Learning Outcomes#
These are the learning outcomes we will be studying in MTH 131, organized by topic. Also included are the relevant sections from the textbook as well as any applicable assessments.
Functions#
Number |
Learning Outcome |
Textbook Sections |
Assessments |
|---|---|---|---|
F1 |
Evaluating functions graphically, numerically, and algebraically. |
1.1 |
HW F1, Checkpoint Exam, Midterm Exam 1, Final Exam |
F2 |
Perform a break-even analysis involving cost, profit, revenue, or supply/demand equations. |
1.2 |
HW F2, Checkpoint Exam, Midterm Exam 1, Final Exam |
F3 |
Find the slope and/or equation for a linear function. |
1.3 |
HW F3, Checkpoint Exam, Midterm Exam 1, Final Exam |
F4 |
Find the vertex, \(y\)-intercept, and any \(x\)-intercepts for a quadratic function. |
2.1 |
HW F4, Checkpoint Exam, Midterm Exam 1, Final Exam |
F5 |
Find an equation for an exponential function. |
2.2 |
HW F5, Checkpoint Exam, Midterm Exam 1, Final Exam |
F6 |
Use an exponential function to model continuously compounded interest. |
2.2 |
HW F6, Checkpoint Exam, Midterm Exam 1, Final Exam |
F7 |
Simplify an expression using logarithmic identities. |
2.3 |
HW F7, Checkpoint Exam, Midterm Exam 1, Final Exam |
F8 |
Use logarithms to help answer questions about continuously compounded interest. |
2.3 |
HW F8, Checkpoint Exam, Midterm Exam 1, Final Exam |
Limits#
Number |
Learning Outcome |
Textbook Sections |
Assessments |
|---|---|---|---|
L1 |
Estimate limits numerically and graphically. |
3.1 |
HW L1, Checkpoint Exam, Midterm Exam 1, Final Exam |
L2 |
Graphically, determine if a function is continuous on its domain. |
3.2 |
HW L2, Checkpoint Exam, Midterm Exam 1, Final Exam |
L3 |
Calculate limits algebraically. |
3.3 |
HW L3, Checkpoint Exam, Midterm Exam 1, Final Exam |
L4 |
Calculate the average rate of change of a function over a given interval. |
3.4 |
HW L4, Checkpoint Exam, Midterm Exam 1, Final Exam |
L5 |
Estimate the value of the derivative numerically and graphically. |
3.5 |
HW L5, Checkpoint Exam, Midterm Exam 1, Final Exam |
L6 |
Calculate the derivative using limits. |
3.6 |
HW L6, Checkpoint Exam, Midterm Exam 1, Final Exam |
L7 |
Find the equation of a tangent line using derivatives. |
3.5 & 3.6 |
HW L7, Checkpoint Exam, Midterm Exam 1, Final Exam |
Derivatives#
Number |
Learning Outcome |
Textbook Sections |
Assessments |
|---|---|---|---|
D1 |
Calculate derivatives using basic derivative rules. |
4.1 |
HW D1, Checkpoint Exam, Midterm Exam 2, Final Exam |
D2 |
Find the marginal cost (marginal profit, marginal revenue) function, given the cost (profit, revenue) function. |
4.2 |
HW D2, Checkpoint Exam, Midterm Exam 2, Final Exam |
D3 |
Use the product rule to calculate a derivative. |
4.3 |
HW D3, Checkpoint Exam, Midterm Exam 2, Final Exam |
D4 |
Use the quotient rule to calculate a derivative. |
4.3 |
HW D4, Checkpoint Exam, Midterm Exam 2, Final Exam |
D5 |
Use the chain rule to calculate a derivative. |
4.4 |
HW D5, Checkpoint Exam, Midterm Exam 2, Final Exam |
D6 |
Calculate derivatives of functions involving logarithmic and exponential functions. |
4.5 |
HW D6, Checkpoint Exam, Midterm Exam 2, Final Exam |
D7 |
Use implicit differentiation to calculate the derivative of an implicitly defined function. |
4.6 |
HW D7, Checkpoint Exam, Midterm Exam 2, Final Exam |
Optimization#
Number |
Learning Outcome |
Textbook Sections |
Assessments |
|---|---|---|---|
O1 |
Find and classify any critical numbers using the First Derivative Test. |
5.1 |
HW O1, Checkpoint Exam, Midterm Exam 2, Final Exam |
O2 |
Find and classify the extrema of a function defined on a closed interval or an unbounded interval. |
5.1 |
HW O2, Checkpoint Exam, Midterm Exam 2, Final Exam |
O3 |
Optimize a cost, profit, or revenue function. |
5.2 |
HW O3, Checkpoint Exam, Midterm Exam 2, Final Exam |
O4 |
Calculate higher order derivatives of a function. |
5.3 |
HW O4, Checkpoint Exam, Midterm Exam 3, Final Exam |
O5 |
Find and classify any critical numbers using the Second Derivative Test. |
5.3 |
HW O5, Checkpoint Exam, Midterm Exam 3, Final Exam |
O6 |
Use the second derivative to determine where a graph is concave up / concave down, where a function is accelerating / decelerating, and where this change happens (points of inflection). |
5.3 & 5.4 |
HW O6, Checkpoint Exam, Midterm Exam 3, Final Exam |
O7 |
Solve related rates problems involving cost, revenue, profit, demand, and production. |
5.5 |
HW O7, Checkpoint Exam, Midterm Exam 3, Final Exam |
O8 |
Solve problems involving the price elasticity and income elasticity of demand functions. |
5.6 |
HW O8, Checkpoint Exam, Midterm Exam 3, Final Exam |
Integration#
Number |
Learning Outcome |
Textbook Sections |
Assessments |
|---|---|---|---|
I1 |
Calculate an indefinite integral using basic antiderivative rules. |
6.1 |
HW I1, Checkpoint Exam, Midterm Exam 3, Final Exam |
I2 |
Calculate a definite integral using the Fundamental Theorem of Calculus. |
6.4 |
HW I2, Checkpoint Exam, Midterm Exam 3, Final Exam |
I3 |
Use substitution rule to calculate an integral (when necessary). |
6.2 |
HW I3, Checkpoint Exam, Midterm Exam 3, Final Exam |
I4 |
Use integration by parts to calculate an integral (when necessary). |
7.1 |
HW I4, Checkpoint Exam, Midterm Exam 3, Final Exam |
Applications of Integration#
Number |
Learning Outcome |
Textbook Sections |
Assessments |
|---|---|---|---|
AI1 |
Find a particular antiderivative in applied problems. (6.1) |
6.1 |
HW AI1, Checkpoint Exam, Midterm Exam 3, Final Exam |
AI2 |
Calculate the area under the graph using definite integrals. |
6.3 |
HW AI2, Checkpoint Exam, Midterm Exam 3, Final Exam |
AI3 |
Calculate the area between two curves using definite integrals. |
7.2 |
HW AI3, Checkpoint Exam, Midterm Exam 3, Final Exam |
AI4 |
Find the average value of a function over a given interval. |
7.3 |
HW AI4, Checkpoint Exam, Final Exam |
AI5 |
Calculate the consumers’ surplus or producers’ surplus at a given price. |
7.4 |
HW AI5, Checkpoint Exam, Final Exam |
AI6 |
Calculate the total value of a continuous income stream. |
7.4 |
HW AI6, Checkpoint Exam, Final Exam |
Meta - Outcomes#
Mastering the above itemized learning outcomes means a student is able to:
Choose appropriate methods or models for a given problem, using information from observed or deduced data and knowledge of the system being studied.
Employ quantitative methods, mathematical models, statistics, and/or logic to solve real-world problems beyond the level of basic algebra.
Identify common mistakes and/or limitations in empirical and deductive reasoning, and in mathematical, quantitative, and/or logical problem solving.
Interpret mathematical models, formulas, graphs, and/or tables, to draw inferences from them, and explain these inferences.