ESSEX COUNTY COLLEGE
Mathematics and Physics Division
MTH 122 – Calculus and Analytic Geometry II
Course Outline
Course Number & Name: MTH 122 Calculus with Analytic Geometry II
Credit Hours: 4 .0
Contact Hours: 4.0
Lecture: 4.0
Lab: N/A
Other: N/A
Prerequisites: Grade of “C” or better in MTH 121 or placement
Co-requisites: None
Concurrent Courses: None
Course Outline Revision Date: Spring 2013
Course Description: This course is a continuation of MTH 121. Topics covered include techniques of
integration with applications of surface area and arc length, parametric equations, polar coordinates,
conic sections, and infinite sequences and series.
General Education Goals: MTH 122 is affirmed in the following General Education Foundation Category:
Quantitative Knowledge and Skills. The corresponding General Education Goal is as follows: Students
will use appropriate mathematical and statistical concepts and operations to interpret data and to solve
problems.
Course Goals: Upon successful completion of this course, students should be able to do the following:
1. demonstrate knowledge of the fundamental concepts and theories from calculus;
2. utilize various problem-solving and critical-thinking techniques to set up and solve applied problems
in engineering, sciences, business, and technology fields;
3. communicate accurate mathematical terminology and notation in written and/or oral form in order
to explain strategies to solve problems as well as to interpret found solutions; and
4. use appropriate technology, such as graphing calculators and computer software, effectively as a
tool to solve such problems as those described above.
Measurable Course Performance Objectives (MPOs): Upon successful completion of this course,
students should specifically be able to do the following:
1. Demonstrate knowledge of the fundamental concepts and theories from calculus:
1.1 calculate integrals using the Fundamental Theorem in Calculus and solve application problems
involving arc length, volume and surface area of revolution;
1.2 evaluate definite (including improper) and indefinite integrals using various techniques such as
substitution, integration by parts, partial fractions, and transformations.
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1.3 use the polar coordinate system and parametric system to solve calculus application problems;
1.4 identify various conic sections by their equations and graph them;
1.5 define convergence and divergence of sequences and series and determine the convergence by
using appropriate tests;
1.6 identify the convergence intervals and radii of power series and find related convergent functions
when possible;
1.7 write power series representations of functions (i.e., Taylor series and Maclaurin series) and
approximate functions with polynomials; and
1.8 apply integration techniques to determine integrals of various functions including exponential,
logarithmic and trigonometric functions
2. Utilize various problem-solving and critical-thinking techniques to set up and solve applied problems
in science, business, engineering, and technology fields:
2.1 apply calculus concepts to evaluate integrals for functions arising from engineering and business
applications
3. Communicate accurate mathematical terminology and notation in written and/or oral form in order
to explain strategies to solve problems as well as to interpret found solutions:
3.1 write and explain solutions to problems including series, areas, and other application problems
4. Use appropriate technology, such as graphing calculators and computer software, effectively as a
tool to solve such problems as those described above:
4.1 use a graphing calculator and/or web-based application programs such as Wolfram Alpha as an
aid to calculus concepts covered; and
4.2 use Computer Algebra Systems (CAS), and other computer software such as Mathematica and/or
Maple as an aid to calculus concepts covered.
Methods of Instruction: Instruction will consist of a combination of lectures, class discussion, group
work, board work, computer lab work, and individual study.
Outcomes Assessment: Test and exam questions are blueprinted to course objectives. Data is collected
and analyzed to determine the level of student performance on these assessment instruments in
regards to meeting course objectives. The results of this data analysis are used to guide necessary
pedagogical and/or curricular revisions.
Course Requirements: All students are required to:
1. Read the textbook and do the suggested review problems in a timely manner.
2. Be an active participant in all classes.
3. Complete all written and/or electronic homework and adhere to assignment deadlines.
4. Take exams/quizzes in class and adhere to the exam/quiz schedule.
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Methods of Evaluation: Final course grades will be computed as follows:
Grading Components



Homework
e.g., problem sets, research projects, etc., designed to
enhance understanding of applications of calculus in
engineering and related disciplines.
3 or more Exams/Quizzes (dates specified by the instructor)
Exams/quizzes will show evidence of the extent to which
students meet course objectives, including, but not
limited to, identifying and applying concepts, analyzing
and solving problems, estimating and interpreting results,
and stating appropriate conclusions using correct
terminology.
Final Exam
The comprehensive final exam will examine the extent to
which students have understood and synthesized all
course content and achieved all course objectives.
% of final course grade
10 – 20%
50 – 60%
20 – 30%
NOTE: The instructor will provide specific weights, which lie in the above-given ranges, for each of the
grading components at the beginning of the semester. Also, students may use a scientific or graphing
calculator or laptop computer to enhance understanding during class or while doing homework.
However, technological aids may only be used on select assessments (exams, quizzes, etc.) – instructors
will inform students in advance when these technological aids are needed and may be used.
Academic Integrity: Dishonesty disrupts the search for truth that is inherent in the learning process and
so devalues the purpose and the mission of the College. Academic dishonesty includes, but is not
limited to, the following:

plagiarism – the failure to acknowledge another writer’s words or ideas or to give proper credit
to sources of information;

cheating – knowingly obtaining or giving unauthorized information on any test/exam or any
other academic assignment;

interference – any interruption of the academic process that prevents others from the proper
engagement in learning or teaching; and

fraud – any act or instance of willful deceit or trickery.
Violations of academic integrity will be dealt with by imposing appropriate sanctions. Sanctions for acts
of academic dishonesty could include the resubmission of an assignment, failure of the test/exam,
failure in the course, probation, suspension from the College, and even expulsion from the College.
Student Code of Conduct: All students are expected to conduct themselves as responsible and
considerate adults who respect the rights of others. Disruptive behavior will not be tolerated. All
students are also expected to attend and be on time all class meetings. No cell phones or similar
electronic devices are permitted in class. Please refer to the Essex County College student handbook,
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Lifeline, for more specific information about the College’s Code of Conduct and attendance
requirements.
Course Content Outline: based on the text Calculus: Early Transcendentals, 2nd edition, by Rogawski;
published by Freeman, 2012; ISBN-10 #: 1-4292-0838-4; ISBN-13 #: 978-1-4292-0838-3.
Class Meeting1
Chapter/Section
1 (1)
1 (2)
1 (3)
1 (4)
CHAPTER 6 APPLICATIONS OF THE INTEGRATAL
6.1
Area Between Two Curves
6.2
Setting Up Integrals
6.3
Volumes of Revolution
6.4
Method of Cylindrical Shells
2 (6)
2 (8)
2 (10)
2 (12)
2 (14)
2 (16)
CHAPTER 7 TECHNIQUES OF INTEGRATION
7.1
Integration by Parts
7.2
Trigonometric Integrals
7.3
Trigonometric Substitution
7.5
Method of Partial Fractions
7.6
Improper Integrals
7.8
Numerical Integration
1 (17)
Testing
1 (18)
2 (20)
CHAPTER 8 FURTHER APPLICATIONS
8.1
Arc length
8.4
Taylor Polynomials
1 (21)
Testing
2 (23)
2 (25)
2 (27)
2 (29)
2 (31)
2 (33)
CHAPTER 10 INFINITE SEQUENCE AND SERIES
10.1 Sequences
10.2 Summing an Infinite Series
10.3 Convergence of Series with Positive Terms
10.4 Absolute and Conditional Convergence
10.5 The Ratio and Root Tests
10.6 Power Series
10.7 Taylor Series
1 (34)
Testing
3 (35)
CHAPTER 11 PARAMETRIC EQUATIONS AND POLAR COORDINATES
11.1 Parametric Equations
1
A guide is available at: http://mth122.mathography.org/. The numbers in parenthesis are
cumulative class periods (80 minutes = 1 class period). The class time does not have to follow
this exact schedule.
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2 (37)
3 (40)
2 (42)
3 (45)
11.2
11.3
11.4
11.5
1 (46)
Review
1 (48)
Testing
Arc Length and Speed
Polar Coordinates
Areas and Arc Lengths in Polar Coordinates
Conic Sections
MTH 122 Suggested Homework/Review Problems
NOTE: The format used below is assignment #. chapter.section.exercise #
1. 6.1.005, 6.1.013, 6.1.017, 6.1.020, 6.1.035
2. 6.2.013, 6.2.039, 6.2.046
3. 6.3.004, 6.3.012, 6.3.016
4. 6.4.007, 6.4.008, 6.4.018
5. 7.1.008, 7.1.010, 7.1.012, 7.1.014, 7.1.019, 7.1.020, 7.1.025, 7.1.027, 7.1.030, 7.1.049
6. 7.2.001, 7.2.003, 7.2.007, 7.2.009, 7.2.013, 7.2.023, 7.2.047, 7.2.048, 7.2.050, 7.2.072
7. 7.3.005, 7.3.006, 7.3.011, 7.3.021, 7.3.022, 7.3.036, 7.3.039
8. 7.5.001, 7.5.002, 7.5.003, 7.5.004, 7.5.005, 7.5.009, 7.5.012, 7.5.017, 7.5.022, 7.5.065
9. 7.6.002, 7.6.004, 7.6.006, 7.6.011, 7.6.016, 7.6.017, 7.6.024, 7.6.029, 7.6.033, 7.6.040
10. 7.8.002, 7.8.011, 7.8.014, 7.8.030
11. 8.1.002, 8.1.007, 8.1.010, 8.1.015, 8.1.018, 8.1.035, 8.1.037, 8.1.039, 8.1.043
12. 8.4.003, 8.4.004, 8.4.005, 8.4.007, 8.4.010, 8.4.013, 8.4.025, 8.4.026
13. 10.1.003, 10.1.005, 10.1.009, 10.1.012, 10.1.013, 10.1.014d, 10.1.016, 10.1.017, 10.1.018,
10.1.019, 10.1.020, 10.1.022, 10.1.024, 10.1.025, 10.1.026, 10.1.030, 10.1.031, 10.1.036,
10.1.039, 10.1.041, 10.1.044, 10.1.045, 10.1.046, 10.1.048, 10.1.050, 10.1.054, 10.1.058,
10.1.059, 10.1.061, 10.1.065
14. 10.2.002, 10.2.004, 10.2.011, 10.2.012, 10.2.013, 10.2.015, 10.2.024, 10.2.025, 10.2.026,
10.2.029, 10.2.032, 10.2.043, 10.2.046
15. 10.3.007, 10.3.009, 10.3.012, 10.3.019, 10.3.025, 10.3.041, 10.3.043, 10.3.052, 10.3.055,
10.3.057, 10.3.060, 10.3.077
16. 10.4.001, 10.4.002, 10.4.003, 10.4.004, 10.4.005, 10.4.007, 10.4.009, 10.4.010, 10.4.011,
10.4.012, 10.4.017, 10.4.019, 10.4.020, 10.4.026
17. 10.5.001, 10.5.003, 10.5.006, 10.5.008, 10.5.009.SA, 10.5.012, 10.5.013, 10.5.016, 10.5.018,
10.5.030, 10.5.037, 10.5.038, 10.5.039, 10.5.040, 10.5.043
18. 10.6.001, 10.6.002, 10.6.007, 10.6.009, 10.6.010, 10.6.015, 10.6.026, 10.6.029, 10.6.033,
10.6.036, 10.6.045, 10.6.047a, 10.6.048, 10.6.051, 10.6.052, 10.6.053
19. 10.7.001, 10.7.003, 10.7.005, 10.7.007, 10.7.012, 10.7.014, 10.7.015, 10.7.019, 10.7.021,
10.7.024, 10.7.025, 10.7.033, 10.7.035, 10.7.042, 10.7.053
20. 11.1.001, 11.1.003, 11.1.007, 11.1.008, 11.1.010, 11.1.013, 11.1.014, 11.1.019, 11.1.020b,
11.1.027.SA, 11.1.049, 11.1.051, 11.1.054, 11.1.060, 11.1.061
21. 11.2.001, 11.2.007, 11.2.008, 11.2.010, 11.2.016, 11.2.017, 11.2.029, 11.2.032
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22. 11.3.004, 11.3.005a, 11.3.006, 11.3.008, 11.3.010, 11.3.011, 11.3.012, 11.3.013, 11.3.014,
11.3.015, 11.3.051, 11.3.053
23. 11.4.001, 11.4.003, 11.4.005, 11.4.006, 11.4.007, 11.4.008, 11.4.010, 11.4.014, 11.4.015,
11.4.017
24. 11.5.001, 11.5.003, 11.5.005, 11.5.007, 11.5.011, 11.5.013, 11.5.015, 11.5.019, 11.5.020,
11.5.021, 11.5.025, 11.5.032, 11.5.033, 11.5.036, 11.5.044.
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