This course will expand on the applications and techniques of differentiation learned in the first quarter and give a depth study of integration including the fundamental methods of integrating elementary algebraic and transcendental functions. It will include the applications of the calculus to transcendental functions, analytical geometry and other relevant topics.
Prerequisites
MATH& 151 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:
- 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
Institutional Outcomes
IO2 Quantitative Reasoning: Students will be able to reason mathematically.
Course Content Outline
- 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