MAT-271 Calculus I

A first course in Calculus focusing on the mathematics of changing rates. The derivative of polynomial and transcendental functions is investigated from a numerical, graphical, and algebraic approach. Applications and interpretations of derivatives are explored. An introduction to the definite integral and the Fundamental Theorem of Calculus is included in this course. Graphing utility is required. This course carries SUNY General Education Mathematics (and Quantitative Reasoning) credit.

Credits

4

Prerequisite

A C- or better in MAT-152 or placement into Math Level 4.

Semesters Course Will Be Offered

• Fall
• Spring
• Summer

For more detailed course information view the Course Outline

MAT 271: Calculus I

Course Description

A first course in Calculus focusing on the mathematics of changing rates. The derivative of polynomial and transcendental functions is investigated from a numerical, graphical, and algebraic approach. Applications and interpretations of derivatives are explored. An introduction to the definite integral and the Fundamental Theorem of Calculus is included in this course. Graphing utility is required. This course carries SUNY General Education Mathematics (and Quantitative Reasoning) credit.

Credit Hours

4

Contact Hours

Lecture	4
Lab	0
Other	0

Semester(s) Course Will Be Offered

Fall, Spring, Summer

Prerequisites

A C- or better in MAT-152 or placement into Math Level 4.

SUNY General Education Course

• Mathematics and Quantitative Reasoning

Course Learning Outcomes

1. Interpret derivatives as instantaneous rates of change.
2. Compute derivatives numerically, algebraically, and graphically.
3. Apply derivatives to solve problems or draw conclusions.
4. Apply the Fundamental Theorem of Calculus

Topic Outline

1. Review algebra and the library of functions as needed.
2. Limits and continuity
3. The Derivative
   1. Derivative at a point
   2. Derivative Function
   3. Interpretation of the derivative as an instantaneous rate of change
   4. Relationship between first and second derivatives with respect to behavior of a function
   5. Sketching the graph of a derivative function from the graph of a given function
   6. Differentiability
4. Create derivative formulas for:
   1. Constant functions
   2. Power functions
   3. Linear functions
   4. Polynomial functions
   5. Exponential functions
   6. Logarithmic functions
   7. Hyperbolic functions
   8. Trigonometric functions
   9. Inverse trigonometric functions
5. Rules of Differentiation
   1. Linearity rules
   2. Product and quotient rules
   3. Chain rule and its application
6. Applications of the Derivative
   1. Use the first and second derivative to describe behavior of the original function
   2. Implicit differentiation
   3. Related rates
   4. Finding extrema and inflection points on an interval
   5. Applied optimization problems
7. The Definite Integral
   1. Fundamental Theorem of Calculus
      1. Interpretations of the definite integral as "net change": ∫_a^b f(t)dt = F(b) - F(a)
      2. Riemann Sums
      3. Definite integral as "area under the curve"
   2. Evaluation of definite integrals (not analytically)
      1. By Riemann Sum approximation
      2. Numerically