MAT 231  Calculus II [SUN# MAT 2230] 4 Credits, 4 Contact Hours 4 lecture periods 0 lab periods
Continuation of MAT 220 . Includes techniques and applications of integration, numerical integration, improper integrals, sequences, infinite series, polar coordinates, parametric equations, and other related topics.
Prerequisite(s): Within the last three years: MAT 220 with a grade of C or better. GenEd: Meets AGEC  MATH; Meets CTE  M&S.
Course Learning Outcomes
 Evaluate indefinite and definite integrals using exact and approximation techniques.
 Use integrals in various applications.
 Determine convergence of infinite series.
Performance Objectives:
 Use definite integrals to calculate areas between curves, volumes of solids, work, arc length, centroids/centers of mass and at least one of the following applications: hydrostatic force, average value of a function, economics, or probability.
 Calculate indefinite integrals and exact values of definite integrals of algebraic and transcendental functions, including powers and products of trigonometric functions, using substitution, integration by parts, partial fractions, and trigonometric substitutions.
 Estimate definite integrals using trapezoid, midpoint, and Simpson’s rules.
 Determine if an improper integral converges or diverges, and if it converges, calculate or estimate its value.
 Determine if an infinite sequence converges or diverges.
 Determine if an infinite series converges or diverges using the divergence test, integral test, comparison test, limit comparison test, alternating series test, ratio and root tests.
 Estimate the error associated with a partial sum approximation of a convergent alternating series
 Determine if a series converges absolutely or conditionally.
 Determine radii of convergence and intervals of convergence of power series.
 Find the power series representation for a given function by integrating or differentiating existing power series.
 Determine Taylor and Maclaurin series using the definition.
 Determine slopes and areas of graphs defined in polar coordinates.
 Determine slopes and arc length of two dimensional curves modeled with parametric equations.
Optional Objectives:
14. Use rationalizing substitutions to calculate indefinite integrals and exact values of definite integrals.
15. Generate the equation of a conic section given a graph, or sketch a graph given an equation.
16. Calculate error bounds for the numerical integration techniques.
17. Generate the binomial series expansion for appropriate functions.
18. Apply integration techniques to solve separable differential equations.
19. Use slope fields and/or Euler’s Method to estimate solutions to differential equations. Outline:
 Techniques of Integration
 Substitution
 Integration by parts
 Products and powers of trigonometric functions
 Partial Fractions
 Trigonometric substitution
 Rationalizing substitutions (optional)
 Numerical integration
 Trapezoid rule
 Midpoint rule
 Simpson’s rule
 Error bounds (optional)
 Improper integrals
 Applications of the Integral
 Area between curves
 Volumes of solids
 Work
 Centroids or centers of mass
 Arc length
 At least 1 of the following:
 Hydrostatic force
 Average value of a function
 Economics
 Probability
 Sequences and Series
 Convergence/divergence of infinite sequences
 Convergence/divergence of infinite series
 Divergence test
 Integral test
 Comparison test
 Limit comparison test
 Alternating series test
 Ratio test
 Root test
 Estimate infinite alternating series
 Absolute and conditional convergence
 Power series
 Radius and interval of convergence
 Integration and differentiation
 Taylor and Maclaurin series
 Binomial series (optional)
 Parametric Equations and Polar Coordinates
 Slopes of parametric curves
 Arc length of parametric curves
 Slopes of polar curves
 Areas of polar curves
 Conic sections (optional)
 Differential Equations
 Separable (optional)
 Slope fields (optional)
 Euler’s method (optional)
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