10804198Calculus 1
Course Information
Description
Analyze and graph algebraic expressions, especially conic sections. Develop an intuitive understanding of limits, derivatives and integrals. Apply the derivative and the integral to certain physical problems.
Total Credits
4
Course Competencies
  1. Evaluate limits of functions
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    use L'hopital's rule to determine the limit
    use the correct limit notation
    determine where functions are continuous or discontinuous
    evaluate limits of various functions at specific points
    evaluate one-sided limits of various functions at specific points
    evaluate infinite limits

  2. Calculate derivatives of algebraic functions
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    use the formal definition of the derivative to find the derivative of an algebraic function
    use appropriate derivative notation
    evaluate derivatives at specific values within the domain of differentiable functions
    differentiate algebraic functions using the product rule
    differentiate algebraic functions using the quotient rule
    differentiate algebraic functions using the chain rule
    differentiate algebraic functions using generalized power rules
    differentiate algebraic functions implicitly
    calculate higher order derivatives of algebraic functions
    use the Mean Value Theorem for derivatives

  3. Calculate derivatives of trigonometric functions
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    use appropriate derivative notation
    evaluate derivatives at specific values within the domain of inverse trigonometric functions
    evaluate derivatives at specific values within the domain of trigonometric functions
    differentiate trigonometric functions using the product rule
    differentiate trigonometric functions using the quotient rule
    differentiate trigonometric functions using the chain rule
    differentiate trigonometric functions using generalized power rules
    differentiate trigonometric functions implicitly
    calculate higher order derivatives of trigonometric functions

  4. Calculate derivatives of exponential functions
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    use appropriate derivative notation
    evaluate derivatives at specific values within the domain of exponential functions
    differentiate exponential functions using the product rule
    differentiate exponential functions using the quotient rule
    differentiate exponential  functions using the chain rule
    differentiate exponential functions implicitly
    calculate higher order derivatives of exponential  functions
    differentiate exponential functions with different bases

  5. Calculate derivatives of logarithmic functions
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    use appropriate derivative notation
    evaluate derivatives at specific values within the domain of logarithmic functions
    differentiate logarithmic functions using the product rule
    differentiate logarithmic functions using the quotient rule
    differentiate logarithmic functions using the chain rule
    differentiate  logarithmic functions using generalized power rules
    differentiate logarithmic functions implicitly
    calculate higher order derivatives of logarithmic functions
    differentiate a function using logarithmic differentiation
    differentiate logarithmic functions with different bases

  6. Use derivatives to solve applied problems
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    solve related rate applications
    solve optimization applications
    determine equation of a tangent line through a given point on a curve
    determine equation of a normal line through a given point on a curve
    use derivatives to establish relationships between position, velocity, and acceleration
    approximate the change in a function using linearization or differentials

  7. Analyze the graph of a function using derivatives
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    use the first derivative to find critical points of a function
    determine absolute extreme values of a function
    determine relative extreme values of a function
    use the first derivative to find intervals on which a function is increasing or decreasing
    use the second derivative to find intervals on which a function is concave up or concave down
    find the inflection points of a function
    sketch a curve using calculus techniques

  8. Calculate indefinite integrals of functions
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    use appropriate integral notation
    calculate antiderivatives of algebraic functions
    find the constant of integration given an initial condition
    calculate antiderivatives of trigonometric functions
    calculate antiderivatives of exponential functions
    calculate antiderivatives that result in inverse trigonometric functions
    calculate antiderivatives that result in logarithmic functions

  9. Calculate definite integrals of functions
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    use the fundamental theorem of calculus to evaluate an integral
    use a definite integral to calculate the area under a curve
    use an integral to determine a total area
    use appropriate integral notation

  10. Calculate area using calculus techniques
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    calculate the surface area of a solid of revolution using integrals
    find the area of a region between curves using integrals
    find the area between two curves by integrating horizontally and vertically

  11. Use integrals to solve applied problems
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    use an integral to calculate an average value
    calculate volume of a solid of revolution using the disk/washer method
    calculate volume of a solid of revolution using the shell method
    use integrals to calculate arc length

  12. Use substitution to calculate integrals
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    calculate indefinite integrals using substitution
    calculate definite integrals using substitution
    change the limits of integration within a substitution problem
    calculate integrals of transcendental functions using substitution
    calculate integrals of algebraic functions using substitution