Student Learning Outcomes –approved 3/26/2015
Student Learning Outcomes for Math 131, Math 132, and Math 231
Math 131
Course Description: First course in calculus and analytic geometry. Includes introductory concepts in analytic geometry,
limits, continuity, differentiation, applications of the derivative, the mean value theorem, the definite and indefinite integral,
and applications of the integral.
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Upon completion of this course, students should be able to:
Verify the value of a limit of a function at a point,
Describe and use the properties of the limit of a function,
Compute the limit of a function,
Define and use the concept of continuity of a function,
Find points of discontinuity of a function and classify them,
Compute the derivative of a function using the definition of the derivative,
Compute the derivative of functions using the power rule, product rule, the quotient rule, and the chain rule
Use rules of differentiation to compute derivatives of polynomial, trigonometric, exponential and logarithmic
functions, and hyperbolic functions,
Compute rates of changes of a distance function and a velocity function and compute tangent lines to a graph,
Find linear approximation and the differential of functions,
Differentiate function implicitly,
Determine where functions are increasing or decreasing,
Find intervals of concavity of functions,
Understand the consequences of Rolle’s Theorem and the Mean Value Theorem ,
Find critical values of functions and classify as relative maxima or minima,
Sketches curves and compute limits involving infinity and asymptotes,
Find optimums in science and engineering problems,
Compute indefinite integrals and area under a curve,
Compute Riemann Sums and the definite integral of a function,
State and use the Fundamental Theorem of Calculus,
Find the average value of a function on an interval,
Integrate functions using substitution technique.
Math 132
Course Description:
The purpose of this course, which is a continuation of MATH 131, is to study the methods of
calculus in more detail. The course will cover the material in the textbook from Chapters 5-9: applications of the integral,
methods of integration, infinite series, polar coordinates as well as complex numbers in more detail.
Prerequisite:
Math 131 or the equivalent passed with a grade C- or better.
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Upon completion of this course, students should be able to:
Compute the length of curves and surface area of surfaces of revolutions.
Compute work, fluid forces, and centroids using integration.
Approximate integrals by numerical integration.
Integrate using techniques such as substitution, integration by parts, trigonometric techniques, and partial fraction
decomposition.
Determine the convergence or divergence of improper integrals and determine the value of an improper integral.
Compute derivatives and integrals of inverse hyperbolic functions.
Compute limits of sequences.
Determine convergence or divergence of sequences using geometric convergence test, integral test, comparison test,
and ratio and root tests.
Determine absolute or conditional convergence of series.
Determine convergence or divergence of power series.
Determine Maclaurin and Taylor series for certain functions.
Use polar coordinates to graph functions, find area and tangent lines.
Sketch the graph of a function, find slope, find area and arc length using parametric equations.
Perform the algebra operations on complex numbers,
Evaluate complex functions and obtain roots in polar form
Math 231
Course Description:
Prerequisite:
Vectors in the plane and 3-space, vector calculus in two dimensions, partial
derivatives, multiple integration, topics in vector calculus, and first and second order differential
equations.
Math 132 or the equivalent passed with a grade C- or better.
Student Learning Outcomes:
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Upon completion of this course, students should be able to:
Perform the algebra operations on vectors in the plane,
Describe lines, planes, and surfaces in 3-space
Compute the tangent and normal vectors to space curves,
Compute tangential and normal components of acceleration,
Sketch functions of several variables,
Compute tangent plane to surfaces,
Describe and use the Chain Rule,
Compute extreme values of functions of several variables,
Compute multiple integrals,
Compute surface area, mass, and moments,
Compute line integrals and test for independence of path,
State and use Green’s Theorem, Stokes' Theorem, and the Divergence Theorem
Solve first and second order differential equations