HomeMy WebLinkAboutMAT-280BERGEN COMMUNITY COLLEGE
DIVISION OF MATHEMATICS, SCIENCE AND TECHNOLOGY
DEPARTMENT OF MATHEMATICS
COURSE SYLLABUS
MAT-280 CALCULUS I
COURSE Calculus I is a study of limits, continuity, the derivative of a function,
DESCRIPTION: differentiation of algebraic, trigonometric, inverse trigonometric,
exponential and logarithmic functions, applications of the derivative,
antidifferentiation, area under a curve, the definite integral, the Fundamental
Theorem of the Calculus and its applications.
CREDITS/HOURS: 4 credits, 4 hours
PREREQUISITE: MAT-180 with a grade of C or better or by proficiency examination.
GENERAL EDUCAION
COURSE: Yes
STUDENT Upon successful completion of this course, the student will be able to:
LEARNING
OBJECTIVES: 1. Evaluate and interpret limits.
2. Recognize and interpret continuous functions.
3. Demonstrate the ability to analyze and solve problems involving rates of change by
applying the derivative.
4. Solve related rates and optimization problems using calculus techniques.
5. Sketch curves using techniques of calculus.
6. Use differentials in the solution of applied problems.
7. Evaluate definite and indefinite integrals using basic formulas and substitution
method.
8. Find the area between two curves.
ASSESSMENT Each of the above listed student learning objectives will be assessed by:
MEASURES: 1. Written assignments and/or quizzes
2. Written examinations
3. Other, as announced by the instructor.
COURSE GRADE: Students should refer to the instructor’s grading policy which will be distributed during
the first meeting of the class.
TEXTBOOKS: Calculus, Early Transcendentals Functions, with CalcChat® and CalcView®,
7th Edition, Larson/Edwards, Cengage Learning Publisher.
COURSE CONTENT:
TOPIC CHAPTER SECTIONS
1. Brief Review of Precalculus 1 1 – 3, 5, 6
a. Graphs and Models
b. Linear Models and Rates of Change
c. Functions and Their Graphs
d. Inverse Functions including Inverse Trigonometric
functions
e. Exponential and Logarithmic functions
2. Limits and their Properties 2 1 - 5
a. A Preview of Calculus
b. Finding Limits Graphically and Numerically
c. Evaluating Limits Analytically
d. Continuity and One-sided Limits
e. Infinite limits
3. Differentiation 3 1 - 6
a. The Derivative and the Tangent Line Problem
b. Basic Differentiation Rules and Rates of Change
c. Product and Quotient Rules and Higher-order Derivatives
d. The Chain Rule
e. Implicit differentiation
f. Derivative of Inverse Functions
4. Applications of Differentiation 3 7
4 1 - 8
a. Related Rates
b. Extrema on an Interval
c. Rolle’s Theorem and the Mean Value Theorem
d. Increasing and Decreasing Functions and The First Derivative Test
e. Concavity and The Second Derivative Test
f. Limits at Infinity
g. A Summary of Curve sketching
h. Optimization problems
i. Differentials
5. Integration 5 1 – 5, 7
a. Anti-derivatives and indefinite integration
b. Area under a curve
c. Riemann sums and definite integrals
d. The Fundamental Theorem of Calculus
e. Integration by substitution
f. Area of a region between two curves 7 1
REFERENCES: Calculus: Early Transcendentals, Stewart, Brooks/Calc.
Calculus: Early Transcendental Function, Smith and Minton, McGraw Hill
Calculus: Early Transcendentals, Thomas, Addison Wesley
3000 Solved Problems in Calculus, Shaum's Solved Problem Series,
McGraw-Hill Pub.
ELECTRONIC The Department of Mathematics prohibits the use of cell-phones,
DEVICES: PDA’s, laptops, headphones, IPODs and other such devices in mathematics
classes unless otherwise specified in the grading policy provided by the
instructor at the beginning of the semester.
FACULTY CLASS CANCELLATIONS may be found at http://www.bergen.edu/classcancellations
ABSENCE A list is also posted in a glass case near A-129, the main corridor on the first floor and
PROCEDURE: in Ender Hall. If a cancelled class is not listed, it should be reported to the Mathematics
Department Office or the Adjunct Office (C-107).
WEBSITE: Go to http://www.bergen.edu/academics/academic-divisions-departments/mathematics
for more information regarding the Mathematics Department.
STUDENT Learning Assistance Center Room: L-125 879-7489
SUPPORT Math and Science Walk-In Room: L-131 879-7489
SERVICES: Office of Specialized Services Room: L-115 612-5269
fa’18