Jan 16, 2022
MATH 1082 - Single Variable Calculus II Credits: 5
Hours/Week: Lecture NoneLab None
Course Description: This course is the second course of the two-semester sequence of single variable calculus. Topics include applications of the definite integral, techniques of integration, numerical integration, improper integrals, infinite series, elementary differential equations, parametric curves, and polar curves. A graphing calculator is required. Instruction will be provided in the use of the TI-83/TI-84 calculator.
4 Mathematics/Logical Reasoning
Prerequisite(s): MATH 1081 with a grade of C or higher.
Recommendation: Assessment score placement in RDNG 1000 or above, or completion of RDNG 0900 or RDNG 0950 with a grade of C or higher.
- Polar Coordinates Polar coordinates and polar curves Calculus in polar coordinates
- Applications of the Definite Integral Volume Work Arc Length
- Improper Integrals Convergence or divergence Indeterminate forms L’Hopital’s rule
- Infinite Series Sequences and Series Convergence or divergence Taylor series Calculus of series
- Numerical Integration Left and Right sums Trapezoid sums and Midpoint sums Simpson’s rule
- Techniques of Integration Integration by parts Substitution Partial fractions
At the end of this course students will be able to:
- Determine the convergence or divergence of an infinite series.
- Determine the integral of a function graphically, numerically, and symbolically.
- Approximate area with approximating sums by hand and with technology.
- Determine whether an improper integral converges or diverges.
- Demonstrate critical and logical reasoning when solving problems.
- Integrate to find arc-length, area, and volume.
- Communicate clearly a problems solution and its explanation for the intended audience in terms of the problem posed.
- Find horizontal and vertical tangents to and sharp corners of a polar curve
- Find the Taylor Series expansion of a function about a point.
- Find the area bounded by a polar curve.
- Find the derivative and anti-derivative of an infinite series.
- Graph a polar curve.
- Model and solve physics and probability problems by applying and evaluating an integral.
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