4 Credit Course
Offered in Lecture Format
Prerequisite required  (MATH 1900 with a grade of A, B, or C; or Appropriate Placement-Test score)

SYLLABUS

I. PRELIMINARY TOPICS

A. Functions
B. Classification of functions
C. Operations on functions
D. Composition of functions
E. Inverse functions
F. Trigonometric functions

II. THE LIMIT CONCEPT

(It is left to the instructor to choose between the epsilon-delta approach and the more intuitive approach.)

A. The definition of a limit at a point
B. Properties of limits
        1. The squeezing theorem
        2. Trigonometric limits
C. One-sided limits
D. Limits involving infinity and asymptotes
E. Continuity
        1. Continuity at a point
        2. Continuity on an interval
        3. The intermediate value theorem

III. THE DERIVATIVE

A. Slopes of tangents and instantaneous rates
B. Defining the derivatives
        1. Terminology
        2. Notation
        3. Finding derivatives
        4. Functions which are not differentiable
C. Derivatives of polynomials
D. Product and quotient rules
E. Higher order derivatives
F. Derivatives of sine and cosine
G. The chain rule
        1. Functions involving integer powers
      2. Functions involving sine and cosine
H. Implicit differentiation
I. The power rule for rational powers

IV. APPLICATIONS OF THE DERIVATIVE

A. Linear approximation; differentials
*B. Newton's method for f(x) = 0
C. The mean value theorem
D. Curve sketching
        1. Maxima and minima
        2. Increasing and decreasing functions
        3. The first derivative test
        4. Concavity
      5. The second derivative test
        6. Intercepts, asymptotes and symmetry
        7. Generating complete sketches using topics 1 through 6
E.     Related rate problems

V. INTRODUCTION TO INTEGRATION

A. Antiderivatives
        1. The indefinite integral
        2. Basic formulas
B. Summation notation
C. Areas as limits of sums
D. The definition of the definite integral
        1. Terminology
        2. Notation
        3. Properties
E. The fundamental theorem of calculus
F. Integration by substitution
        1. The power rule
        2. The general sine and cosine formulas

VI. SOME APPLICATIONS OF INTEGRATION

A. Area
B. Volume
        1. Washer method
        2. Shell method
      *3. By slicing
*C. Arclength
*D. Work
*E. Liquid pressure and force
*F. Centers of mass; centroids

*Optional

Click here to go back to Courses