10605132Technical Calculus 2
Course Information
Description
This course is a continuation of Technical Calculus 1. Topics include integration techniques, partial derivatives, graphing conics, double integrals, polar coordinates, and first and second order differential equations. Emphasis is placed on applications to problems in science and engineering.
Total Credits
4
Course Competencies
  1. 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

  2. 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

  3. 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

  4. 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

  5. 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

  6. 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

  7. 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

  8. 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

  9. 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

  10. 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

  11. 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

  12. 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

  13. 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

  14. 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

  15. 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