3 Credit Course
Offered in Lecture Format
Prerequisite required  (MATH 1670)

SYLLABUS

I. LIMITS AND CONTINUITY

A. Definition and basic properties of limits
B. One-sided limits
C. Limits involving infinity
D. Definition of a continuous function
E. Determination of points of discontinuity of a function

II. INTRODUCTION TO THE DERIVATIVE

A. Definition of the derivative
B. Using the definition to find the derivative of a function
C. Derivative as a slope
D. Derivative as a rate of change

III. DIFFERENTIATION FORMULAS

A. Power function rule
B. Sum and difference rules
C. Product and quotient rules
D. Chain rule
E. Power rule
*F. Implicit differentiation

IV. DERIVATIVES OF SPECIAL FUNCTIONS

A. Exponential function
B. Logarithmic function

V. HIGHER ORDER DERIVATIVES: NOTATION AND COMPUTATION

VI. CURVE SKETCHING WITH FIRST AND SECOND DERIVATIVES

A. Increasing and decreasing functions
B. Relative extrema using first derivative test
C. Relative extrema using second derivative test
D. Absolute extrema
E. Concavity and points of inflection
F. Sketching graphs

VII. BUSINESS APPLICATIONS OF THE DERIVATIVE

A. Marginal cost and marginal revenue
B. Marginal propensity to consume and save
C. Applied maxima and minima
        1. Cost and revenue problems
        2. Area problems
        3. Volume problems
D. Point elasticity of demand

VIII. INTRODUCTION TO INTEGRATION

A. Antiderivatives
B. Integral notation and terminology

IX. INTEGRATION FORMULAS

A. Power rule
B. Exponential rule
C. Logarithmic rule
*D. Integration by parts

X. THE DEFINITE INTEGRAL

A. Definition
B. Properties
C. Fundamental theorem of integral calculus

XI. DEFINITE INTEGRAL AS AREA

A. Area under a curve
B. Area between curves

XII. APPLICATIONS OF INTEGRATION

A. Area as revenue, cost, profit
*B. Consumers' and producers' surplus
*C. Profit over time

*Optional

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