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Multivariable calculus: everything you need to know before rolling into the online course

If you think about it, you can find variables everywhere, surrounding you in everyday life. Temperatures, colors, locations, profit, spending, and many other examples of variables used by people and encountered in daily routine. Multivariable calculus is an instrument for the analysis of complex relations of 2 and up to hundreds of variables. Multivariable calculus online course is exactly what you need to get a grasp of this level of calculus for academic purposes in various fields. 

This article is about the discovery of a basic introduction to multivariable calculus and the benefits of learning it.

Application of multivariable calculus in different fields 

By mastering the concept of multivariable functions and 3D calculus, one can find answers on robot motion control, build a prediction model based on data analysis, design a strategy to influence consumers’ behavior, and much more. 

One can apply the knowledge you gain from multivariable calculus online classes in various fields of study and work, which puts such courses in demand among students of different specializations. 

  • In physics, multivariable calculus is used for the research in three-dimensional space and continuous time-dynamic systems.
  • 3D calculus is used for the estimation of future trends in the stock market in finance. 
  • It’s essential for everyone who is planning to proceed to work in engineering, computer science, and software engineering. 
  • Machine learning specialists use multivariable functions for further programming. 

The requirements  needed for taking a multivariable calculus class

Multivariable calculus is a subject at the College/ University level. The curriculum covers all levels, from Calculus III and IV to vector calculus and multivariable. That way, the main recommendation before taking a class is to be confident in Calculus I and II. For those who took I and II calculus a long time ago or are not confident in single-variable differential or integration theory, it’s recommended to refresh their memory before entering multivariable calculus class. 

However, students should be careful before submitting online courses for extra academic credit as different educational institutions use other names for multivariable calculus. Being not cautious enough, you might go through something that you already know, or the class might be too hard for you. To avoid such a situation, it would be wise to go through the actual curriculum of an online platform to compare what’s covered in the course to previously learned materials. 

Multivariable calculus: a basic introduction

Three Dimensional (3D) Calculus, or as it is also known as the calculus of many variables, is one of the most fascinating math courses. Some would say that 2D calculus has quite boring and easy graphs. At the same time, multivariable 3D graphs are complicated and essential for investigation. Can you imagine doing microbiology research without a microscope? No. Same as you cannot do multivariable calculus without a graph that comes to life on computer algebra software. 

Example of a 3D graph from https://www.distancecalculus.com 

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Multivariable calculus online course usually includes:

  • Learning the LiveMath. A quick course on getting familiar with computer algebra software.
  • Getting into vectors. Graphing, adding, and subtracting 2D and 3D vectors. Planning in 3D. Learning basics of vector fields.
  • Exploring differentiation in 2 and more variables. Learning how gradient vector fields could be used for analyzing and measuring the properties of the f(x,y) function.
  • Studying integration in multivariable calculus. The integral in 3D calculus is formed in numerous ways. Through the learning process, you can discover what it means by single and multiple integrals, as well as curve and surface integrals. 
  • Learning how to apply The Generalized Fundamental Theorem of Calculus (GFTOC) in 3D Calculus.  Exploring the difference between using GFTOC in 2D and 3D calculus, ways of vector integration in higher dimensions. 

What is the format of the learning process?  

The modern learning process on online courses is 80% of online work on your computer or tablet and only 20% of actually using pen and paper. There is no need to explain how easy a learning process is, as it guarantees you won’t miss a sign while doing an equation and can always rely on computer algebra. Most online schools use computer math software called LiveMath. 

Of Course, as with any application, it takes students some time to get a handle on LiveMath, but it is no harder than understanding Excel. However, using LiveMath optimizes the learning process and makes students progress faster. Operating on a computer algebra software system is essential for any mathematics academic but not the only skill they learn. After all, while you’re getting a degree, you cannot rely exclusively on computers. It’s necessary to be able to solve equations on paper too. 

That’s the reason any professional online course will make sure students know how to solve calculus problems both ways. And to ensure students’ progress exams have zero multiple-choice questions.

Another benefit of getting an online course is having access to videotext. Videotext is considered to be a modern digital solution and a replacement for regular textbooks. Students can have access to videotext from their smartphones and tablets. The advantage of videotext to standard online textbooks is that you can actually follow your teacher. It’s a combination of theoretical knowledge with practical solutions. 


As shown in an image from a screencast video with a videotext, students can clearly see a teacher’s actions, which is more efficient for the learning process and gives a better understanding of  LiveMath in the beginning. No matter what part of the world you’re in at the moment, it seems like the teacher is next to you with videotext. 

The course’s online format also allows students to communicate with teachers, ask questions, and get feedback, corrections, and explanations. That way, there is a clear communication process as in the real-life course. 

Wrapping it up, there are definitely many benefits of taking a multivariable calculus online course for your academic ambitions. The course’s online format allows students to combine it with other work or travel, while digital solutions guarantee a quality learning process and clear communication with teachers. Mastering multivariable calculus will open opportunities in various fields and improve your professional and academic levels.

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