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MATH105: Calculus I

Description:Limits and contitnuity of functions in one variable, differentiation rules, implicit differentiation, introductory integration, the fundamental theorem of calculus, optimization problems and related rates, the first and second derivative tests and curve sketching.
Credit Hours.:3
Text Book: Smith, R. T. and Minton, R. B. Calculus, McGraw Hill
Coordinator: Walid Ibrahim
Topics Outline:
  1. Limits and their computation
  2. Continuity and limits involving infinity
  3. Tangent lines and velocity
  4. Computation of derivatives
  5. Logarithmic and exponential functions
  6. Mean value theorem
  7. Linear approximation, l?Hopital?s rule and Newton?s method
  8. Concavity, curve sketch and optimization
  9. Anti-derivatives and Fundamental theorem of calculus
  10. The natural logarithmic function
  11. Inverse functions
  12. The inverse trigonometric functions
  1. Compute limits and explain continuity
  2. Compute derivatives and apply derivatives to optimization problems.
  3. Use limits and derivatives to sketch graphs of elementary functions in one variable.
  4. Estimate values and roots of functions using the linear approximation method and Newton's method.
  5. Apply the fundamental theorem of calculus to differentiate and to integrate.
Mapping of Topics Outline to Outcomes
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Volume of the Course that Contributes to CIT Students Outcomes(SOs)
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18% 43% 0% 0% 0% 0%0% 18% 18% 0% 0% 0% 0% 0%
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