# MAT 191 Calculus I

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

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### Course Description

Limits, continuity, derivatives, differentiation formulas, applications of derivatives, introduction to integration, fundamental theorem of calculus, inverse functions.

MAT 191 satisfies the General Education Quantitative Reasoning Requirement.

5 units credit.

### Prerequisite

MAT 153 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 191 covers the following topics from chapters 1-5 in the text.

• 1. FUNCTIONS AND LIMITS
• Functions and Their Representations
• A Catalog of Essential Functions
• The Limit of a Function
• Calculating Limits
• Continuity.
• Limits Involving Infinity
• 2. DERIVATIVES
• Derivatives and Rates of Change
• The Derivative as a Function
• Basic Differentiation Formulas
• The Product and Quotient Rules
• The Chain Rule
• Implicit Differentiation
• Related Rates
• Linear Approximations and Differentials
• 3. APPLICATIONS OF DIFFERENTIATION
• Maximum and Minimum Values
• The Mean Value Theorem
• Derivatives and the Shape of Graphs
• Curve Sketching
• Optimization Problems
• Newton's Method
• Antiderivatives
• 4. INTEGRALS
• Areas and Distances
• The Definite Integral
• Evaluating Definite Integrals
• The Fundamental Theorem of Calculus
• The Substitution Rule
• 5. INVERSE FUNCTIONS
• The Natural Logarithmic Function
• The Natural Exponential Function<
• General Logarithmic ad Exponential Functions<
• Exponential Growth and Decay
• Inverse Trigonometric Functions
• Hyperbolic Functions
• Indeterminate Forms and l'Hospital Rule

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 191 the student will

• Demonstrate understanding of the four basic concepts of one-variable calculus; the limit, the concept of continuity, the derivative and the integral of a function of one variable
• Use the rules of differentiation to compute derivatives of algebraic and trigonometric functions
• Use derivatives to solve problems involving rates of change, tangent lines, velocity (speed), acceleration, optimization, and related rates.
• Investigate the graph of a function with the aid of its first and second derivatives: asymptotes, continuity, tangency, monotonicity, concavity, extrema, inflection points, etc.
• Demonstrate understanding of the meanings of the indefinite integral and the definite integral of a function of one variable, and their relationship to the derivative of a function via the Fundamental Theorem of Calculus
• Use rules of integration including the Substitution Rule to evaluate indefinite and definite integrals
• Differentiate Exponential, Logarithmic, and Inverse Trigonometric Functions
• Use l'Hospital's Rule

### 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.

### Grading Policy, Grading Scale, Weighted Value of Assignments and Tests

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 1/2/01, 7/7/01, 7/13/03, 7/25/06 (G. Jennings), 8/11/06 (S. Raianu).