Multi-Variable Calculus

What is Multi-Variable Calculus?

Multivariable calculus is the extension of calculus in one variable to calculus with functions of several variables: the differentiation and integration of functions involving several variables, rather than just one. Multivariable calculus may be thought of as an elementary part of advanced calculus. 

Where is Multi-Variable Calculus used?

Multivariable calculus is widely accepted in many fields such as science, engineering, finance, research etc. some of the major applications of multivariable are mentioned below:

• In a dynamic system, multivariable calculus is the core tool used which is used for optimal control.

• Multivariable calculus is helpful in evaluating empirical data in regression analysis.

• In the field of finance, quantitative analysts use multivariable calculus which is helpful in predicting the future trends in the stock market.

• Multivariable calculus is also used to determine the 2D and 3D motion of fluid particles and streams in mechanical engineering.

• Multivariable calculus is used to study the high dimensional model system which has deterministic nature in engineering as well as social science.

Pre-requistes for Multi-Variable Calculus

The most important and pretty much only prerequisite for learning multivariable calculus is having a solid grasp on single variable calculus. Also, visualizing in 3 dimensions is quite important in several topics of multivariable calculus. This is a little tougher than most people think as representing 3 dimensions on a piece of paper or a computer screen requires converting it to a 2-dimensional figure. Some basic vector algebra might be useful (even if you're not interested in vector calculus). Determinants are used in multiple places throughout multivariable calculus so you should at least know what a determinant and a matrix are and some basic properties. Keep in mind that multivariable calculus is all about taking a problem and converting it to an equivalent single variable calculus problem (roughly speaking). There's not nearly as many new concepts as in one-variable calculus and it is mostly about generalizing properties of functions that take one argument to functions that take multiple arguments.

Required Books

The main aim is to find complex topics with the easiest explanations and you probably won't be able to find that in one book only. Look for simple explanations in as many different books as possible. These are the books that I used to grasp the understanding of complicated topics covered throughout the syllabus. 

1. Advanced Engineering Mathematics 10th Edition by Erwin Kreyszig

2. Calculus by Howard Anton, Irl Bivens, and Stephen Davis

3. Multivariable Calculus 7th Edition by James Stewart

4. Calculus and Analytic Geometry 9th Edition by George B. Thomas, Jr.

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