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
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
IO2 Quantitative Reasoning: Students will be able to reason mathematically.
- 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)
In order to give the instructor the greatest flexibility in assigning a grade for the course, grades will be based on various instruments at the instructor’s discretion. However, to maintain instructional integrity there must be four class exams or three class exams and a project. A final exam will be given if there are less than four exams or a project may be substituted for the final exam if there are four in-class exams. At least 60% of the grade will be based on quantifiable work (exams, homework, quizzes, etc.). The remaining portion of the grade may be based on quantifiable work, attendance, projects, journal work, etc., at the instructor's discretion.
The following is a compilation of acceptable grading instruments: In class exams and a final, attendance, homework or quizzes, research paper, modeling projects on the calculator or computer. Other projects or assignments may be assigned as deemed appropriate at the instructor's discretion.