MATH 1134 - Calculus II
5 Credits
Prepares students for Multivariable Calculus (MATH 2219 ). Is the second course in the two-semester sequence of single variable calculus. The topics include applications of the integral: area, volume, surface area, center of mass, work, liquid pressure and arc length; techniques of integration; improper integrals; conics; calculus in polar coordinates; calculus involving parametrically-defined curves; and infinite series. Familiarity with a computer algebra system is expected. Use of technology will be embedded throughout the course.
Pre-Requisites MATH 1133
Major Content Areas
Applications of the integral 20% Parametric and Polar curves, conics 20% Techniques of integration and improper integrals 35% Infinite series 25%
Learning Outcomes
Apply a variety of integration techniques including u-substitution, integration by parts, trigonometric substitution, and partial fractions. Graph functions in polar coordinates and fine slopes of tangent lines. Apply tests of convergence to determine the behavior of an infinite series. Determine convergence or divergence of an improper integral. Use definite integrals to solve problems such as finding area, work volume, arc length, fluid forces, and center of mass. Approximate a definite integral using Simpson’s Rule and/or the Trapezoid Rule Find Taylor series representations of basic functions. Find the slope of a line tangent to a parametric curve. Apply the definition of convergence to calculate the limit of a sequence or the sum of a convergent series.
Minnesota Transfer Curriculum (MNTC) Goals
02 - Critical Thinking 04 - Mathematical/Logical Reasoning
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