Active Calculus Multivariable

Format:

Book

Author/Creator:

Schlicker, Steve, author.

Austin, David, author.

Boelkins, Matthew, author.

Language:

English

Subjects (All):

Mathematics--Textbooks.

Mathematics.

Physical Description:

1 online resource

Place of Publication:

[Place of publication not identified] Grand Valley State University 2018.

Language Note:

In English.

Summary:

Active Calculus Multivariable is the continuation of Active Calculus to multivariable functions. The Active Calculus texts are different from most existing calculus texts in at least the following ways: the texts are free for download by students and instructors in .pdf format; in the electronic format, graphics are in full color and there are live html links to java applets; the texts are open source, and interested instructors can gain access to the original source files upon request; the style of the texts requires students to be active learners — there are very few worked examples in the texts, with there instead being 3-4 activities per section that engage students in connecting ideas, solving problems, and developing understanding of key calculus concepts; each section begins with motivating questions, a brief introduction, and a preview activity, all of which are designed to be read and completed prior to class; the exercises are few in number and challenging in nature.

Contents:

Preface9 Multivariable and Vector Functions

9.1 Functions of Several Variables and Three Dimensional Space

9.2 Vectors

9.3 The Dot Product

9.4 The Cross Product

9.5 Lines and Planes in Space

9.6 Vector-Valued Functions

9.7 Derivatives and Integrals of Vector-Valued Functions9.8 Arc Length and Curvature

10 Derivatives of Multivariable Functions

10.1 Limits

10.2 First-Order Partial Derivatives

10.3 Second-Order Partial Derivatives

10.4 Linearization: Tangent Planes and Differentials

10.5 The Chain Rule

10.6 Directional Derivatives and the Gradient

10.7 Optimization

10.8 Constrained Optimization:Lagrange Multipliers

11 Multiple Integrals

11.1 Double Riemann Sums and Double Integrals over Rectangles

11.2 Iterated Integrals

11.3 Double Integrals over General Regions

11.4 Applications of Double Integrals

11.5 Double Integrals in Polar Coordinates

11.6 Surfaces Defined Parametrically and Surface Area

11.7 Triple Integrals

11.8 Triple Integrals in Cylindrical and Spherical Coordinates

11.9 Change of Variables

Notes:

Description based on print resource