Math and Society
If you’ve gotten this far in the field of calculus, you probably know how important it is for society. It’s even a key part of the computer algorithms in the search engines that might have led you here. From these algorithms to public health studies, architecture, and more, life would be very different for all of us if it weren’t for calculus. In Multivariable Calculus (Calculus 3 by Example) you’ll get one step closer to understanding the many methods and applications of the field.
Calculus 3: What’s Inside
Chapter 1 of the Multivariable Calculus book starts with a review of materials found in previous books in the series. Material from Calculus 1 in particular is a big focus in this chapter, and is of great importance for keeping up in the rest of the book. If you’re not completely comfortable with the concepts of derivatives and integrals found in Calculus 1, be sure to brush up on them here. Beyond the review of Calculus 1 topics, the first chapter also applies these topics to vector functions and space curves.
Chapter 2 of Multivariable Calculus then takes a look at partial differentiation. It includes sections on multivariable functions, limits and continuity, the chain rule, and related topics, finishing off with Lagrange multipliers. In Chapter 3 you’ll learn about multiple integrations, the differences between double and iterated integrals, and change of variables. This section is very thorough and includes integrals in various coordinate systems. These include the typical Cartesian (rectangular) system as well as the spherical and cylindrical systems.
The fourth and last chapter of Multivariable Calculus delves into vector calculus and vector fields. Similar to material from Chapter 1, vector calculus involves inputting numbers to get an output. But instead of putting in one number and getting a vector, you input multiple numbers to get several vectors. You’ll also find important theorems in this chapter such as Green’s Theorem, and of course the crucial Fundamental Theorem of Line Integrals. Also known as the Gradient Theorem, this theorem has a powerful role in calculus.
Always Lead by Example
Because math can be abstract and hard to mentally picture, it helps to have visual guides and hands-on practice. Thus, each of these chapters in Multivariable Calculus covers applications of the topics and provides thorough explanations. They also have many detailed diagrams as well as examples to aid comprehension. You’ll often find that typical Calculus 3 textbooks don’t always contain these types of helpful tools. So, this book serves well as a supplement for classroom texts that are heavy in proofs and theory. If used together with drier classroom materials, or even as material for those doing independent study, it will help students gain a more in-depth understanding of the ideas.