Multivariable Calculus with Applications is a textbook that introduces multivariable calculus and its applications to students in the fields of engineering, economics, and science.

The book provides a comprehensive introduction to multivariable calculus by comparing and contrasting it to the one-variable version of the subject. It explains how the concepts learned in this multivariable course can be applied to numerous disciplines, such as economics, engineering, and physics.

The book begins with an overview of vector algebra, which is used throughout the text. Students are introduced to vectors and functions of several variables, with examples illustrating how to manipulate both algebraic and geometric objects. The author then goes on to discuss double integrals and their applications before covering triple integrals and several other topics including differential equations with boundary values between two regions.

In addition to covering these basic concepts, Multivariable Calculus with Applications also introduces vector functions and line integrals followed by surface integrals, Stoke’s theorem, isoperimetric problems, Green’s theorem, Stokes’ theorem, Green-Lambert’s formula for capacitance problems in planar regions, and Gauss’ law for electrostatics.

As a student, you’re probably aware that high school calculus courses offer a depth and breadth of material that may seem unrelated to what you’ll need later in life. But the truth is, this information will be important—and even crucial—to your future endeavors.

To help you navigate the challenges of multivariable calculus with applications, we’ve taken the time to gather resources for you that will ease your journey through school and into your career.

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**About Multivariable Calculus with Applications PDF Book**

Burstein, and Lax’s Calculus with Applications and Computing offers meaningful explanations of the important theorems of single variable calculus. Written with students in mathematics, the physical sciences, and engineering in mind, and revised with their help, it shows that the themes of calculation, approximation, and modeling are central to mathematics and the main ideas of single variable calculus. This edition brings the innovation of the first edition to a new generation of students. New sections in this book use simple, elementary examples to show that when applying calculus concepts to approximations of functions, uniform convergence is more natural and easier to use than point-wise convergence. As in the original, this edition includes material that is essential for students in science and engineering, including an elementary introduction to complex numbers and complex-valued functions, applications of calculus to modeling vibrations and population dynamics, and an introduction to probability and information theory.

## Table of Content: Multivariable Calculus with Applications PDF

Vectors and matrices

Functions

Differentiation

More about differentiation

Applications to motion

Integration

Line and surface integrals

Divergence and Stokes’ Theorems and conservation laws

Partial differential equations