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Analyze Parametric equations and Vectors
Assessment Strategies
by completing satisfactorily all graded class assignments and homework
by achieving satisfactory scores on all tests and quizzes pertaining to this topic
Criteria
you sketch graphs from parametric equations
you differentiate parametric equations implicitly
Parametric equations should contain appropriate notation and variables
you represent vectors appropriately as sum of components
you calculate magnitude and direction of vectors
you relate parametric equations to vectors in magnitude velocity problems
written assignments have all calculation and steps shown
written assignments are neat
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Convert from Cartesian to Polar coordinates including graphing in Polar coordinates
Assessment Strategies
by completing satisfactorily all graded class assignments and homework
by achieving satisfactory scores on all tests and quizzes pertaining to this topic
Criteria
you represent points in polar coordinates
you convert between polar and cartesian coordinates
you are consistent in the use of variables between the two coordinate systems
you sketch a cardioid from the equation
you sketch a limacon from the equation
you sketch a lemniscate from the equation
sketch is neat
sketch is labelled appropriately indicating polar angles
you calculate area under curve by integrating in polar coordinates
you sketch the graphs before evaluating the area under curve
written assignments have all calculation and steps shown
written assignments are neat
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Apply derivatives to Logarithmic and Exponential functions
Assessment Strategies
by completing satisfactorily all graded class assignments and homework
by achieving satisfactory scores on all tests and quizzes pertaining to this topic
Criteria
you apply and recognize appropriate trigonometric identities and formulas
you use derivatives of basic trigonometric functions to solve problems
you apply appropriate (chain, generalized power, product, quotient) rule to differentiate trigonometric functions
you evaluate inverse trigonometric functions at given points
you evaluate derivatives of inverse trigonometric functions
you sketch the graph of logarithmic and exponential functions
you apply the definition and three laws of logarithms to solve problems
you evaluate the derivatives of logarithms using definitions, laws of logarithms and the rules of differentiation
you apply the definition and properties of exponents to solve problems
you evaluate the derivatives of exponents using definitions, properties and rules of differentiation
you determine conditions when the L'Hospital's rule can be applied
you evaluate limits of undefined functions using L'Hospital's rule when it applies
written assignments have all calculation and steps shown
written assignments are neat
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Solve derivative problems using Newton's methods, L'Hospital's rule, and other methods
Assessment Strategies
by completing satisfactorily all graded class assignments and homework
by achieving satisfactory scores on all tests and quizzes pertaining to this topic
Criteria
you iterate using the Newton's method
you apply Newton's method to find the x-intercept
you use Newton's methods to find roots of equations
evaluated values are accurate up to the specified decimal places
evaluations are done appropriately using radians or degrees for trigonometric functions
written assignments have all calculation and steps shown
written assignments are neat
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Apply integration techniques to Power, Logarithmic, Exponential, Trigonometric and Inverse Trigonometric forms
Assessment Strategies
by completing satisfactorily all graded class assignments and homework
by achieving satisfactory scores on all tests and quizzes pertaining to this topic
Criteria
you apply substitution method and rules of integration to integrate appropriate trigonometric forms
you use the integral of the logarithm and exponential with suitable substitution to integrate certain functions
you apply trigonometric integral formulas to solve problems
you use trigonometric identities to solve integration problems
you recognize inverse trigonometric formulas
you apply inverse trigonometric identities with substitution to solve integration problems
final result, while using substitution, is in terms of the original variable
final result includes the appropriate constant of integration
written assignments have all calculation and steps shown
written assignments are neat
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Integrate using Trigonometric Substitution, Parts, and Tables
Assessment Strategies
by completing satisfactorily all graded class assignments and homework
by achieving satisfactory scores on all tests and quizzes pertaining to this topic
Criteria
you evaluate integrals using trigonometric substitutions and identities
final result, while using substitution, is in terms of original variable
you apply formula for integration by parts to integrate functions that are products
final result includes appropriate constant of integration
written assignments have all calculation and steps shown
written assignments are neat
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Analyze surfaces in 3-dimensions
Assessment Strategies
by completing satisfactorily all graded class assignments and homework
by achieving satisfactory scores on all tests and quizzes pertaining to this topic
Criteria
you sketch a 3-D surface from its equation
the sketch contains all the axis labeled
the sketches are neat
sketches include traces in the different coordinate plane
assignments have all calculation and steps shown
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Apply partial derivatives
Assessment Strategies
by completing satisfactorily all graded class assignments and homework
by achieving satisfactory scores on all tests and quizzes pertaining to this topic
Criteria
you evaluate the partial differential equation of a function with two variables
you solve minimization and maximization problems pertaining to functions of two variables
you correctly evaluate higher order partial derivatives
written assignments have all calculation and steps shown
written assignments contain correct notation
written assignments are neat
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Evaluate multiple integrals including Iterated integrals, Volumes by double integration, Mass, Centroids and Moments of inertia
Assessment Strategies
by completing satisfactorily all graded class assignments and homework
by achieving satisfactory scores on all tests and quizzes pertaining to this topic
Criteria
you solve area problems using iterated integrals
you evaluate an iterated integral
you solve for volume of a solid using double integrals
you find the mass of an area using multiple integrals
you find the centroid of an area using multiple integrals
you find the moment of inertia of an area using multiple integrals
you include the appropriate sketches
written assignments have all calculation and steps shown
written assignments are neat
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Determine convergence of Infinite series
Assessment Strategies
by completing satisfactorily all graded class assignments and homework
by achieving satisfactory scores on all tests and quizzes pertaining to this topic
Criteria
you recognize a geometric series
you determine the convergence or divergence of an infinite series using convergence test
you determine Maclaurin's expansion of certain functions
written assignments have all calculation and steps shown
written assignments contain correct notation for infinite series
written assignments are neat
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Compute and operate with Infinite series
Assessment Strategies
by completing satisfactorily all graded class assignments and homework
by achieving satisfactory scores on all tests and quizzes pertaining to this topic
Criteria
you evaluate Maclaurin's series of functions using operations on series
you compute the approximate value of an infinite series
you represent functions as an appropriate Taylor, Maclaurin or other infinite series
written assignments have all calculation and steps shown
written assignments are neat
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Analyze Fourier series
Assessment Strategies
by completing satisfactorily all graded class assignments and homework
by achieving satisfactory scores on all tests and quizzes pertaining to this topic
Criteria
you represent periodic functions using Fourier series
written assignments have all calculation and steps shown
written assignments are neat
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Evaluate Differential equations using Separation of variables
Assessment Strategies
by completing satisfactorily all graded class assignments and homework
by achieving satisfactory scores on all tests and quizzes pertaining to this topic
Criteria
you find the general solution to differential equations
you evaluate constants to find the particular solution to differential equation
you solve problems that involve differential equations
written assignments have all calculation and steps shown
written assignments contain appropriate notation
written assignments are neat
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Apply first order differential equations
Assessment Strategies
by completing satisfactorily all graded class assignments and homework
by achieving satisfactory scores on all tests and quizzes pertaining to this topic
Criteria
you identify the Integrating Factor for first order differential equations
you find solutions to first order linear differential equations
you interpret word problems as appropriate first order differential equations
you solve for the constants using initial conditions or other appropriate data
written assignments have all calculation and steps shown
written assignments are neat
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Analyze higher order differential equations
Assessment Strategies
by completing satisfactorily all graded class assignments and homework
by achieving satisfactory scores on all tests and quizzes pertaining to this topic
Criteria
you identify the auxiliary equation of a nth order differential equation
you obtain the general solution of a homogeneous linear differential equation
you obtain general solutions for auxiliary equations with repeating or complex roots
you identify the constant terms when initial conditions are provided
you formulate the differential equations from application problems
written assignments have all calculation and steps shown
written assignments contain appropriate notation and variable changes
written assignments are neat