Math 174
Calculus with Analytic Geometry II
I.
Course Description:
This course continues the study of analytic geometry and the calculus of algebraic and
transcendental functions including rectangular, polar and parametric graphing, indefinite
and definite integrals, methods of integration, and power series along their applications. It
is designed for mathematical, physical and engineering science programs. Lecture 4
hours per week.
II.
Prerequisites:
Math 173 (Calculus with Analytic Geometry I) or equivalent.
III.
Instructional Materials:
Textbook: Calculus by Larson, Hostetler, and Edwards, 9th. edition; Houghton Mifflin
Publishing, 2010.
Required Materials: Graphing Calculator.
IV.
Overall Objectives:
1.
2.
3.
4.
5.
6.
V.
Develop applications of integration including volume, work, arc length, surfaces
of revolution.
Develop additional techniques of integration.
Develop concepts of indeterminate forms and improper integrals.
Develop concepts of parametric equations and polar coordinates.
Develop infinite series concepts.
Develop concepts of vectors.
Attendance Policy:
It is expected that you will attend every class session. Mathematics is a comprehensive
subject and builds on itself. If you are unable to attend a session, contact the instructor or
a classmate to find out what was missed. You are responsible for reading the sections
covered that day, and completing the assignments as listed on the syllabus. More that
20% absence of the class sessions for the semester constitutes unsatisfactory attendance
and will place you in jeopardy of being withdrawn from class.
VI.
Disability Services Policy:
Reasonable accommodations will be made for students with disabilities provided those students
have registered with the Office of Disability Services. Present your teacher with the
documentation .
1
TIDEWATER COMMUNITY COLLEGE
CLASSROOM AND LABORATORY
EMERGENCY PROCEDURES FOR FACULTY
In the event of a bomb threat, tornado, or fire, students and staff may be asked to
evacuate the building or move to a secure location within the building. Evacuation
routes for movement to an external location or to a shelter within the building are posted
at the front of the room. Students should review the maps and make sure that the exit
route and assembly location for the building are clearly understood. If you have a
disability that may require assistance during an evacuation, please let your faculty know
at the end of the first class.
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Course Content
Chapter Eight: Integration Techniques, L’Hopital’s Rule, and Improper Integrals
8.1
Basic Integration Rules
8.2
Integration by Parts
8.3
Trigonometric Integrals
8.4
Trigonometric Substitution
8.5
Partial Fractions
8.6
Integration by Tables and Other Integration Techniques
8.7
Indeterminate Forms and L’Hopital’s Rule
8.8
Improper Integrals
Chapter Nine: Infinite Series
9.1
Sequences
9.2
Series and Convergence
9.3
The Integral Test and p-Series
9.4
Comparisons of Series
9.5
Alternating Series
9.6
The Ratio and Root Tests
9.7
Taylor Polynomials and Approximations
9.8
Power Series
9.9
Representation of Functions by Power Series
9.10 Taylor and Maclaurin Series
Chapter Ten: Conics, Parametric Equations, and Polar Coordinates
10.1 Conics and Calculus
10.2 Plane Curves and Parametric Equations
10.3 Parametric Equations and Calculus
10.4 Polar Coordinates and Polar Graphs
10.5 Area and Arc Length in Polar Coordinates
Chapter Eleven: Vectors and the Geometry of Space
11.1 Vectors in the Plane
11.2 Space coordinates and Vectors in Space
11.3 The Dot Product of Two Vectors
11.4 The Cross Product of Two Vectors in Space
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VI.
Math 174 Assignments
Textbook: Calculus by Larson, Hostetler, and Edwards, 9th edition
******************************************************************************
Section
Page
Assignment
******************************************************************************
8.1
524
5-29 odd
8.2
533
11,13,15,16,17,19,23,24,27,28,30,35, 36
8.3
542
5,7,8,9,11,13,15,25,33,51,53,67, 71
8.4
551
5,7,9,13,15,21-35 odd, 43
8.5
561
1-23 odd, 29
8.6
567
1-15 odd
8.7
576
5-37 odd , 45, 49,51, 59, 61
8.8
587
1-23 odd, 27, 31,39,47,49
Test #1
9.1
9.2
604
614
9.3
9.4
9.5
9.6
9.7
9.8
9.10
Test #2
10.1
10.2
10.3
622
630
638
647
658
668
687
10.4
738
10.5
11.1
747
771
11.2
780
11.3
11.4
Test #3
Final Exam,
789
798
1,3,11,13,15, 17, 23- 39 odd, 45-63 odd
1,5,9,13,15,17,25,29,31,33, 35, 37, 45, 47
53, 61, 63, 69
1,5, 9, 13,15,17,25,29,31, 33, 35, 41
15-23 odd, 29-35 odd
11,13,19,21,31
1,13-29 odd, 30,51,55, 57, 63, 65
13,15,17,25, 29,41,43
1,3,11-25 odd, 29
1,7, 9,17,27, 31
706
718
727
1-8, 67-76
1,3-11 odd, 17,19,23,25,33,39,41
1-11 odd, 15, 19, 29,33,49,51, 53
53,59,65,81,83,85,91
1,3, 11, 13 , 21,27, 31,33, 37, 39, 43, 57,
63, 69, 85, 87, 89, 95
1-13 odd, 17, 19, 25, 29, 37, 39, 43, 45
1,3, 5, 9, 11, 13, 17, 19, 21, 23, 39, 41,
49,51,53,73, 83
1,3,7,11,13,25,27,29,35,39,41, 43,49, 51
53, 59, 65, 83, 85, 93
1, 5, 9, 11, 17, 23, 31, 35, 43, 73
1, 7, 11, 13, 15, 17, 19, 29, 33, 43, 45, 59, 638
4