**Calculus Volume 3**

The comprehensive contents from this book, combined with Odigia’s Teaching and Learning Tools have everything you need to engage, collaborate, track and assess your students.

**This course includes:**

**465**

### example problems

**351**

### practice questions

**Helping Teachers Do What They Do Best: Teach**

**Customize**

Use our courses as is or easily customize them to fit your teaching style and the needs of your students. You can add your favorite resources, hide and show our existing content and pre-built assessments, or make them your own. Everything your students need, in one place!

**Engage and Collaborate**

Odigia combines learning materials, discussions, and tools to create a familiar social experience for students allowing you to easily connect and redirect students attention.

**Track**

See how much time students are spending on different areas of the course, which areas are creating the most amount of engagement and identify topics the students are struggling with. Flag and provide feedback on assignments to proactively meet individual students' needs.

**Assess**

Game theory allows students to monitor their progress visually and motivates them to stay on track. Students can see exactly what activities they need to complete, which ones have been flagged and compare their progress against the overall class.

### Calculus Volume 3 Course Outline

### What is the significance of parametric equations and polar coordinates?

Concepts Covered:

- How are parametric equations recognized?
- What is the calculus of parametric curves?
- What are polar coordinates?
- How are the area and arc lenth in polar coordinates found?
- How are conic sections evaluated?

### Why are vectors in space important?

Concepts Covered:

- What are plane vectors?
- How are vectors in three dimensions located and evaluated?
- How is the dot product of given vectors calculated?
- How is the cross product of vectors determined?
- How are equations of lines and planes in space solved?
- What are quadratic surfaces?
- How are cylindrical and spherical coordinates converted to different forms?

### In what situations are vector-valued functions used?

Concepts Covered:

- What are vector-valued functions and space curves?
- What is the Calculus of Vector-Valued Functions?
- How are arc lengths and curvatures of curves in space calculated?
- How does motion behave in space?

### How is the differentiation of functions with several variables conducted?

Concepts Covered:

- How are functions with several variables recognized and calculated?
- How are the limits and continuity of functions with multiple variables determined?
- How are partial derivatives calculated?
- How are tangent planes used to make linear approximations?
- What is the Chain Rule for multivariable calculus?
- What is the relationship between directional derivatives and the gradient?
- What are the problems with maxima and minima?
- What are Lagrange Multipliers?

### How is the integration of functions with multiple variables achieved?

Concepts Covered:

- How are double integrals over a rectangular region evaluated?
- How are double integrals over general regions evaluated?
- How are double integrals in polar coordinates evaluated?
- What are triple integrals, and how are they evaluated?
- How are triple integrals in cylindrical and spherical coordinates evaluated?
- How are centers of mass and moments of inertia calculated?
- What is the change of variables in multiple integrals?

### What concepts are studied in vector calculus?

Concepts Covered:

- What are vector fields?
- How are line integrals evaluated?
- How are conservative vector fields determined?
- What is Green’s Theorem?
- How are the divergence and curl from a formula for a given vector field determined?
- How are surface integrals used to solve problems?
- What is the meaning of Stokes’ Therem?
- How is the Divergence Theorem Applied?

### How are second-order differential equations solved?

Concepts Covered:

- How are second-order linear equations recognized and solved?
- How are nonhomogeneous linear equations solved?
- What are the applications of second-order differential equations?
- What are series solutions of differential equations?

Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 3 covers parametric equations and polar coordinates, vectors, functions of several variables, multiple integration, and second-order differential equations.

**About the authors:**

## Senior Contributing Authors

**Gilbert Strang, **Massachusetts Institute of Technology**
Edwin “Jed” Herman,** University of Wisconsin-Stevens Point

## Contributing Authors

Nicoleta Virginia Bila, Fayetteville State University

Sheri J. Boyd, Rollins College

David Smith, University of the Virgin Islands

Elaine A. Terry, Saint Joseph’s University

David Torain, Hampton University

Kirsten R. Messer, Colorado State University-Pueblo

Alfred K. Mulzet, Florida State College at Jacksonville

William Radulovich, Formerly at Florida State College at Jacksonville

Erica M. Rutter, Arizona State University

David McCune, William Jewell College

Michelle Merriweather, Bronxville High School

Joseph Lakey, New Mexico State University

Julie Levandosky, Framingham State University

Valeree Falduto, Palm Beach State College

Catherine Abbott, Keuka College

Joyati Debnath, Winona State University