This site is devoted to mathematics and its applications. Created and run by Peter Saveliev.

# Calculus with Analytic Geometry III -- Spring 2014

### From Mathematics Is A Science

**MTH 231 - Calculus with Analytic Geometry III.** Vectors, curves, and surfaces in space. Derivatives and integrals of functions of more than one variable. A study of the calculus of vector-valued functions. PR: MTH230. 4 hours.

- Time and Place: 5:00 - 5:50 pm MTWR at 513 Smith Hall.
- Instructor: Peter Saveliev (call me Peter)
- Office: 325 Smith Hall
- Office Hours: TR 2:30-4:30 (tentative), or by appointment
- Office Phone: x4639
- E-mail: saveliev@marshall.edu
- Class Web-Page: math01.com
- Prerequisites: Calculus II -- Fall 2012
- Text: Calculus by Rogawski, Chapters 11 - 17
- Computer Restrictions: graphic calculator TI-83 or TI-83+
- Goals: Calculus in dimension 2 and 3: parametric curves, functions of several variables, line, surface, and volume integrals, some vector calculus
- Quizzes: taken from the exercise sets, open book
- Homework: online via Webwork, weekly
- Grade Breakdown: TOTAL = .05×A + .40×(Q + HW) + .20×M + .35×F
- attendance and participation: 5%
- quizzes and homework: 40%
- midterm: 20%
- final exam: 35%

- Letter Grades: A: 90-100, B: 80-89, C: 70-79, D: 60-69, F: <60

See also **Course policy**.

## 1 Lectures

They will appear exactly as you see them in class and, as the course progresses, will be updated weekly.

## 2 Schedule

Tentative...

**Week 1** -- 1/13

*Chapter 11: Parametric Equations, Polar Coordinates, and Conic Sections*

11.1 Parametric Equations, 11.2 Arc Length and Speed, 11.3 Polar Coordinates,

**Week 2** -- 1/20

*Chapter 12: Vector Geometry*

12.1 Vectors in the Plane, 12.2 Vectors in Three Dimensions,

**Week 3** -- 1/27

12.3 Dot Product and the Angle Between Two Vectors, 12.4 Cross Product,

**Week 4** -- 2/3

12.5 Planes in Three-Space, [12.6 A Survey of Quadric Surfaces], 12.7 Cylindrical and Spherical Coordinates,

*Chapter 13: Calculus of Vector-Valued Functions*

13.1 Vector-Valued Functions,

**Week 5** -- 2/10

13.2 Calculus of Vector-Valued Functions, 13.3 Arc Length and Speed,

**Week 6** -- 2/17

13.4 Curvature, [13.5 Motion in Three-Space,] [13.6 Planetary Motion According to Kepler and Newton],

*Chapter 14: Differentiation in Several Variables*

14.1 Functions of Two or More Variables,

**Week 7** -- 2/24

14.2 Limits and Continuity in Several Variables, 14.3 Partial Derivatives,

**Week 8** -- 3/3

14.4 Differentiability and Tangent Planes,

**<<Midterm>> 3/10**

**Week 9** -- 3/10

14.5 Directional Derivatives, 14.6 The Chain Rule,

**Spring Break** -- 3/17

**Week 10** -- 3/24

14.7 Optimization in Several Variables, [14.8 Lagrange Multipliers: Optimizing with a Constraint],

*Chapter 15: Multiple Integration*

15.1 Integration in $2$ Variables,

**Week 11** -- 3/31

15.2 Double Integrals over More General Regions, 15.3 Triple Integrals, [15.4 Integration in Polar, Cylindrical, and Spherical Coordinates],

**Week 12** -- 4/7

15.5 Applications of Multiple Integrals, 15.6 Change of variables Change of Variables,

*Chapter 16: Line and Surface Integrals*

16.1 Vector Fields,

**Week 13** -- 4/14

16.2 Line Integrals, 16.3 Conservative Vector Fields,

**Week 14** -- 4/21

16.4 Parametrized Surfaces and Surface Integrals, 16.5 Surface Integrals of Vector Fields,

*Chapter 17: Fundamental Theorems of Vector Analysis*

17.1 Green’s Theorem,

**Week 15** -- 4/28

[17.2 Stokes’ Theorem,] [17.3 Divergence Theorem,]

**May 2, Friday Last Class Day**

## 3 Notes

Calculus III -- Spring 2014 -- midterm, Monday March 10.

Calculus III -- Spring 2014 -- final exam, Monday May 5, 5:00-7:00 pm, same place. Note: If the two-hour time allowance results in a conflict in exam times, it is the student’s responsibility to notify the professor of the later course and to reschedule the later exam.

Old exams: