# MAT 193 Calculus II

This is a sample syllabus only. Ask your instructor for the official syllabus for your course.

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### Revised Course Description

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

MAT 193 meets for five hours of lecture per week.

### Prerequisites

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

### Objectives

After completing MAT 193 the student should be able to

• 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.
• Understand and use polar coordinates.
• Test for convergence or divergence of sequence and series, find interval of convergence for power series and represent functions as Taylor series.

### Expected outcomes

Students should be able to demonstrate through written assignments, tests, and/or oral presentations, that they have achieved the objectives of MAT 193.

### Method of Evaluating Outcomes

Evaluations are based on homework, class participation, short tests and scheduled examinations covering students' understanding of topics covered in MAT 193.

### Text

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

#### Course Outline

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

Students' grades are based on homework, class participation, short tests, and scheduled examinations covering students' understanding of the topics covered in MAT 193. The instructor determines the relative weights of these factors.

### Attendance Requirements

Attendance policy is set by the instructor.

### Policy on Due Dates and Make-Up Work

Due dates and policy regarding make-up work are set by the instructor.

### Schedule of Examinations

The instructor sets all test dates except the date of the final exam. The final exam is given at the date and time announced in the Schedule of Classes.