### Prerequisites

Upon successful completion of the course, students should be able to demonstrate the following knowledge or skills:

- Use appropriate methodology to compute definite and indefinite integrals, including improper integrals
- Use integrals to compute geometric and physical properties
- Use integrals to model and solve problems in physics

**Quantitative Reasoning:**Students will be able to reason mathematically.

- Riemann Sums and Definite Integrals
- Basic Properties, Area, and the Mean Value Theorem for Integrals
- The Fundamental Theorem of Calculus
- Indefinite Integrals
- Integration by Substitution
- Exponential Functions and the Derivative of ex
- Inverse Functions and Their Derivatives
- Logarithmic Functions and the Derivative of ln x
- Exponential and Logarithmic Integrals
- L’Hopital’s Rule
- Inverse Trigonometric Functions
- Integrals of Inverse Trigonometric Functions;
- Areas Between Curves
- Volumes of Solids of Revolution -Disks and Washers
- Cylindrical Shells -An Alternative to Washers
- Curve Length and Surface Area
- Work
- Fluid Pressures and Fluid Forces
- Centers of Mass
- Basic Integration Formulas
- Integration by Parts
- Partial Fractions
- Trigonometric Substitutions
- Integral Tables
- Improper Integrals
- Introduction to Double Integrals

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.