SHAW UNIVERSITY

College of Arts and Sciences

Department of Natural Sciences and Mathematics

MAT202 (4 credit hours)  SPR. 2010  (PRE: MAT 201)

 

Calculus II

___________________________________________________________________________________________________________________

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)

 

1.1 Students will be able to draw the graphs of various functions, find their derivatives, integrals, identify some properties of functions, find the maximum and minimum values of functions using algebraic and calculus techniques. They will also be able to use numerical techniques to find definite integrals of functions and apply all these techniques to solve application problems.

1.2 Students will be able to represent a given data in diagrams, find various measures of central tendencies, dispersions, correlation between variables, and other statistical parameters. They will also be able to find probabilities of certain simple and compound events using various techniques of probability using probability distributions. Students will also be able to apply these techniques to solve application problems.

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.

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.

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.

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;

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.

 

Conceptual Framework Theme

 

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)

 

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

Apply integration in solving Physics and Engineering problems, problems in Economics and Biology, Probability problems, etc.

Exams, Quizzes, Homework, & Comprehensive Final Exam

# 2.2

Solve problems in population growth, exponential growth and decay, compound interest, and other applications.

Exams, Quizzes, Homework, & Comprehensive Final Exam

# 2.2

Find areas of regions bounded by curves.

Exams, Quizzes, Homework, & Comprehensive Final Exam

# 2.2

Find the volumes of solids of revolution, find the volumes by shell or disc method.

Exams, Quizzes, Homework, & Comprehensive Final Exam

# 2.2

Find lengths of segments of curves, work done by a given force.

Exams, Quizzes, Homework, & Comprehensive Final Exam

# 2.2

Solve differential equation problems by separation of variables and by Euler method

Exams, Quizzes, Homework, & Comprehensive Final Exam

# 1.3

Find if a sequence converges or diverges and evaluate the limit of a convergent sequence.

Exams, Quizzes, Homework, & Comprehensive Final Exam

# 2.2

Use different tests to find if an infinite series converges or not.

Exams, Quizzes, Homework, & Comprehensive Final Exam

#2.2

Obtain a binomial series expansion of certain functions

Exams, Quizzes, Homework, & Comprehensive Final Exam

# 1.1, 2.2

Represent functions as power series

Exams, Quizzes, Homework, & Comprehensive Final Exam

# 1.1, 2.2

Find the sum of a convergent series.

Exams, Quizzes, Homework, & Comprehensive Final Exam

# 2.2

Know the relationship between absolute and ordinary convergences.

Exams, Quizzes, Homework, & Comprehensive Final Exam

# 2.2

Determine if a power series converges or not and find the radius of convergence.

Exams, Quizzes, Homework, & Comprehensive Final Exam

# 1.1, 2.2

Use Taylor or McLaurin series to find the power series expansions of certain functions.

Exams, Quizzes, Homework, & Comprehensive Final Exam

# 1.1, 2.2

Successfully perform operations on vectors using the three-dimensional  coordinate system

Exams, Quizzes, Homework, & Comprehensive Final Exam

# 2.2

Find the dot and cross products of vectors

Exams, Quizzes, Homework, & Comprehensive Final Exam

# 2.2

Solve problems involving equations of lines and planes

 

Exams, Quizzes, Homework, & Comprehensive Final Exam

 

# 2.2

Demonstrate an understanding of functions of two and three variables in representing surfaces

Exams, Quizzes, Homework, & Comprehensive Final Exam

# 1.1, 2.2

Solve problems involving cyindrical and spherical coordinates

Exams, Quizzes, Homework, & Comprehensive Final Exam

# 2.2

Find derivatives and ntegrals of vector functions

Exams, Quizzes, Homework, & Comprehensive Final Exam

# 2.2

Represent space curves using vector functions

Exams, Quizzes, Homework, & Comprehensive Final Exam

# 2.2

Find the arc length and curvature of vector functions

Exams, Quizzes, Homework, & Comprehensive Final Exam

# 2.2

Find the velocity and acceleration of an object moving in space

Exams, Quizzes, Homework, & Comprehensive Final Exam

# 2.2

Demonstrate an understanding of the concept of parametric surfaces

Exams, Quizzes, Homework, & Comprehensive Final Exam

# 2.2

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:

 

Text: CALCULUS, Concepts & Texts 3E; James Stewart,

 Copyright  © 2005 by Thompson Learning, Inc.

 

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

·         Feb.03            Wednesday   Academic Major’s Fair

·            07-10          Sun. – Mon. Religious Emphasis Week

·            16             Tuesday     Spring Assessment Day

·         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

·            26             Friday      Last Day to Withdraw from a Course (with a “W”)

·         Apr.2-11          Fri.-Sun.   Easter and Spring Break (Academic Only)

·            12             Monday      Classes Resume

·            22             Thursday    University Awards Day (11:00 AM)

·            28-30          Wed.-Fri.   Final Exams for Graduating Seniors

·            29             Thursday    Last day of Classes (Formal classes end)

·            30             Friday      Reading only

·         May 3             Wednesday   Grades due for Graduating Seniors

·            03-06          Mon–Thurs.  Final Exams

·            07             Friday      Spring Semester ends for Students

·            11             Tuesday     All Grades Due at 5:00 PM

·            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

 

Course Evaluation:

 

Testing Instrumrnt/Activity

Percentage of Final Course Grade

Quizzes, Homework, Projects,  Attendance, & Participation

30 %

Tests

40 %

Comprehensive Final Examination

30 %

Total

100 %

 

Grading Scale:

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.

 

90 - 100

A

80 - 89

B

70 - 79

C

60 - 69

D

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.