This course will introduce the student to the basic concepts of the calculus. It will give the student an appreciation of the calculus and its applications in the real world and will prepare the student for future work in mathematics and the sciences. Course includes functions, limits, continuity, derivatives and their applications, and integration and its applications. (Formerly Math 171)
Prerequisites
MATH& 141 & MATH& 142, or BBCC placement exam, or instructor permission
Quarters Offered
Fall,
Winter,
Spring
Course Outcomes
Upon successful completion of the course, students should be able to demonstrate the following knowledge or skills:
- Calculate and derive limits of functions
- Calculate derivatives of functions
- Use derivatives to model and optimize situation of change
Institutional Outcomes
IO2 Quantitative Reasoning: Students will be able to reason mathematically.
Course Content Outline
- Limits of Function Values
- Limits Involving Infinity
- Continuous Functions
- Defining Limits Formally with Epsilons and Deltas
- Slopes, Tangent Lines, and Derivatives
- Differentiation Rules
- Velocity, Speed, and Other Rates of Change
- Derivatives of Trigonometric Functions
- The Chain Rule
- Implicit Differentiation
- Derivatives with Rational Exponents
- Differentials and Linearizations
- Newton’s Method
- Related Rates of Change
- Extreme Values of Functions
- How y’ and y” Determine the Shape of a Graph
- Using the Calculus to Graph Functions
- Optimization
- The Mean Value Theorem
- Introduction to Partial Derivatives and Simple Applications (optional)