MATH 1082 - Single Variable Calculus II

Credits: 5
Hours/Week: Lecture None Lab 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.
MnTC Goals
4 Mathematics/Logical Reasoning

Prerequisite(s): MATH 1081  with a grade of C or higher.
Corequisite(s): None
Recommendation: Eligible for college-level Reading and English.

Major Content

1. Polar Coordinates Polar coordinates and polar curves Calculus in polar coordinates
2. Applications of the Definite Integral Volume Work Arc Length
3. Improper Integrals Convergence or divergence Indeterminate forms L’Hopital’s rule
4. Infinite Series Sequences and Series Convergence or divergence Taylor series Calculus of series
5. Numerical Integration Left and Right sums Trapezoid sums and Midpoint sums Simpson’s rule
6. Techniques of Integration Integration by parts Substitution Partial fractions

1. Determine the convergence or divergence of an infinite series.
2. Determine the integral of a function graphically, numerically, and symbolically.
3. Approximate area with approximating sums by hand and with technology.
4. Determine whether an improper integral converges or diverges.
5. Demonstrate critical and logical reasoning when solving problems.
6. Integrate to find arc-length, area, and volume.
7. Communicate clearly a problems solution and its explanation for the intended audience in terms of the problem posed.
8. Find horizontal and vertical tangents to and sharp corners of a polar curve
9. Find the Taylor Series expansion of a function about a point.
10. Find the area bounded by a polar curve.
11. Find the derivative and anti-derivative of an infinite series.
12. Graph a polar curve.
13. Model and solve physics and probability problems by applying and evaluating an integral.

04. 02. Clearly express mathematical/logical ideas in writing.

04. 04. Apply higher-order problem-solving and/or modeling strategies.

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