Course Description
Integration techniques, indeterminate forms, improper integrals, and power series expansions are the principal topics of the course. Specific topics include integration (by parts, substitutions, partial fractions, and inverse circular and hyperbolic functions), L'Hopital's rule, convergences tests for infinite series, and Taylor polynomials.
Prerequisite(s)
MATH 2515 with a grade of C or better or appropriate advanced placement exam score
Prerequisite(s) or Corequisite(s)
Appropriate assessment score or completion/concurrent enrollment in ENGL 1422 with a grade of C or better
IAI Number
M1 900-2
MTH 902
IAI Title
Calculus II
Calculus II
Topical Outline
- Logarithmic and Exponential Functions Revisited
- Exponential Models
- L'Hopital's Rule
- Hyperbolic Functions
- Basic Approaches
- Integration by Parts
- Trigonometric Integrals
- Trigonometric Substitutions
- Partial Fractions
- Other Integration Strategies
- Numerical Integration
- Improper Integrals
- An Overview
- Sequences
- Infinite Series
- The Divergence and Integral Tests
- Comparison Tests
- Alternating Series Test
- The Ratio and Root Tests
- Choosing a Convergence Test
- Approximating Functions with Polynomials
- Properties of Power Series
- Taylor Series
- Working with Taylor Series
- Vectors in the Plane
- Vectors in Three Dimensions
- Dot Products
- Cross Products
At the end of this course, students will be able to:
- Apply integration by parts, partial fractions, and trigonometric substitutions to solve integral problems.
- Solve indeterminate forms of limit problems using l’Hopital’s Rule.
- Identify and evaluate simple improper integrals
- Identify infinite series as convergent or divergent using the basic tests presented.
- Expand simple analytic functions in a Taylor series.
- Find the derivatives of parabolas, ellipses, and hyperbolas using implicit differentiation.
- Solve simple vector problems involving magnitude, unit vectors, dot, and cross products