MATH 2511 - Calculus for Geomatics
Part-time Studies Course
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Differentiation rules for algebraic, trigonometric, inverse trigonometric, logarithmic and exponential functions; related rates, differentials and approximations used in surveying, radius of curvature; selected integration, arc length, the spiral curve; Taylor and Maclaurin series; 3D analytic geometry, partial differentiation with applications in geomatics.
MATH 1511 Credits
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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
MATH 2511 is offered as a part of the following programs:
School of Construction and the Environment
Geomatics Engineering Technology Full-time Diploma
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