Last Reviewed by:
Steve Smotherman
Date Approved:
Date Revised:
New Rubrics:
June 2006
Fa11 2014
Fall 2001
COURSE SYLLABUS
-----------------------------------------------------------------------------------Syllabus for:
MATH 2110
Calculus III
-----------------------------------------------------------------------------------Former Course and Title:
MAT 2530 Calculus III
Former Quarter Course(s):
MAT 207 Calculus III and MAT 208 Calculus IV
-----------------------------------------------------------------------------------Catalog
Description: This course is a study of parametric and polar equations; vectors in the
plane and in space; solid analytic geometry, including cylindrical and
spherical coordinates; functions of several variables, including partial
derivates and their applications; multiple integrals with applications;
selected topics from vector calculus.
Prerequisites: MATH 1920
-----------------------------------------------------------------------------------Credit Hours:
4 sem hrs
Contact Hours:
4 hrs/wk
Lab Hours:
0
-----------------------------------------------------------------------------------Prerequisite(s):
MATH 1920
Calculus II
-----------------------------------------------------------------------------------Required
Text(s): (1)
Calculus
Title
Larson, Hostetler,
Edwards
10th/2014
Author(s)
Edition/Date
Brooks/Cole
Publisher
-----------------------------------------------------------------------------------Required Supplies/Material(s):
Graphing Calculator
-----------------------------------------------------------------------------------Recommended Supplementary Material(s):
Complete Solutions Guide/Bruce Edwards
Study and Solutions Guide/David Heyd
-----------------------------------------------------------------------------------Student Group for Whom Course is Required/Intended:
Students who have completed two semesters of calculus and who have generally
chosen options in math, physics, computer science, chemistry, and pre-engineering.
Motlow State Community College
Lynchburg, TN
SYLLABUS: MATH 2110, page 2
-------------------------------------------------------------------------------------GOALS
-------------------------------------------------------------------------------------The goals of instruction of MATH 2110 are:
1.
to acquire the ability to understand the definitions of the four conic sections,
construct their graphs, and name their various parts;
2.
to study plane curves in parametric and polar form as well as surfaces and curves
in space;
3.
to develop proficiency in the study and application of vectors in the plane and in
space;
4.
to develop skill in finding appropriate partial derivatives and apply this skill
to application problems in multivariable calculus;
5.
to evaluate multiple integrals and apply the results to finding volume, mass, and
center of mass; and
6.
to further develop skills in calculus that are necessary for students to succeed
in mathematics, science, and engineering courses that are part of their
curriculum.
---------------------------------------------------------------------------------------OBJECTIVES
---------------------------------------------------------------------------------------Through the study of Calculus III, the student should develop the ability to:
1.
write the equation of a parabola in standard form; identify (locate) the vertex,
focus, directrix, and sketch;
2.
write the equation of an ellipse in standard form; identify (locate) the center,
foci, vertices, eccentricity, and sketch;
3.
write the equation of a hyperbola in standard form; identify (locate) the center,
foci, vertices, eccentricity, directrices, and sketch;
4.
classify equations, in general form, as the equation of a circle, parabola,
ellipse, or hyperbola;
5.
use a graphing calculator to sketch certain equations in parametric form;
6.
eliminate the parameter and sketch "by hand" certain equations in parametric form;
7.
write the equations of certain conic sections in parametric form;
8.
use calculus to find the first and second derivatives of equations in parametric
form;
9.
write the equations of tangent lines, and optionally, find arc length and surface
areas of revolution for parametric curves;
10.
convert points and equations from polar to rectangular form and vice versa;
11.
recognize and sketch curves in polar form "by hand" and with the use of
technology;
Motlow State Community College
Lynchburg, TN
SYLLABUS: MATH 2110, page 3
----------------------------------------------------------------------------------OBJECTIVES, continued
12.
calculate slopes of, and tangent lines to, the graphs of equations in polar form;
13.
find intersection points of graphs and use calculus to find appropriate areas, and
optionally, arc lengths, and surface areas of revolution for given curves in polar
form;
14.
write equations of conic sections in polar form and graph (optional);
15.
write the component form of a vector, perform vector operations and interpret the
results geometrically, and write a vector as a linear combination of standard unit
vectors, all in the plane;
16.
understand the three-dimensional rectangular coordinate system and analyze vectors
in space;
17.
use properties of the dot product of two vectors, find the angle between two
vectors, find the direction cosines of a vector in space, and find the projection
of one vector onto another;
18.
find the cross product of two vectors in space and apply properties of the cross
product;
19.
write equations of lines and planes in space and sketch;
20.
find distances in space, including distance from a point to a line, between
parallel and skew lines, from a point to a plane, and between parallel planes;
21.
classify quadric surfaces from one of their six basic forms;
22.
sketch quadric surfaces and, optionally, certain surfaces of revolution;
23.
convert points and equations in cylindrical, spherical or rectangular coordinates
from any one of these systems to another of these systems;
24.
understand basic concepts concerning functions of several variables;
25.
understand the basic ideas of limits and continuity in three dimensions
(optional);
26.
determine specified partial derivatives of multivariable functions;
27.
interpret specified partial derivatives as the appropriate slopes of curves in
space;
28.
find the total differential of a multivariable function;
29.
determine and compare the values Δf and df for multivariable functions;
30.
determine how the total differential can be applied to absolute error and percent
error (optional);
31.
write the appropriate chain rule form for a multivariable function whose variables
are defined in terms of other parameters;
32.
find and determine specified directional derivatives at indicated points;
Motlow State Community College
Lynchburg, TN
SYLLABUS: MATH 2110, page 4
----------------------------------------------------------------------------------OBJECTIVES, continued
33.
find, determine, and interpret the gradient vector for a multivariable function;
34.
given a point on a surface, write the equation of the tangent plane and normal
line;
35.
find extrema for a multivariable function and test to determine if these extrema
are maxima or minima;
36.
write the model for required optimization problems and determine the maximum or
minimum value as appropriate (optional);
37.
evaluate iterated integrals;
38.
apply iterated integrals to finding areas;
39.
apply double integrals to finding volumes under surfaces;
40.
write and evaluate double integrals in polar form (optional);
41.
apply the polar form of double integrals to finding volumes of solids that can
best be expressed in polar form (optional);
42.
use double integrals to find the mass, the center of mass, and the moment of
inertia and radius of gyration for lamina with variable densities (optional);
43.
use double integrals to find the area of a surface over a region R (optional);
44.
evaluate triple integrals;
45.
apply triple integrals to finding volume, mass, center of mass and, optionally,
moment of inertia;
46.
graph vector functions (optional);
47.
find and interpret the derivatives and integrals of vector functions (optional);
48.
write, sketch, and interpret models for projectiles in motion, including velocity
and acceleration (optional);
49.
find tangent and normal vectors to graphs of vector functions (optional);
50.
find the arclength of the graph of a vector function and the curvature of a vector
function at a specified point and interpret the concept of curvature and radius of
curvature (optional).
Motlow State Community College
Lynchburg, TN
SYLLABUS: MATH 2110, page 5
-----------------------------------------------------------------------------------
SUGGESTED EVALUATION PLAN
TASK
WEIGHT
OBJECTIVES
Test 1
100 points
1-14
Test 2
100 points
15-23
Test 3
100 points
24-36
Test 4
100 points
37-45
Test 5 (Final Exam)
150 points
46-50 (50 points)
1-45 (100 points)
Notebooks/Homework
100 points
1-50
FINAL GRADING PLAN
Based Upon Percentages
A =
585 - 650 points (90-100%)
B =
520 - 584 points (80-89%)
C =
455 - 519 points (70-79%)
D =
390 - 454 points (60-69%)
F =
Below 390 points (below 60%)
Additional Comments:
Motlow State Community College
Lynchburg, TN
SYLLABUS: MATH 2110, page 6
----------------------------------------------------------------------------------INSTRUCTIONAL SCHEDULE
for
MATH 2110- Calculus III
Course Number and Name
Week
Objective
Numbers
Content to be Covered
Student Assignments/
Supplementary Material(s)
I.
1,2,3,4
5,6,7
Parabola, Ellipse, Hyberbola
Parametric Equations
Section 10.1
Section 10.2
II.
8,9
10,11,12
Parametric Equations and Calculus
Polar Coordinates and Graphs
Section 10.3
Section 10.4
III.
13
14
1-14
Polar Coordinates and Calculus
Polar Coordinates and Conics (optional)
Test #1 (Chapter 10)
Section 10.5
Section 10.6
IV.
15
16
Vectors in the Plane
Vectors in Space
Section 11.1
Section 11.2
V.
17
18
Dot Product
Cross Product
Section 11.3
Section 11.4
VI.
19,20
21,22
Lines and Planes in Space
Surfaces
Section 11.5
Section 11.6
VII.
23
15-23
24
Cylindrical and Spherical Coordinates
Test #2 (Chapter 11)
Introduction to Functions of Several
Variables
Section 11.7
Limits and Continuity in Three
Dimensions (optional)
Partial Derivatives
Section 13.2
Section 13.4
31
Differentials in Three Dimensions
(objective 30 optional)
Multi-Variable Chain Rules
Section 13.5
32,33
34
Directional Derivatives and Gradients
Tangent Planes and Normal Lines
Section 13.6
Section 13.7
VIII. 25
26,27
IX.
X.
28,29,30
Motlow State Community College
Lynchburg, TN
Section 13.1
Section 13.3
SYLLABUS: MATH 2110, pg 7
----------------------------------------------------------------------------------INSTRUCTIONAL SCHEDULE
for
Math 2110 - Calculus III
Course Number and Name
Week
XI.
Objective
Numbers
35
36
Section 13.8
Section 13.9
Iterated Integrals and Area
Volumes with Double Integrals
Polar Coordinates and Double
Integrals (optional)
Section 14.1
Section 14.2
Section 14.3
Center of Mass and Moment of
Inertia by Double Integrals (optional)
Surface Area by Double Integrals
(optional)
Triple Integrals and Applications
Test #4 (Chapter 14)
Section 14.4
Section 12.1
Section 12.2
48
49
50
Vector-Valued Functions (optional)
Calculus and Vector-Valued Functions
(optional)
Velocity and Acceleration (optional)
Tangent and Normal Vectors (optional)
Arclength and Curvature (optional)
1-50
Final Exam
37,38
39
40,41
XIII. 42
43
44,45
37-45
XIV.
XV.
Student Assignments/
Supplementary Material(s)
Extrema in Two Variables
Applications of Extrema in Two
Variables (optional)
Test #3 (Chapter 13)
24-36
XII.
Content to be Covered
46
47
Motlow State Community College
Lynchburg, TN
Section 14.5
Section 14.6
Section 12.3
Section 12.4
Section 12.5