MATH 161 — CALCULUS I
Learning Objectives & Matches
Demonstrate a conceptual knowledge of the derivative as a limit of slopes of secants, as the slope of non-vertical tangents and as the rate of change of one quantity with respect to another
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.
Describe the derivative as a function derived from another function
State the definition of the derivative
Interpret and explain policies, rules, regulations, or laws to organizations, government or corporate officials, or individuals.
Interpret laws, rulings and regulations for individuals and businesses.
Develop or implement policies, standards, or procedures for engineering and technical work.
Find the equation of the tangent line to a curve at a given point
Sketch the qualitatively valid graph of the derivative of a function presented graphically (formulas not used)
Create graphs, charts, or other visualizations to convey the results of data analysis using specialized software.
Prepare tables and graphs to present clinical data or results.
Report results of statistical analyses, including information in the form of graphs, charts, and tables.
Use the definition of the derivative to find the derivative of a first-degree polynomial
Find the points on the graph with a vertical tangent
Calculate the exact horizontal and vertical position of points on the Earth's surface.
Calculate angles and courses and determine vertical and horizontal alignment of courses.
Check slopes for conformance to requirements, using levels or lasers.
Find the points where the derivative is zero for such derived functions as acceleration and velocity
Calculate the exact horizontal and vertical position of points on the Earth's surface.
State the chain rule in terms of rate of change
Review or update supply chain practices in accordance with new or changing environmental policies, standards, regulations, or laws.
Determine price schedules and discount rates.
Calculate duty and tariff payments owed on shipments.
Implement new or improved supply chain processes to improve efficiency or performance.
Explain changes in contract provisions to customers.
Demonstrate the role of continuity in evaluating limits graphically and numerically
Create graphs, charts, or other visualizations to convey the results of data analysis using specialized software.
Perform computations and apply methods of numerical analysis to data.
Construct simple epsilon and delta proofs
Check preliminary and final proofs for errors and make necessary corrections.
Read copy or proof to detect and correct errors in spelling, punctuation, and syntax.
Verify signatures and required information on checks.
Testify in court and present evidence.
Read corrected copies or proofs to ensure that all corrections have been made.
Compute, without consulting a table of derivatives, derivatives of polynomial functions combining products, sums, quotients, compositions and exponentiations
Compute sales prices, total purchases, and receive and process cash or credit payment.
Compute total charges for merchandise or services and shipping charges.
Compute amounts, such as space available, shipping, storage, or demurrage charges, using computer or price list.
Compute cost of travel and accommodations, using calculator, computer, carrier tariff books, and hotel rate books, or quote package tour's costs.
Compute mathematical formulas to develop and design detailed specifications for components or machinery, using computer-assisted equipment.
Perform financial calculations, such as amounts due, interest charges, balances, discounts, equity, and principal.
Calculate purchase subtotals, taxes, and shipping costs for submission to customers.
Calculate, review, and correct errors on interest, principal, payment, and closing costs, using computers or calculators.
Calculate revenue, sales, and expenses, using financial accounting or spreadsheet software.
Perform complex calculations as part of the analysis and evaluation of data, using computers.
Sketch graphs for polynomial functions giving the rational critical points, indicating concavity, increasing and decreasing regions, and including the behavior near special points
Draw maps, diagrams, and profiles, using cross-sections and surveys, to represent elevations, topographical contours, subsurface formations, and structures.
Prepare graphs, charts, diagrams, or other aids to illustrate observations or conclusions.
Draw sketches to illustrate specified materials or assembly sequence.
Review and detail shop drawings for construction plans.
Given distance function, derive the velocity and acceleration functions and vice versa
Apply implicit differentiation in solving maximum-minimum and related rate problems
Determine price schedules and discount rates.
Negotiate with carriers, warehouse operators, or insurance company representatives for services and preferential rates.
Define the integral as a limit of Riemann sums and/or as the limit of upper and lower sums
Give the geometric interpretations of the definite integral
Integrate and develop visual elements, such as line, space, mass, color, and perspective, to produce desired effects, such as the illustration of ideas, emotions, or moods.
Create visual representations of geospatial data, using complex procedures such as analytical modeling, three-dimensional renderings, or plot creation.
Describe the integral in terms of the antiderivative
Understand and apply the fundamental theorem of calculus
Understand and apply the Mean Value Theorem
Sketch the graph of the antiderivative, F, through (a, b) given a sketch of f
Draw details on outlined parts to indicate where parts are to be joined, as well as the positions of pleats, pockets, buttonholes, and other features, using computers or drafting instruments.
Determine plumb of walls or ceilings, using plumb lines and levels.
Draw and print charts, graphs, illustrations, and other artwork, using computer.
Measure and lay out fence lines and mark posthole positions, following instructions, drawings, or specifications.
Evaluate (approximately) definite integrals using approximate sums
Compute areas under a curve
Perform computations and apply methods of numerical analysis to data.