ModelCourses/Reform Calculus

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This calculus model covers the entire calculus sequence from a reform point of view. A specific course can be created from this mega-course by choosing choosing the appropriate topics (and deleting the rest).

Try out Reformed Calculus

  • Properties of elementary functions
  • Find limits.
  • Concepts of continuity and differentiability
  • Symbolically compute derivatives.
  • Find derivatives graphically and numerically.
  • Solve optimization problems
  • Solve related rates problems
  • Local linearity
  • The geometric interpretation of the integral
  • Riemann Sums.
  • Integrate basic functions.
  • Fundamental theorem of calculus.
  • Symbolically integrate functions using a variety of techniques.
  • Find integrals numerically.
  • Determine if an improper integral converges or diverges.
  • Compute volumes of rotation
  • Apply knowledge of integration in an applied setting.
  • Compute Taylor and McLaurin Series.
  • Determine if a sequence converges or diverges
  • Determine if a series converges or diverges
  • Solve simple differential equations
  • Students will understand functions of two and three variables from symbolic, numerical and graphical viewpoints (making use of cross-sections and contour lines and surfaces) and will recognize the equations and shapes of common surfaces.

Students will understand and correlate geometric and algebraic descriptions of vectors and vector operations in the plane and in space.

  • Continuity and differentiability for functions of two or more variables.
  • Symbolically compute partial and directional derivatives.
  • Polar, cylindrical and spherical coordinate systems and recognize contexts in which the use of these is appropriate.
  • Set up and compute double and triple integrals in rectangular, polar, spherical and cylindrical coordinate systems.
  • Develop and use parametric descriptions for common curves and surfaces.
  • Use the techniques of multivariable calculus to solve applied problems.
  • Vector fields and their calculus.
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