Technical Mathematics MATH 1050

Upon successful completion, the student is expected to be able to:

• Demonstrate unit conversions involving the Imperial System and Systeme International (SI), and percent, ppm and ppb.
• Determine reasonable precision and accuracy in computations involving measured quantities in both scientific and fixed format.
• Calculate perimeters, areas and volumes of regular geometric shapes, and estimate irregular areas and volumes, using numerical methods such as the Trapezoid Rule, Simpson's Rule, and Three-Eighths Rule [e.g., for pools, toxic spill sites, pesticide and toxic waste containers, and septic fields].
• Formulate and solve mixture, flow and circuit problems in up to three unknowns [e.g., applications to include pesticide or chemical mixtures, water flow in streams and pipes, air flow in ventilation ducts, loop currents in multi-loop circuits].
• Algebraically rearrange relevant formulae including rectification of units.
• Formulate and solve problems using common and natural logarithms and corresponding exponential functions [e.g., applications to include pH level, radioactive decay, noise (decibels), sound intensity and sound pressure, serial dilution problems, running log mean, exponential growth, exponential growth to a limiting value, attenuation, amplification, signal-to-noise ratio, circuit transients and time constants in serial RC and RL circuits, implementation of low- and high- pass frequency filters, Nernst potential for gated ion flow across polarized membranes, resting potential for membranes permeable to multiple ionic species].
• Formulate and solve applied problems involving ratio and proportion [e.g. applications to include unit conversions, rates, inverse square law (noise and absorbed radiation dose), areas and volumes of similar figures, map scaling].
• Determine the equation of a curve to represent an experimental data set using the principles of linear regression (least squares) and correlation, and use the equation to appropriately interpolate and extrapolate [e.g., applications to include linear, exponential and power function relationships using Cartesian, semi-log and log-log papers].
• Distinguish between exponential and power function relationships including transformations to linearize data sets of these types [e.g., radioactive decay versus absorbed radiation dose].
• Formulate and solve applied problems requiring trigonometry for both right angle and non-right angle triangles [e.g. applications to include percent grade or slope, transit/clinometer readings for septic field layout, sector areas, as well as Sine and Cosine Law applications to surveying problems, tomography, resolving forces].
• Analyze the graphs of sine and cosine functions to determine amplitude, period, frequency and phase shift, with applications to AC circuits.
• Formulate and solve problems demonstrating an understanding of AC circuit concepts such as voltage-current phase relationships, capacitive reactance, inductive reactance, and impedance in series RLC circuits.
• Use analytic and phasor methods to add sinusoidal waveforms of the same frequency, with applications to simple AC circuits.
• Demonstrate an understanding of Fourier series decomposition of complex waveforms, digital sampling, the Nyquist limit, and the concept of aliasing.
• Demonstrate calculator fluency for all relevant applications.

Effective as of Fall 2005