MATH 221 - Calculus and Analytic Geometry I

4 Credits: (4 lecture)

Course Description
This course is basic to the further study of mathematics, engineering, and the physical sciences. It includes the study of coordinates and related variables, polynomials, and their graphs, differentiation of functions with applications, and integration of functions with applications.

Prerequisite MATH 102 or MATH 118.

Anton, H., Bivens, I., & Davis, S. (2022).  Calculus, early transcendentals (12th ed.).  Hoboken, NJ: Wiley.

OR

Briggs, W., Cochran, L., Gillett, B., & Schultz, E. (2019).  Calculus early transcendentals MyLab Math with eText (3rd ed.).  Upper Saddle River, NJ: Pearson.

Objectives
The student will be able to:

A. Calculate the limits of functions.

B. Calculate limits using the formal definition of a limit.

C. Verify the conditions of continuity at a point and on intervals.

D. Calculate derivatives of algebraic and transcendental functions explicitly and implicitly.

E. Calculate higher order derivatives.

F. Plot curves by using the information obtained from the first and second derivatives, asymptotes, and intercepts.

G. Use differentiation to solve related rates, optimization, rates of change, and other application problems.

H. Use Riemann sums to derive the indefinite integral.

I. Calculate definite and indefinite integrals involving algebraic and transcendental functions.

J. Use the Fundamental Theorem of Calculus to solve applications of the definite integral.

Content
A. Limits and continuity.

B. Differentiation of algebraic, trigonometric, exponential, and logarithmic functions.

C. Product, quotient, and chain rules.

D. Implicit differentiation.

E. Curve sketching.

F. Related rates, optimization, and rates of change.      

G. Riemann sums.

H. Definite and indefinite integration.

I. Integration of algebraic, trigonometric, exponential, and logarithmic functions.

J. Area between two curves, disc and shell methods, arc length, work, and moments.

Student Evaluation
The objectives will be evaluated as follows:  A, B, C, D, E, F, G, H, I, and J will be evaluated using examinations.