The course covers concepts, techniques, and applications of integration and infinite series, and introduces differential equations. Topics include integration methods such as substitution, integration by parts, partial fractions, and integration tables. Additional subjects are numerical methods for integration, applications of integration, infinite series, Taylor series and polynomials, separable differential equations, and parametric and polar curves.
Prerequisites
MAT 221 with a grade of “C” or higher.
1. Define and describe the fundamental hyperbolic functions.
2. Compute definite and indefinite integrals utilizing advanced integration techniques.
3. Employ numerical methods to approximate definite integrals.
4. Utilize a range of techniques to evaluate complex integrals.
5. Apply integration techniques to solve real-world problems.
6. Apply relevant theorems and analytical techniques to evaluate infinite series and to determine the convergence or divergence of sequences and series.
7. Approximate functions through the use of Taylor series and polynomial expansions.
8. Solve separable differential equations using appropriate analytical methods.
9. Utilize parametric and polar equations to solve mathematical problems.
10. Define parametric equations and polar curves in the context of their respective coordinate systems.