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# Calculus with Analytic Geometry III -- Spring 2015

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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: 713 Smith Hall
• Office Hours: MW 2:30-4:45 (walk-in), or by appointment
• Office Phone: x4639
• E-mail: saveliev@marshall.edu
• Class Web-Page: math02.com
• Prerequisites: excellent algebra skills, good understanding of the derivative and the integral, fluent differentiation and integration -- Calculus I -- Fall 2012 and Calculus II -- Fall 2014
• Text: Calculus by Rogawski, Chapters 11 - 17
• Computer Restrictions: no better than graphic calculator TI-83 or TI-83+
• Outcomes: the student will learn to analyze parametric curves, functions of several variables, and vector fields, apply these concepts and tools to study processes and patterns in physical and other sciences, become familiar with vector calculus.
• Activities: the student will practice each outcome via the homework given in the textbook and online.
• Evaluation: the student achievement of each outcome will be assessed via
• Grade Breakdown: TOTAL = .05×A + .40×(Q + H) + .20×M + .35×F (see the spreadsheet)
• attendance and participation: 5%
• quizzes and online homework: 40%
• midterm: 20%
• final exam: 35%

For details, see Course policy.

Mathematics Tutor Lab: Smith Music 115

## 1 Lectures

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

## 2 Homework

Follow this link to access the online homework: Webwork

Assignments:

• Orientation -- not for credit
• Chapter11
• Chapter11-12
• Chapter12
• Chapter12-13
• Chapter13
• Chapter13-14
• Chapter14
• Chapter14-15
• Chapter15
• Chapter15b
• Chapter15-16
• Chapter16
• Chapter16-17
• Chapter17 (still about chapter 16)
• Chapter17a -- not for credit

## 3 Schedule

Week 1 -- 1/12

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 -- 1/19

Chapter 12: Vector Geometry

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

Week 3 -- 1/26

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

Week 4 -- 2/2

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 -- 2/9

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

Week 6 -- 2/16

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 -- 2/23

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

Week 8 -- 3/2

14.4 Differentiability and Tangent Planes, 14.5 Directional Derivatives, 14.6 The Chain Rule,

Week 9 -- 3/9

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

Chapter 15: Multiple Integration

15.1 Integration in $2$ Variables, 15.2 Double Integrals over More General Regions,

<< Midterm >> 3/11

Spring Break -- 3/16

Week 10 -- 3/23

15.3 Triple Integrals, [15.4 Integration in Polar, Cylindrical, and Spherical Coordinates], 15.5 Applications of Multiple Integrals,

Week 11 -- 3/30

15.6 Change of variables,

Chapter 16: Line and Surface Integrals

16.1 Vector Fields,

Week 12 -- 4/6

16.2 Line Integrals,

Week 13 -- 4/13

16.3 Conservative Vector Fields, 16.4 Parametrized Surfaces and Surface Integrals,

Week 14 -- 4/20

16.5 Surface Integrals of Vector Fields,

Week 15 -- 4/27

Chapter 17: Fundamental Theorems of Vector Analysis

17.1 Green’s Theorem, 17.2 Stokes’ Theorem, 17.3 Divergence Theorem,

May 1, Friday Last Class Day

## 4 Exams

Upcoming:

• 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.
• Note: the grades won't be released until posted by the university.

Each old exam below is a very small (<5%) sample of the types of problems that may appear: