# MAT 193 Calculus II

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### Course Description

Differentiation and integration of transcendental functions. Techniques and applications of integration. Polar coordinates. Infinite sequences and series, power series, convergence.

Note: Differentiation of transcendental functions is now covered in MAT 191, so it's not necessary to cover this topic in MAT 193.

Satisfies the General Education Quantitative Reasoning Requirement.

5 units credit.

### Prerequisite

MAT 191 or equivalent with a grade of "C" or better.

### Text

Essential Calculus, by James Stewart, Brooks/Cole 2007. (Covers MAT 191, MAT 193, and MAT 211.)

### Course Requirements, Tentative Schedule of Class Meetings and Topics, Readings, Assignments and Due dates, Exams

MAT 193 covers Chapters 6-9 from the text.

• 6. TECHNIQUES OF INTEGRATION
• Integration by Parts
• Trigonometric Integrals and Substitutions
• Partial Fractions
• Integration with Tables and Computer Algebra Systems
• Approximate Integration
• Improper Integrals
• 7. APPLICATIONS OF INTEGRATION
• Areas between Curves
• Volumes
• Volumes by Cylindrical Shells
• Arc Length
• Applications to Physics and Engineering
• Differential Equations
• 8. SERIES
• Sequences
• Series
• The Integral and Comparison Tests
• Other Convergence Tests
• Power Series
• Representing Functions as Power Series
• Taylor and Maclaurin Series
• Applications of Taylor Polynomials
• 9. PARAMETRIC EQUATIONS AND POLAR COORDINATES
• Parametric Curves
• Calculus with Parametric Curves
• Polar Coordinates
• Areas and Lengths in Polar Coordinates
• Conic Sections in Polar Coordinates

A schedule of class meetings, topics, assignments, due dates, exam dates, etc. will be provided by instructor. See your class syllabus.

The final exam is given at the date and time announced in the Schedule of Classes.

### Learning Objectives

After completing MAT 193 the student will

• Use more advanced techniques of integration such as integration by parts or integration by trigonometric substitution to evaluate common integrals without the use of tables.
• Apply theory of integration in finding volumes of solids, arc length, work, moments, centers of gravity and average values of functions.
• Attain good working skills, with the aid of graphing calculators, in obtaining approximate values of definite integrals.
• Use and demonatrate understanding of polar coordinates.
• Test for convergence or divergence of sequence and series, find interval of convergence for power series and represent functions as Taylor series.

### Computers and Calculators, Computer Literacy

Most instructors encourage the use of machines, calculators computers, phones etc., for analyzing data. The use of machines may be restricted during examinations or at certain other times. Ask your instructor for the policy in your class.

Students are not expected to be programmers or to know any particular computer language before starting this class. Some instructors may expect students to be able to access information on the internet, or to use calculators, or to learn to use particular software with instruction. Basic skill in algebra and the use of mathematical symbols, order of operations etc., and the willingness to read and follow instruction manuals and help files will suffice.

Students' grades are based on homework, class participation, short tests, and scheduled examinations covering students' understanding of the topics covered in this course. The instructor determines the relative weights of these factors and the grading scale. See the syllabus for your particular class.

### Location of Class Meetings

Classes meet on the dates and room announced in the official Schedule of Classes. This is a traditional, face-to-face class.

### Attendance Requirements

Attendance policy is set by the instructor.

### Policy on Due Dates, Make-Up Work, Missed Exams, and Extra-Credit Assignments

Due dates and policy regarding make-up work and missed exams are set by the instructor. Instructors may, or may not, choose to offer extra credit assignments. If extra credit assignments are offered they will be available to all students.

The mathematics department does not tolerate cheating. Students who have questions or concerns about academic integrity should ask their professors or the counselors in the Student Development Office, or refer to the University Catalog for more information. (Look in the index under "academic integrity".)

### Accomodations for Students with Disabilities

Cal State Dominguez Hills adheres to all applicable federal, state, and local laws, regulations, and guidelines with respect to providing reasonable accommodations for students with temporary and permanent disabilities. If you have a disability that may adversely affect your work in this class, I encourage you to register with Disabled Student Services (DSS) and to talk with me about how we best can help you. All disclosures of disabilities will be kept strictly confidential. Please note: you must register with DSS to arrange an no accommodation. For information call (310) 243-3660 or send an email message to dss@csudh.edu or visit the DSS website http://www4.csudh.edu/dss/contact-us/index or visit their office WH D-180

### Behavioral Expectations

We all are adults so behavior rarely is an issue. Just follow the Golden Rule: "do unto others as you would have them do unto you" then everything will be fine.

The university must maintain a classroom environment that is suitable for learning, so anyone who insists on disrupting that environment will be expelled from the class.

Revision history:

Prepared 3/9/00 (C. Chang). Revised 7/7/01, 7/13/03, 7/25/06 (G. Jennings), 1/20/07 (S. Raianu).