Dec 09, 2022
MATH 215 - Calculus II
Credit Hours: 4
Lecture Hours: 4
Laboratory Hours: 0
Prerequisite(s): MATH 210 or equivalent
This course is concerned with the integral and its applications, and numerical approximation methods. Technology used is a graphing calculator and a Computer Algebra System. Topics studied are algebraic techniques of integration (such as substitution, parts, and partial fraction decomposition), Reimann, Trapezoid and Simpson numerical approximations to the definite integral, improper integrals, Taylor series, polynomials, and Fourier series. If time permits, a brief introduction to differential equations is included.
Student Learning Outcomes of the Course: General Education SLO’s:
- 1.Students will demonstrate the ability to interpret and draw inferences from mathematical models such as formulas, graphs, tables, and schematics.
- Students will demonstrate the ability to represent mathematical information symbolically, visually, numerically and verbally.
- Students will demonstrate the ability to employ quantitative methods such as, arithmetic, algebra, geometry, or statistics to solve problems.
- Students will demonstrate the ability to estimate and check mathematical results for reasonableness.
- Students will demonstrate the ability to recognize the limits of mathematical and statistical methods.
- Recognize and be able to successfully integrate by hand using substitution, integration by parts and partial fractions
- Use a brief Table of Integrals to perform integration
- Show how various numerical integration schemes work: Left, Right, Midpoint, Trapezoid, Simpsons
- Evaluate improper integrals
- Use knowledge of integration to solve application problems
- Apply a variety of tests for convergence of infinite series
- Approximate functions using Taylor series and Fourier series
- Use a computer algebra system to investigate various aspects of integration