COURSE OUTLINE (Fall 2006)

MAT 202 CALCULUS-II

 

Instructor: Simon Ugwuoke             Office Phone: 546-8543

Office Location:Graphics, Room 4      Email: sugwuoke@shawu.edu

Office Hours: TBA

 

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

Copyright  © 2005 by Thompson Learning, Inc.

Use of Technology: TI-92 Graphing Calculator; PcCalculator; Maples

 

GENERAL 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.

COURSE OBJECTIVES

.After completing this course, the students should be able to do the following:
bulletIntegrate logarithmic and exponential functions and solve problems in population growth, compound interest, and other applications.
bulletIntegrate functions of the form eax cos bx using the polar representation of complex numbers.
bulletFind inverse functions (including trigonometric functions) and integrate them.
bulletEvaluate limits of functions using L'Hospitale'.s rule.
bulletFind areas of regions bounded by curves.
bulletFind the volumes of solids of revolution, find the volumes by shell or disc method.
bulletFind lengths of segments of curves, work done by a given force.
bulletEvaluate integrals using substitution, integration by parts formula., partial fractions, and other techniques.
bulletFind if some improper integrals exist and evaluate them.
bulletFind if a. sequence converges or diverges and evaluate the limit of a. convergent sequence. Use different tests to find if an infinite series converges or not.
bulletFind the sum of a convergent series.
bulletKnow the relationship between absolute and ordinary convergences.
bulletDetermine if a power series converges or not and find the radius of convergence.
bulletUse Taylor or McLaurin series to find the power series expansions of certain functions.

 

Topic Outline

Chapter 5: INTEGRALS

5.1 Areas and Distances (p.343)

5.2 The Definite Integral (p.354)

5.3 Evaluating Definite Integrals

5.4  The Fundamental Theorem of Calculus

5.5 The Substitution Rule (p.386)

5.6 Integration by Parts (p.393)

5.7  Additional Techniques of Integration

5.8  Integration Using Tables (p.405)

5.8contd. Integration Using Technology

(Graphing Calculator, PcCalculator, Maples)

5.9 Approximate Integration (p.412)

5.10 Improper Integrals (p.423)

 

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)

 

Alignment with NCDPI Standards

NCDPI 3.4, 3.4 – 3.6, 5.1 – 5.4, 5.12, 5.12 – 5.18

 

GRADING

Attendance         10% of the final grade

Quiz/Homework      20% of the final grade

Tests              40% of the final grade

Final Exam         30% of the :final grade

 

ATTENDANCE POLICY

More than 4 unexcused absences will result in an "F" in the course. You are responsible for the classes you missed and for the information passed out 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 behavior, 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. Students will turn off telephones 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.