Calculus for Geomatics MATH 2511

Learning Outcomes

Upon successful completion, the student will be able to:

• Compute functional values.
• Calculate the limits of functions.
• Use the limiting process to find the derivative of a polynomial.
• Apply general rules for differentiating products and quotients.
• Use differentiation to determine the radius of curvature for curves such as vertical curves.
• Apply the rules of differentiation to find the derivatives of implicit functions.
• Determine the maxima and minima of functions.
• Locate the maximum and minimum of a vertical curve.
• Use maxima and minima as an aid to curve sketching.
• Use the graphics calculator to graph curves.
• Solve related rates problems.
• Use Newton-Raphson to solve non-linear equations such as can be found in map projections.
• Find approximate and relative errors using differentials.
• Find the derivatives of trigonometric and inverse trigonometric functions.
• Apply trigonometric differentiation to problems such as finding the radius of curvature at a point on a spheroid.
• Find the derivatives of logarithmic and exponential functions.
• Carry out indefinite integration of polynomials.
• Solve indefinite integrals using more advanced methods of integration.
• Compute the values of definite integrals using a variety of methods including Simpson's Rule and a graphics calculator.
• Apply definite integration to finding areas, volumes and arc lengths particularly of irregular areas and volumes.
• Determine polar moments of inertia in order to help understand the physics of a gyroscope.
• Carry out the expansion of functions using Taylor and Maclaurin series.
• Use series expansions to find some approximate formulae used in geomatics such as reduction of EDM lines.
• Derive some of the formulae used in spiral curves.
• Employ basic calculus laws to find partial derivatives.
• Use partial differentiation to determine some of the parameters used in map projections.
• Carry out the partial differentiation necessary for the solution of small level net problems.
• Use Lagrange multipliers to solve simple minimum/maximum problems.

Effective as of Fall 2003

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