# MATH 1910 Syllabus

# Course Syllabus

## MATH 1910 - Calculus I

### 4 Credit Hours

Course Information

This course is a study of differential calculus with an introduction to integration.

The topics studied in this course include:

- plane analytical geometry
- limits
- continuity
- the derivative and integral of functions of one variable with applications

Goals:

- to understand and apply the concepts of continuity and limit of a function both intuitively and precisely, by use of their definitions;
- to understand and apply the definition and methods of differentiation of algebraic functions;
- to use the derivative in sketching the graphs of algebraic functions and relations;
- to apply the derivative to specific modeling problems involving, for example, motion,
- optimization, and related rates;
- to understand and apply the Fundamental Theorem of Calculus;
- to understand and apply the concept of integration, show its application to
- area under curves, and practice basic integration techniques;
- to fulfill the mathematics requirement for those students required to take only MATH 1910 as
- well as to prepare those students who are required to take MATH 1920; and,
- to promote better understanding of concepts introduced throughout the course by the
- appropriate use technology.

Objectives:

- examine and determine by tables and graphs whether or not the limit of a function exists at a given value of x and if so, find that limit;
- apply the formal e, definition of a limit;
- discuss general properties of the limits of algebraic functions; examine techniques and
- strategies such as substitution, graphing, cancellation, and rationalizing for evaluating limits;
- indicate whether a given function is continuous or discontinuous at a given value of x or on an
- interval containing x and examine removable and non-removable discontinuities;
- evaluate one-sided limits and discuss their relationship to the ideas of continuity;
- graph and investigate the greatest integer function and compound functions in relation to limits and continuity;
- evaluate infinite limits by graphic and algebraic processes and discuss their relationship to vertical and slant asymptotes;
- find the slope of a curve at point A by use of the slope of a secant line through A and another point on the curve near A;
- find the derivative of a function by use of the definition and discuss the relationship between differentiability and continuity;
- write the equation of the line tangent to a given curve at a given point;
- differentiate functions using basic rules and apply to simple motion problems;
- differentiate algebraic using product, quotient, chain and general power rules and evaluate at given values of x;
- find the derivative of a function using implicit differentiation;
- find the higher order derivatives of functions by both explicit and implicit differentiation and apply to equations of motion;
- apply differentiation processes to related rates problems;
- find critical numbers and locate extrema of a function on an interval, including endpoints;
- state Rolle's Theorem and the Mean Value Theorem and apply for given functions;
- determine intervals over which a curve is increasing or decreasing and determine relative maximum and minimum values of given functions by use of the first derivative;
- determine intervals of concavity, find points of inflection, and test for maxima and minima by use of the second derivative;
- evaluate limits at infinity graphically and algebraically and discuss their horizontal asymptotes;
- sketch the graphs of given functions by use of intercepts, asymptotes, symmetry, and information obtained by use of the first and second derivatives;
- apply derivatives to solve optimization problems;
- use Newton's method to find zeros of functions;
- understand and find differentials of functions and apply to determining error;
- define anti-differentiation and find the anti-derivative of given polynomial, power, and rational functions;
- use anti-derivatives to find the equation of motion when given acceleration or velocity of a particle at a given time;
- perform operations with sigma notation and use it to find the area under the graphs of certain polynomial functions by using rectangular subdivisions;
- study properties of the definite and indefinite integral;
- study the Fundamental Theorem of Calculus and use to evaluate definite integrals of polynomial and other algebraic relations and transcendental functions, and apply to finding the area under curves; and,
- evaluate indefinite and definite integrals of algebraic expressions by using substitution procedures and the general power rule for integration.

MATH 1710 and MATH 1720.

- Functions and Models
- Limits and Rates of Change
- Derivatives
- Applications of Derivation
- Integrals
- Applications of Integration

Students will be required to learn and use a graphing calculator, install free browser plug-ins, and install and use free downloadable mathematics software.

Textbooks, Supplementary Materials, Hardware and Software Requirements

Please visit the Virtual Bookstore to obtain textbook information for this course. Move your cursor over the "Books" link in the navigation bar and select "Textbooks & Course Materials." Select your Program, Term, Department, and Course; then select "Submit."

A graphing calculator is highly recommended. The Texas Instruments TI-83, TI-83 Plus, and/or TI-89 will be used in demonstrations. Other graphing calculators may work but will not be supported by the instructor.

Minimum hardware requirements can be found here.

Minimum software requirements can be found here.

**Common applications you might need:**

- To read a PDF file download the latest version of Adobe Reader here
- Don't have Microsoft Word? Explore an alternative OpenOffice here
- Accessing a PowerPoint file? Download the PowerPoint Viewer here

Purdue OWL Online Writing Lab (for APA, MLA, or Chicago style)

The Writing Center Online Writer's Handbook

- Technical support information can be found on the TN eCampus Help Desk page.
- Smarthinking virtual tutoring is available
**FREE**of charge. to access Smarthinking, visit the course homepage and select Smarthinking under Course Resources. You also view sample sessions to see what Smarthinking offers and how it works. - Information on other student issues or concerns can be located on the TN eCampus Student Resources page.

Instructor Information

Please see "Instructor Information" in the Getting Started Module for instructor contact information, virtual office hours, and other communication information. You can expect to receive a response from the instructor within 24-48 hours unless notified of extenuating circumstances.

Participation, Assessments, & Grading

Four chapter tests (timed, open book) will be given online. A comprehensive final exam will be given online.

There will be 8 quizzes administered throughout the semester. These small quizzes, in most cases, may be attempted three to ensure mastery. The quiz average will count 10% of the final average. Homework problems (usually selected odd problems) will be assigned and worked through webassign.net. The homework grade will count 5% toward the semester average. Each chapter test will count 15% points and the final exam will be 25%.

The assigned weights to calculate the semester average:

Chapter 1 Test 15%, Chapter 2 Test 15%, Chapter 3 Test 15%, Chapter 4 Test 15%, Quizzes (average of eight quizzes taken where the highest attempt will be the final individual score of each quiz) 10%, Final Exam (comprehensive and new material) 25%, Homework (through webassign) 5%. All quizzes, homework, tests and final exam will be given through webassign.net.

90-100 | A |

80-89 | B |

70-79 | C |

60-69 | D |

0-59 | F |

Homework will be assigned for each textbook section. These problems will usually consist of selected odd-numbered problems.

Students are encouraged to participate in this class. Students are encouraged to have organized discussion for assigned homework problems.

Quizzes, homework assignments, tests, and the final exam will all have specific deadlines. These graded activities must be completed by the due date and time. Make-up work will be accepted only under documented extreme circumstances.

Course Ground Rules

*The following two statements (1., 2.) were derived from the TBR System-wide Student Rules document, released January 2012: *

RULES OF THE TENNESSEE BOARD OF REGENTS STATE UNIVERSITY AND COMMUNITY COLLEGE SYSTEM OF TENNESSEE SYSTEMWIDE STUDENT RULES CHAPTER 0240-02-03 STUDENT CONDUCT AND DISCIPLINARY SANCTIONS

**Read the document in its entirety here.**

**1. Standards of Conduct:**

- Students are required to adhere to the same professional, legal and ethical standards of conduct online as on campus. In addition, students should conform to generally accepted standards of "netiquette" while sending e-mail, posting comments to the discussion board, and while participating in other means of communicating online. Specifically, students should refrain from inappropriate and/or offensive language, comments and actions.

**2. Review the TN eCampus Academic Integrity/Academic Honesty Policy:**

- In their academic activities, students are expected to maintain high standards of honesty and integrity. Academic dishonesty is prohibited.

Such conduct includes, but is not limited to:

- an attempt by one or more students to use unauthorized information in the taking of an exam
- to submit as one's own work, themes, reports, drawings, laboratory notes, computer programs, or other products prepared by another person,
- or to knowingly assist another student in obtaining or using unauthorized materials.

Plagiarism, cheating, and other forms of academic dishonesty are prohibited.

Students guilty of academic misconduct, either directly or indirectly through participation or assistance, are subject to disciplinary action through the regular procedures of the student’s home institution. Refer to the student handbook provided by your home institution to review the student conduct policy.

In addition to other possible disciplinary sanctions that may be imposed, the instructor has the authority to assign an "F" or zero for an activity or to assign an "F" for the course.

**Other Course Rules:**

Students are expected to:

- Participate in all aspects of the course
- Communicate with other students
- Learn how to navigate in Brightspace
- Keep abreast of course announcements
- Use the assigned course management (Brightspace) email address rather than a personal email address
- Address technical problems immediately:
- Observe course netiquette at all times.

Guidelines for Communications

**Email:**

- Always include a subject line.
- Remember without facial expressions some comments may be taken the wrong way. Be careful in wording your emails. Use of emoticons might be helpful in some cases.
- Use standard fonts.
- Do not send large attachments without permission.
- Special formatting such as centering, audio messages, tables, html, etc. should be avoided unless necessary to complete an assignment or other communication.
- Respect the privacy of other class members

**Discussions:**

- Review the discussion threads thoroughly before entering the discussion. Be a lurker then a discussant.
- Try to maintain threads by using the "Reply" button rather starting a new topic.
- Do not make insulting or inflammatory statements to other members of the discussion group. Be respectful of other’s ideas.
- Be patient and read the comments of other group members thoroughly before entering your remarks.
- Be cooperative with group leaders in completing assigned tasks.
- Be positive and constructive in group discussions.
- Respond in a thoughtful and timely manner.

Library

The Tennessee Virtual Library is available to all students enrolled in TN eCampus programs and courses. Links to library materials (such as electronic journals, databases, interlibrary loans, digital reserves, dictionaries, encyclopedias, maps, and librarian support) and Internet resources needed by learners to complete online assignments and as background reading will be included within the course modules. To access the Virtual Library, go to the course homepage and select the * Virtual Library* link under Course Resources.

Students with Disabilities

Qualified students with disabilities will be provided reasonable and necessary academic accommodations if determined eligible by the appropriate disability services staff at their home institution. Prior to granting disability accommodations in this course, the instructor must receive written verification of a student's eligibility for specific accommodations from the disability services staff at the home institution. It is the student's responsibility to initiate contact with their home institution's disability services staff and to follow the established procedures for having the accommodation notice sent to the instructor.

Syllabus Changes

The instructor reserves the right to make changes as necessary to this syllabus. If changes are necessitated during the term of the course, the instructor will immediately notify students of such changes both by individual email communication and posting both notification and nature of change(s) on the course bulletin board.

Disclaimer

The information contained in this syllabus is for general information purposes only. While we endeavor to keep this information up-to-date and accurate, there may be some discrepancies between this syllabus and the one found in your online course. The syllabus of record is the one found in your online course. Please make sure you read the syllabus in your course at the beginning of the semester. Questions regarding course content should be directed to your instructor.