SHAW
UNIVERSITY
MAT202 (4 credit hours)
SPR. 2010 (PRE: MAT 201)
___________________________________________________________________________________________________________________
Instructor
Dr.Simon N.Ugwuoke
Office:
Robert Science Bldg
Email:
sugwuoke@shawu.edu
Research Wing, RM 122
Office
Hours:
TBA
Phone:(919)
546-8543(O); 612-6864(C)
Program Mission
The mission of the Mathematics
Program is to prepare students with the knowledge, skills, and competencies,
for employment in fields of work requiring quantitative and problem solving
skills, and also to pursue graduate studies in Pure and Applied Mathematics.
The mission is also to produce graduates who are equipped with analytical and
critical thinking skills to enable them to formulate problems, solve them, and
interpret their solutions, and communicate the solution.
Program Goals
The
primary goals of the Mathematics unit for this period are as follows:
1.
produce
graduates with the mathematical knowledge and competence with computational
and quantitative skills to succeed in the field of work requiring quantitative
and problem solving skills;
2.
produce
graduates with the knowledge and competencies that that get equip them for
graduate studies in Pure and Applied Mathematics and further research;
3.
To improve
the academic performance of students and increase retention.
Program Learning Outcomes (PLOs)
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1.3 Students
will be able to solve systems of linear equations, find the matrices
representing linear transformations, do matrix computations. They will
also be able to solve ordinary differential equations both algebraically
and numerically. Students will be able to apply these techniques to solve
application problems. |
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2.1 Students
will be able to understand the various techniques of proving theorems and
will be able to state and prove theorems using definitions and properties. |
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2.2 Students
will be able to use differentiation and integration techniques to solve
application problems in optimizing techniques for functions in Business,
Economics, Sociology etc, also find areas and volumes of planes and solids
using definite integrals, and multiple integrals. |
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2.3 Students
will be able to use Eigen values, Eigen vectors in solving and predicting
long range effects in other areas of study. Students will be able to
solve application problems using these techniques; |
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3.1 Periodic
meetings of all major students with all the math faculty will be arranged
to give an opportunity to students and faculty to communicate and exchange
ideas to provide the students with what their academic needs are and make
their learning experience more enjoyable. |
To produce graduates who are critical-thinking problem solvers with the
knowledge, pedagogical and technological skills, and professional dispositions
needed to function productively and effectively in a diverse world.
Course Description
This is the second Calculus course out
of a sequence of three. This course is intended for all Science, Math
Education and Business majors including Pre-Engineering students. The
pre-requisite is MAT-201-Calculus-I or equivalent. It deals with integration
of functions, sequences, infinite series, power series, conic sections,
different coordinate systems, and various applications of integration.
STUDENT LEARNING
OUTCOMES (SLO)
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After completing this course successfully,
the students should be able to do the following: |
Assessment of Student Learning Outcomes
(Assessment Tools) |
Program Learning Outcome link to the SLO |
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Apply integration in solving Physics and Engineering problems, problems in
Economics and Biology, Probability problems, etc. |
Exams, Quizzes,
Homework, & Comprehensive Final Exam |
# 2.2 |
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Exams, Quizzes,
Homework, & Comprehensive Final Exam |
# 2.2 |
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Find areas of regions bounded by curves. |
Exams, Quizzes,
Homework, & Comprehensive Final Exam |
# 2.2 |
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Find the volumes of solids of revolution, find the volumes by shell or
disc method. |
Exams, Quizzes,
Homework, & Comprehensive Final Exam |
# 2.2 |
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Find lengths of segments of curves, work done by a given force. |
Exams, Quizzes,
Homework, & Comprehensive Final Exam |
# 2.2 |
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Solve differential equation problems by separation of variables and by
Euler method |
Exams, Quizzes,
Homework, & Comprehensive Final Exam |
# 1.3 |
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Find if a sequence converges or diverges and evaluate the limit of a
convergent sequence. |
Exams, Quizzes,
Homework, & Comprehensive Final Exam |
# 2.2 |
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Use different tests to find if an infinite series converges or not. |
Exams, Quizzes,
Homework, & Comprehensive Final Exam |
#2.2 |
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Obtain a binomial series expansion of certain functions |
Exams, Quizzes, Homework, & Comprehensive
Final Exam |
# 1.1, 2.2 |
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Represent functions as power series |
Exams, Quizzes, Homework, & Comprehensive
Final Exam |
# 1.1, 2.2 |
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Find the sum of a convergent series. |
Exams, Quizzes,
Homework, & Comprehensive Final Exam |
# 2.2 |
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Know the relationship between absolute and ordinary convergences. |
Exams, Quizzes,
Homework, & Comprehensive Final Exam |
# 2.2 |
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Determine if a power series converges or not and find the radius of
convergence. |
Exams, Quizzes,
Homework, & Comprehensive Final Exam |
# 1.1, 2.2 |
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Use Taylor or McLaurin series to find the power series expansions of
certain functions. |
Exams, Quizzes,
Homework, & Comprehensive Final Exam |
# 1.1, 2.2 |
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Successfully perform operations on vectors using the three-dimensional
coordinate system |
Exams, Quizzes,
Homework, & Comprehensive Final Exam |
# 2.2 |
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Find the dot and cross products of vectors |
Exams, Quizzes,
Homework, & Comprehensive Final Exam |
# 2.2 |
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Solve problems involving equations of lines and planes |
Exams, Quizzes,
Homework, & Comprehensive Final Exam |
# 2.2 |
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Demonstrate an understanding of functions of two and three variables in
representing surfaces |
Exams, Quizzes,
Homework, & Comprehensive Final Exam |
# 1.1, 2.2 |
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Solve problems involving cyindrical and spherical coordinates |
Exams, Quizzes,
Homework, & Comprehensive Final Exam |
# 2.2 |
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Find derivatives and ntegrals of vector functions |
Exams, Quizzes,
Homework, & Comprehensive Final Exam |
# 2.2 |
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Represent space curves using vector functions |
Exams, Quizzes,
Homework, & Comprehensive Final Exam |
# 2.2 |
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Find the arc length and curvature of vector functions |
Exams, Quizzes,
Homework, & Comprehensive Final Exam |
# 2.2 |
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Find the velocity and acceleration of an object moving in space |
Exams, Quizzes,
Homework, & Comprehensive Final Exam |
# 2.2 |
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Demonstrate an understanding of the concept of parametric surfaces |
Exams, Quizzes,
Homework, & Comprehensive Final Exam |
# 2.2 |
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Use PcCalculator and/or TI-92 Graphing calculator and other technologies
as tools for solving problems or enhancing learning. |
Exams, Quizzes,
Homework, & Comprehensive Final Exam |
# 2.2 |
Required
Textbook & Technology Resources:
Technology: BLACKBOARD (Practice, Quizzes, and Assignments);
PcCalculator and Graphing Calculator
(TI-92 or TI-83/85)
Other Technology Resources:Internet Mathematics-related Links
Student Expectations
Individual
and Group Class Participation; Regular Class Attendance.
Important
Dates:
·
Jan14
Thursday First
Day of Classes
·
18
Monday
MLK’s Birthday, Legal Holiday
·
25
Monday
Last Day to Add/Drop Course
·
29
Friday
NR Reports Due
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Feb.03
Wednesday Academic
Major’s Fair
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07-10
Sun. – Mon. Religious Emphasis
Week
·
16
Tuesday
Spring Assessment Day
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Mar.8-10
Mon.-Wed. Mid-Sem.
Progress Report (Due 4:00 PM, Wed.)
·
12
Friday
Last Day to Withdraw from a Course with partial
refund
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26
Friday
Last Day to Withdraw from a Course (with a “W”)
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Apr.2-11
Fri.-Sun. Easter and
Spring Break (Academic Only)
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12
Monday
Classes Resume
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22
Thursday
University Awards Day (11:00 AM)
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28-30
Wed.-Fri. Final Exams
for Graduating Seniors
·
29
Thursday Last
day of Classes (Formal classes end)
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30
Friday
Reading only
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May 3
Wednesday Grades due
for Graduating Seniors
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03-06
Mon–Thurs. Final Exams
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07
Friday
Spring Semester ends for Students
·
11
Tuesday
All Grades Due at 5:00 PM
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12-14
Wed. – Fri. Dept. Assessment and
Planning
Topic
Outline:
Chapter 6:
Applications of Integration
6.1 More about Areas(p. 441)
6.2 Volumes (p.447)
6.3 Arc Length (p.461)
6.4 Average Value of a Function
6.5 Applications to Physics &
Engineering
6.6 Applications to Economics and
Biology
6.7
Probability (p.486)
Ch.6
Review(p.493)
Chapter 7:
Differential Equations
7.1
Modeling with Differential Equations (p.499)
7.2
Direction Fields and Euler’s Method (p.504)
7.3
Separable Equations (p.513)
7.4
Exponential Growth and Decay (p.524)
7.5 The
Logistic Equation (p.535)
7.6 The
Predator-Prey Systems (p.544)
Ch.7 Review
(p.551)
Chapter 8:
Infinite Sequences and Series
8.1
Sequences (p.557)
8.2 Series
(p.567)
8.3 The
integral and Comparison Tests; Estimating Sums (p.577)
8.4 Other
Convergence Tests (p.586)
8.5 Power
Series (p.594)
8.6
Representations of Functions as Power Series (p.599)
8.7 Taylor
and MacLaurin Series (p.605)
8.8 The
Binomial Series
8.9
Application of Taylor Series (p.621)
Ch.8 Review
(p.631)
Chapter 9:
Vectors and the Geometry of Space
9.1
Three-Dimensional Coordinate Systems
9.2 Vectors
(p.642) 9.3 The Dot Product
9.4 The
Cross Product
9.5
Equations of Lines and Planes
9.6
Functions and Surfaces
9.7
Cylindrical and Spherical Coordinates
Ch.9 Review
(p.690)
Chapter 10:
Vector Functions
10.1 Vector
Functions and Space Curves (p.695)
10.2
Derivatives and Integrals of Vector Functions (p.702)
10.3 Arc
Length and Curvature (p.708)
10.4 Motion
in Space: Velocity and Acceleration (p.716)
10.5
Parametric Surfaces (p.728)
Alignment with NCDPI Standards
NCDPI 3.4, 3.4 – 3.6, 5.1 – 5.4, 5.12, 5.12 – 5.18
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Testing
Instrumrnt/Activity |
Percentage of
Final Course Grade |
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Quizzes,
Homework, Projects,
Attendance, & Participation |
30 % |
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Tests |
40 % |
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Comprehensive
Final Examination |
30 % |
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Total |
100 % |
The
following grading scale will be used. However, grading on a pseudo-curve may
be used, depending on the general performance of students, and other
circumstances, in consideration of fairness, meaningfulness, and validity. In
general, no make-ups for tests and quizzes will be given, unless there is some
proof of extra-ordinary circumstances.
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90 - 100 |
A |
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80 - 89 |
B |
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70 - 79 |
C |
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60 - 69 |
D |
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59 or less |
F |
Attendance
Policy:
Students
who miss classes are responsible for subject matter covered, any announcements
made regarding quiz, test or any other relevant matter, during their absence.
More than 3 (if class meets 3 times a week ) or 2 (if class meets 2
times a week ) unexcused absences may result in failure in the course.
You are responsible to find out or know about any announcements or the
subject matter covered, during your absence.
Student
Classroom Decorum Expectations:
To enhance
the learning atmosphere of the classroom, students are expected to dress and
behave in a fashion conducive to learning in the classroom. More specifically,
students will refrain from disruptive classroom behaviors,
e.g. talking to classmates,
disrespectful responses to teacher instructions; swearing; wearing
clothes that impede academic learning, such as, but not limited to,
wearing body-revealing clothing and excessively baggy pants; hats/caps, and/or
headdress . No food or drinks will be allowed inside the classroom or lab.
Students will turn off their cell phones prior to entering the classroom.
Students
who exhibit the behaviors described above, or similar behaviors will be
immediately dismissed from class at the third documented offense. The student
will be readmitted to class only following a decision by the department chair.
The student may appeal the decision of the department chair to the Dean of the
College offering the course, and, subsequently, to the Office of the Vice
President for Academic Affairs, and then to the President of Shaw University.
The decision of the President will be final. Failure to follow the procedures
herein outlined will result in termination of the appeal, and revert to the
decision of the department chair.
Each
behavior construed by the teacher/professor as noncontributive to learning
will be recorded, properly documented, and appropriately reported to the
student and to the chair of the academic department offering the course. The
report will be in written form with a copy provided to both the student and
the department chair. The faculty member should retain a copy for his/her own
records.
Additional
student behavior codes may be found in Student Affairs.