gauging or relation between two random variables in statistics and mathematics. This is also an important aspect in many statistical and statistical mechanics problems. Again, students generally have to work out manually and then use an online covariance calculator to measure the final result.However, this can also be avoided by using online covariance calculators where you only have to input the random variables and the tools reinvent the wheel for you while you work on the main problems. Concluding thoughts:The primary purpose of this article is to highlight the fact that there are a lot of mathematical and statistical functions that aren’t included in calculators and students have to waste their valuable time to work these calculations out manually when they can let technology do this work. The internet has come a long way and there is an online tool to help you solve a lot of problems. See More

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Derivatives:The changing rate of a function is known as a derivative.These functions act to the real numbers.Integration:The alternative term of derivation is integration. The process of finding integrals is integration. Integrals have been used to find many useful measures such as volumes, area, displacement, and many more.Derivative and integration are an inverse function of each other. These are inversive in the way that derivatives find slopes and integration find volumes, areas, etc.The area is a product of a and b and the slope is a ratio of y/x. And, this division and multiplication are an inverse function of each other. Why derivatives and integration are beneficial?Derivatives and integration have been used for understanding the basics of other subjects such as Physics, history, and economics. For example, acceleration and speed are terms of physics. These two terms are required to find these terms. Derivatives also help in finding the growth rate. Derivative calculator makes it easy to get quick results.Applications of derivatives and integration:Application of derivative:1: To find the minimum and maximum values of functions2: Helps to model the objects in motion3: Used to measure the air pressure4: To measure the change rate5: To draw complex curves and graphsApplications of integration:1: To determine the under curve area2: To determine the angles between curves4: Used to calculate the work done of a variable force5: Used in history, economics, mathematics, and geography. Undergraduate students face difficulty to solve derivative and integration problems. A study has been conducted to find why students feel difficulty in learning derivative and integration. The result of this study showed that these difficulties include weakness to recall previous knowledge, connection weakness between the symbolic and embodied mathematical world, and problem-solving inability. To solve equations quickly once can use an integral calculator as well.Moreover, this difficulty is also because of insufficient practice and geometrical intuition. It’s also because of insufficient knowledge of functions. Is integration more problematic than differentiation?Some studies showed that integration is more problematic than differentiation.From a symbolic computational viewpoint, integration is more severe than differentiation.Solving differential equations is always possible. Integration is not possible in many cases.Consider an example. Let suppose a question of differentiation and integration has been given. You’ll get a simple expression after applying the chain rule, quotient rule, or product rule. On the other hand, you have to match the templates in case of integration. It is the reason that makes differentiation easier than integration. Also, it is a personal thing. Some people find differentiation difficult.But some consider that integration problematic. It depends on the student which term he understands faster. How to remove difficulties in solving derivatives and integration?Calculus is an important subject. You’ll get command over calculus if you put effort into it.The practice is the easiest way to get mastery. Try to get a problem relatable to your daily life and then find a solution according to this image. In this way, things will become relatable.Before solving the questions, you must understand its basics. It is because poor knowledge will only enhance your problems.Firstly, you need to be familiar with derivatives. You should understand the concept of derivatives properly then come towards integration. Understanding of differential makes the integration easy to understand. Moreover, practice problems, tutorials are an excellent source for understanding this concept.Try to solve problems in your mind also. Also, one of the efficient ways is to solve a lot ofproblems. It is because math is a subject of practice. Try to solve the problems step by step.See More

Ever heard about vector algebra? Well! It is a branch of algebra that deals with the vector and scalar quantities and their operations, like addition, multiplication etc. The most significant is the cross product and dot product.Both involve multiplication of two vectors, but the difference lies in the fact that a cross product or vector product always results in a vector quantity. On the other hand, a dot product always results in a scalar quantity (having magnitude but no direction).In this article, we will discuss the vector product its definition, history and real world applications. Now, let’s get started.Cross product definition:It is defined as a binary operation on two vectors that are present in a three dimensional space, and the product results in a third vector, which is perpendicular to both vectors and standard to the space containing them. The image below illustrates the cross product of two vectors a, b that results in a third vector a×b and its direction is perpendicular to the initial vectors.History:The introduction of the dot and cross products dates back to the 18th century, for the first time used by an Italian mathematician and astronomer Joseph Louis.These components were introduced for the study of tetrahedron, a polyhedron composed of four triangular faces. To study it in three dimensions, these two products were used.Later in 1843, William Rowan invented the quaternion product and also explained the terms vector and scalar. After 40 years of the discovery of quaternion, Josiah Willard Gibbs found that the existing quaternion system was too cumbersome. Because the result of scalar products was to be worked separately. Here, the cross product and dot product were accepted as standard for vector and scalar geometrical studies.Practical Applications:The vector product has a wide range of practical significance, particularly in the fields of physics and geometry.Torque and Angular momentumIn mechanics, the torque, is defined as the turning effect or rotational effect of a linear force applied on an object. Whereas, the angular momentum is the same as the rotational effect that is correspondent to linear momentum, denoted by L.Vector products are used to define these two vector quantities. For instance, the above expression; L = r × pHere, L is the resulting vector (angular momentum), r is a position vector in relation to the origin, and p represents the linear momentum.In the field of computational geometryThe vector product appears in the estimation of the distance and direction of two skew lines (having different planes) this distance is measured in 3d space. These are used to perform a frequent operation of geometry called computing the normal for a polygon or triangle. For instance, to estimate the curving of a polygon, whether clockwise or anticlockwise. It is measured at some point within the polygon. The method used to calculate it is called triangulating the polygon, dividing into triangles and then summing up the angles, here we use the vector product to keep track of each angle. These cross products can also be used to measure the volume of a polyhedron.In the end, I sum up this article, these components of vector algebra, the dot and cross products are quite important operations, in terms of both physics and geometry. If you are interested in solving problems related to vector products, we suggest you try some online tools that are specifically designed to compute the above mentioned problems. Give cross product calculator a try. Good luck!See More

Hello! Digital Marketers, we hope that you’re doing well. We have designated this article to aid all of the freshers who don’t know much about tricks and hacks of digital marketing. To know about the cost-effectiveness of your digital marketing (PPC) campaign, all you need to do is to calculate either the CPM or CPC. Whereas CPM means cost per mile (1000 ad views), and CPC means cost per click. Keep in mind that it is all concerned with online advertising that is one of the fundamental parts of digital marketing. In this article, we will tell you about CPM, and its significance in the evaluation of the cost-effectiveness of a digital advertising campaign. What Do We Mean By CPM?CPM stands for cost per mile that denotes the amount of money per 1000 impressions. Whereas an impression is what we call the displayed advertisement on one's online screen. So, if you are a digital marketer and you want to figure out how much your campaign (Online Display Ads) is effective in terms of its cost then CPM is what that can assist you in knowing so. To calculate CPM, we have a formula. What is CPM Formula?CPM = 1000 (cost/impressions)It is the formula of CPM that we use to calculate the cost per 1000 impressions. Example- How to Calculate CPM Using FormulaFor example, if the cost of your digital marketing campaign is $20, and the number of impressions is 2000 then you can calculate CPM as follows:1000 (20/2000)1000* 0.01CPM= $10So, in this way, the cost-effectiveness of your digital marketing campaign can be determined by the calculated value of CPM. Why Do We Need to Calculate CPM?As we have stated above CPM is for those who are in the field of digital marketing. So, to become a successful digital marketer you are required to invest and work smartly, and this smartness makes you evaluate the cost-effectiveness of your campaign(s). Whereas the cost-effectiveness of a digital marketing campaign tells you about how much profit or loss you'll gonna get through it. Therefore, it is somehow mandatory to calculate the CPM so that you can determine the expected profit or loss from your investment(s) in the digital marketing campaign(s). In simple words, the calculated CPM can help you to know how much the impressions (viewed but not clicked ads) will be cost-effective as per your campaign budget or investment. Probably, manual calculation of CPM can be a bit time-consuming. To save your time and energy, you can use Online CPM Calculators. Whereas, CPM calculator is a computing tool that has been designed to calculate the value of cost per mile (100 impressions). This smart is for those who are in the field of digital marketing. If you are a digital marketer then it is exactly what you need to evaluate the cost-effectiveness of your campaigns (Online Ads).This smart calculating device can aid you in calculating cost per mile within a few seconds so that you won't have to waste your energy in calculating CPM manually. So, don't rely upon the time consuming manual method of CPM calculation and use this smart and efficient CPM calculator. It won't require you to put too much effort. All you're required to do to use this smart CPM calculator, you have to provide it with the value of the cost of your campaign budget and the value of the impressions of the ad(s). As per the given input, the CPM Calculator will calculate the value of cost per mile. In this way, you will be able to evaluate the cost-effectiveness of the respective digital marketing campaign. Precisely, you need to calculate CPM so that you can set the best strategies for your campaigns as per the required cost-effectiveness. See More

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