COURSE SYLLABUS
Ohio Northern University
College of Arts and Sciences
Department of Mathematics and Statistics
Date: Fall 2013
Course Math 2631
Name: Calculus 3
Credit hours: 4
Lecture hours/week: 4
Lab hours/week: 0
Instructor: Staff
Usual Student Level: Sophomore
Course required of students in: Mathematics, Engineering, Physics, Chemistry
Course frequency per semester/year: Offered yearly; fall and spring semesters
Average enrollment per year: 120
This course has a prerequisite:
Math 1641 Calculus 2
This course is a prerequisite for:
Math 3631 Complex Analysis
Math 3611 Real Analysis
Catalogue Description:
Vectors and vector valued functions, planes and lines in space, multivariate functions, differential and
integral calculus of multivariate functions.
Course Objectives:
To give students the necessary tools, concepts and methods to work in engineering, science and
mathematics.
Textbook: Calculus, 7th Edition, by J. Stewart
A graphing calculator is required too.
Notes:
This course is aimed towards the Green, Stokes and Divergence theorems and should be organized
correspondingly. The students have to be advised that the course requires intensive work and full cooperation.
The instructor should focus on the main topics and avoid small details, deviations and time consuming
computations.
Maple can be used for graphing vector functions, surfaces and for the illustration of max/min points and tangent
planes.
The main theorems should be accompanied by short proofs, avoiding long formal details and using more
geometrical intuition.
Outline of content follows: (see attached)
Course Outline (Stewart 7th)
Math 2631
Calculus 3
Section
Topic
Days
Vectors and Vector Functions
12.2
Vectors
12.3
The Dot product
12.4
The Cross Product
12.5
Equations of lines and planes
12.6
Cylinders and Quadric Surfaces (optional)
1
1
1
2
1
13.1
13.2
13.3
13.4
2
2
2
1
Vector functions and space curves
Derivatives and Integrals of Vector Functions
Arclength and curvature
Motion in space: Velocity and Acceleration
Partial Derivatives
14.1
Functions of several variables
14.3
Partial derivatives
14.4
Tangent planes and Linear Approximation
14.5
The chain rule
14.6
Directional derivatives and the gradient
14.7
Maximum and minimum values
14.8
Lagrange multipliers
(optional)
1
2
2
1
2
2
1
Multiple Integrals
15.1
Double integrals over rectangles
15.2
Iterated integrals
15.3
Double integrals over general regions
15.4
Double integrals in polar coordinates
15.7
Triple integrals
15.8
Triple integrals in cylindrical coordinates
15.9
Triple integrals in spherical coordinates
1.5
2
2
2
1.5
2
1
Vector Calculus
16.1
Vector fields
16.2
Line integrals
16.3
The Fundamental Theorem for line integrals
16.4
Green’s Theorem
16.5
Curl and Divergence
16.6
Parametric surfaces
16.7
Surface integrals
16.8
Stokes’ Theorem
16.9
The Divergence Theorem
1
2
2
2
2
1
2
2
2
This is a total of about 52 hours and about 8 hours are left for testing and reviews.