Calculus I ENGI 1301

Course description:

This course is designed to develop the topics of real numbers, rate of change and slope, limits, continuity, and graphs. The course also introduces students to the first derivative , and second derivative. Optimization is briefly tackled studying the absolute maxim and minima. The course covers: the constant and continuous compound interest, derivatives of logarithmic and exponential functions, chain rule, implicit differentiation, related rates, antiderivatives and indefinite integrals. Integration by Substitution; Differential equations; Fundamental theorem of calculus; Area between curves, application volumes using cylindrical shells , disks and washers, arc length and surface area of revolution, Taylor and Maclaurin sereis.

Course Aims:

"The aims of this course are to explore the following points: 
  •  Demonstrate ability to explain the various concepts of calculus: Limits, Continuity, Derivative and Integration verbally, algebraically and graphically.
  •  Demonstrate knowledge of the various computational techniques and rules to compute limits and derivatives.
  •  Demonstrate a through understanding of the physical applications of derivatives in real life problems such as related rates, optimization problems.
  •  Know how to use derivative to analyze functions and how to sketch the curves of polynomials, rational functions, trigonometric functions and inverse functions.
  •  Know how to use Mathematica to solve certain calculus problems such as curve sketching, differentiation, integration, root finding and other applications.
  •  Demonstrate ability to compute the integration of certain functions and its applications.
  •  Demonstrate ability to work independently and in teams.

Course outcomes:

Upon completion of this course, the student should be able to: 
  •  Understand the fundamental theorem of calculus. 
  •  Solve inequalities.
  •  Find the basic characteristics of real valued functions.
  •  Find derivatives using several techniques.
  •  Find critical and inflection points.
  •  Understand the intermediate value theorem.
  •  Perform optimization using the first and second derivative tests.
  •  Interpret mathematical and/or logical models such as formulas, graphs, tables and schematics, and draw inference from them. .
  •  Evaluate definite and indefinite integral.
  •  Find volume of solids.
  •  Find arc length and surface area of revolution.