Course Title:
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Course Materials:
Anton, H., Bivens, I, & Davis, S. (2005). Calculus (8th ed.). New York: John Wiley & Sons, Inc.
Scientific Calculator required.
An equation editor - DE required. | |
Course Description:
| MATH 130 Calculus A (3) Prerequisite: MATH 108, MATH 115, or an appropriate result on the placement test. An introduction to calculus. Topics include functions, continuity, derivatives, and applications of derivatives including maximum-minimum problems, related rates and graphs of functions. Students may receive credit for only one of the following courses: MATH 130, MATH 140, or MATH 220. | |
Course Goals/Objectives:
Upon successful completion of this course, minimal objectives the student has achieved include the following:
* Compute limits, both numerically and algebraically.
* Use limits to compute asymptotes, determine continuity at a point, and define derivatives and tangents to curves.
* Use Newton's method to numerically approximate the roots of polynomials.
* Compute derivatives of algebraic and trigonometric functions.
* Calculate velocity and acceleration in linear motion.
* Determine the equations of the tangent line and the normal to a curve .
* Use derivatives to interpret/sketch the graph of a function.
* Solve related rates and optimization problems.
* Compute differentials. | |
Course Introduction:
| This is a course in differential calculus. It covers functions, continuity, limits, derivatives, implicit differentiation, and applications of the derivative including maxima, minima, curve sketching, optimization and related rates problems. MATH130 is the first of a three course sequence (Math 130-131-132) in calculus. Historically, differential calculus, which deals with motion and change, was invented by Newton and Leibniz to be used as a tool primarily in physics. Today is used in many other areas, such as economics, business, biology, linguistics, medicine, and even psychology. This is a rigorous mathematics course. Emphasis will be placed both on the theory and on the applied and practical aspect of the subject matter. Problem solving will be stressed. | |
Grading Information and Criteria:
There will be three 75-minute exams each worth 15% of the final grade and a comprehensive final exam that is worth 40% of the final grade. The remaining 15% of the final course grade will be comprised of optional projects, quizzes, or homework assignments.
Assessment Item
Points
% of Final Grade
Exam 1
15 points
15
Exam 2
15 points
15
Exam 3
15 points
15
Projects/Quizzes/Homework Assignments
15 points
15
Final Exam
40 points
40
Grades will be determined by the number of points you have earned as follows:
Grade/Points
A = 90-100
B = 80-89.9
C = 70-79.9
D = 60-69.9
F = <60
NOTE: Faculty may edit this model. Participation as a component is advisable for online classes and may be incorporated in f2f classes. If the faculty wishes to incorporate participation as part of the course grade, then the above percentages will change. Assignment of projects is optional. | |
Other Information:
* Study time (including reading and exercises) can be expected to be 2 to 3 times the amount of lecture time. That is, for every hour in class expect to spend 2 to 3 hours out of class studying.
* Students who fall behind or fail to attempt the exercises could well find themselves in difficulty. Try to incorporate the skills and methods learned in this course in everyday life. It is the best way to learn.
* Attendance: It will be to the student's advantage to attend all classes. When absence is unavoidable, it is a student's own responsibility to makeup any work missed before the next class session. For administrative purposes, attendance will be recorded. Students expecting or experiencing long absences during the term should contact the faculty.
* Class Discussions: Students are encouraged (indeed, expected) to participate. Ask questions.
* Homework assignments will be given for each class session. You are responsible for solving all problems assigned. Completing all the homework problems should help you prepare for the exams. If there are any problems that you found difficult or were unable to solve, be prepared to ask questions concerning those problems. Mastery of math depends on practice, practice, practice!
* In addition to the textbook, you will need a scientific calculator and may need graph paper with grid size large enough to see without the aid of a magnifying glass. A straight edge and a few different colored pencils or pens may also be useful.
* Please do not tape record class sessions.
* Please turn off telephones before class. | |
Project Descriptions:
| If the faculty member incorporates projects as part of the course grade, the problems comprising the projects might come from the textbook or the faculty member might create projects based upon current events or items that are useful and of interest to the class. | |
Academic Policies:
Cases of plagiarism are handled consistent with current UMUC guidelines.
See the UMUC policies at the following URL:
http://www.umuc.edu/policy/ | |
Course Schedule:
Tentative Schedule; may be modified by instructor as circumstances deem necessary. All readings and assignments are from Calculus, 7th Edition by Anton, Bivens, Davis. Please read the sections to be covered prior to the class meeting. Homework assignments will be comprised of the odd numbered problems in each section unless specified otherwise during the class meetings.
Class Sections, Meeting, Covered Topics, and Exams
1 1.1-1.6 Functions, Lines
2 1.7-2.1 Mathematical Models, Parametric Equations, Limits
3 2.2-2.4 Limits
4 2.5-3.1 Continuity, Slopes and Rates of Change
5 3.2 Exam I, The Derivative
6 3.3, 3.4 Techniques of Differentiation, Derivatives of Trigonometric Functions
7 3.5, 3.6 Chain Rule, Implicit Differentiation
8 3.6-3.7 Implicit Differentiation, Related Rates
9 3.8 Exam II, Local Linear Approximation, Differentials,
10 4.1, 4.2 Analysis of Functions, First and Second Derivative Tests
11 4.3, 4.4 Analysis of Functions, Rectilinear Motion
12 4.5, 4.6 Absolute Maxima and Minima, Applied Problems
13 4.7 Exam III, Applied Problems, Newton's Method
14 4.8 Rolle's Theorem, Mean-value Theorem
15 Review
16 Final Exam
NOTE: Exam I covers 1.1-2.6
Exam II covers 3.1- 3.7
Exam III covers 3.8, 4.1-4.6
Final Exam is comprehensive | |
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