```

MATH 140

COURSE DESCRIPTION:  (GQ) Calculus with Analytic Geometry I (4:4:0)
Derivatives, differentials, applications, integrals.  Students may
take only one course for credit from among MATH 110, 140, 140A and
140B.  During Spring and Fall semesters the course is offered in
60 fifty minute lectures, four per week; in the summer session it
is offered in 40 seventy-five minute lectures, five per week.

PREREQUISITES: MATH 022, 026; or MATH 040; or MATH 41; or
satisfactory performance on the mathematics (both algebra and
trigonometry) proficiency examination.

TOPICS

LIMITS AND RATES OF CHANGE
The Tangent and Velocity Problems
The Limit of a Function
Calculating Limits using the Limit Laws
The Precise Definition of a Limit
Continuity
Tangents, Velocities, and Other Rates of Change

THE DERIVATIVE
Derivatives
Differentiation Formulas
Rates of Change in the Natural and Social Sciences
Derivatives of Trigonometric Functions
The Chain Rule
Implicit Differentiation
Higher Derivatives
Related Rates
Newton's Method

THE MEAN VALUE THEOREM AND CURVE SKETCHING
Maximum and Minimum Values
The Mean Value Theorem
Monotonic Functions and the First Derivative Test
Concavity and Points of Inflection
Limits at Infinity: Horizontal Asymptotes
Curve Sketching
Graphing with Calculus and Calculators
Applied Maximum and Minimum Problems
Applications to Economics
Antiderivatives

INTEGRALS
Sigma Notation
Area
The Definite Integral
The Fundamental Theorem of Calculus
The Substitution Rule

APPLICATIONS OF INTEGRATION
Areas between Curves
Volume
Volumes by Cylindrical Shells
Work
Average Value of a Function

(6/97)

```