MATH 162 — CALCULUS II
Learning Objectives & Matches
Compute volumes using a variety of methods
Perform computations and apply methods of numerical analysis to data.
Examine theories, such as those of probability and inference, to discover mathematical bases for new or improved methods of obtaining and evaluating numerical data.
Break systems into their components, assign numerical values to each component, and examine the mathematical relationships between them.
Develop computational methods for solving problems that occur in areas of science and engineering or that come from applications in business or industry.
Apply the change of variable theorem to integrals
Compute areas between graphs of function
Compute dimensions, areas, volumes, and weights.
Smooth, polish, and bevel surfaces, using hand tools and power tools.
Determine reference points, machine cutting paths, or hole locations, and compute angular and linear dimensions, radii, and curvatures.
Take measurements and study floor sketches to calculate the area to be carpeted and the amount of material needed.
Cement the edges of the paved area.
Prepare and alter trace maps, charts, tables, detailed drawings, and three-dimensional optical models of terrain using stereoscopic plotting and computer graphics equipment.
Smooth or sand surfaces to remove ridges, tool marks, glue, or caulking.
Remove extra compound after surfaces have been covered sufficiently.
Calculate the exact horizontal and vertical position of points on the Earth's surface.
Create graphs, charts, or other visualizations to convey the results of data analysis using specialized software.
Apply differential and integral calculus techniques to trigonometric functions, exponential functions, logarithmic functions and the inverses of these functions
Apply mathematical theories and techniques to the solution of practical problems in business, engineering, the sciences, or other fields.
Propose solutions in engineering, the sciences, and other fields using mathematical theories and techniques.
Develop computational methods for solving problems that occur in areas of science and engineering or that come from applications in business or industry.
Conduct logical analyses of business, scientific, engineering, and other technical problems, formulating mathematical models of problems for solution by computers.
Analyze problems to develop solutions involving computer hardware and software.
Adapt statistical methods to solve specific problems in many fields, such as economics, biology, and engineering.
Perform computations and apply methods of numerical analysis to data.
Formulate mathematical or simulation models of problems, relating constants and variables, restrictions, alternatives, conflicting objectives, and their numerical parameters.
Examine theories, such as those of probability and inference, to discover mathematical bases for new or improved methods of obtaining and evaluating numerical data.
Write new functions or applications in programming languages to conduct analyses.
Write description of the improper integral as a limit
Evaluate improper integrals
Derive formulas for the derivatives of such functions as arcsin(Q) and arctan(Q) by using the chain rule and the trigonometric identities
Demonstrate knowledge of relationships between exponents and logarithms and their derivatives
Develop new principles and new relationships between existing mathematical principles to advance mathematical science.
Address the relationships of quantities, magnitudes, and forms through the use of numbers and symbols.
Break systems into their components, assign numerical values to each component, and examine the mathematical relationships between them.
Mentor others on mathematical techniques.
Apply mathematical theories and techniques to the solution of practical problems in business, engineering, the sciences, or other fields.
Examine theories, such as those of probability and inference, to discover mathematical bases for new or improved methods of obtaining and evaluating numerical data.
Conduct logical analyses of business, scientific, engineering, and other technical problems, formulating mathematical models of problems for solution by computers.
Propose solutions in engineering, the sciences, and other fields using mathematical theories and techniques.
Educate staff in the use of mathematical models.
Conduct research to extend mathematical knowledge in traditional areas, such as algebra, geometry, probability, and logic.
Demonstrate the ability to perform integration by applying one of the following techniques: Powers of trigonometric functions, Trigonometric substitution, Algebraic substitution, Method of parts, Partial fractions for the linear and the quadratic case
Apply mathematical theories and techniques to the solution of practical problems in business, engineering, the sciences, or other fields.
Understand the development of the natural logarithmic function
Develop new principles and new relationships between existing mathematical principles to advance mathematical science.
Compute arc lengths of curves
Compute numbers, widths, and angles of cutting tools, micrometers, scales, and gauges, and adjust tools to produce specified cuts.
Determine reference points, machine cutting paths, or hole locations, and compute angular and linear dimensions, radii, and curvatures.
Cut rails to specified lengths, using rail saws.
Cut pipes to required lengths.
Position and adjust cutting tools to specified curvature, dimensions, and depth of cut.
Measure, cut, and bend wire and conduit, using measuring instruments and hand tools.
Measure and lay out fence lines and mark posthole positions, following instructions, drawings, or specifications.
Count sections of drill rod to determine depths of boreholes.
Examine finished ware for defects and measure dimensions, using rule and thickness gauge.
Guide lengths of pipe into and out of elevators.
Compute areas of surfaces of revolution
Compute horizontal and vertical coordinates of control networks, using direct leveling or other geodetic survey techniques, such as triangulation, trilateration, and traversing, to establish features of the Earth's surface.
Calculate orbits and determine sizes, shapes, brightness, and motions of different celestial bodies.
Install or maintain landscaped areas, performing tasks such as removing snow, pouring cement curbs, or repairing sidewalks.
Spread, level, or smooth concrete or terrazzo mixtures to form bases or finished surfaces, using rakes, shovels, hand or power trowels, hand or power screeds, or floats.
Fill holes, cracks, and other surface imperfections preparatory to covering surfaces.
Trim, smooth, and shape surfaces, and plane, shave, file, scrape, and sand models to attain specified shapes, using hand tools.
Trim, smooth, and shape surfaces, and plane, shave, file, scrape, and sand models to attain specified shapes, using hand tools.
Apply caulk, sealants, or other agents to installed surfaces.
Shovel, sweep, or otherwise clean work areas.
Measure and mark surfaces to be tiled, following blueprints.