Learning Outcomes#
These are the learning outcomes we will be studying in MTH 141, organized by topic. Also included are the relevant sections from the textbook as well as any applicable assessments.
Limits#
Number |
Learning Outcome |
Textbook Sections |
Assessments |
|---|---|---|---|
L1 |
Estimate the limit of a function at a point using graphical methods. |
2.2 |
HW L1, Checkpoint Exam, Midterm Exam 1, Final Exam |
L2 |
Estimate the limit of a function at a point using numerical methods. |
2.2 |
HW L2, Checkpoint Exam, Midterm Exam 1, Final Exam |
L3 |
Find the limit of a continuous function at a point using algebraic methods. |
2.3, 2.5 |
HW L3, Checkpoint Exam, Midterm Exam 1, Final Exam |
L4 |
Find the limit of a function in a \(c/0\) form. Find any vertical asymptotes. |
2.2 |
HW L4, Checkpoint Exam, Midterm Exam 1, Final Exam |
L5 |
Find the limit of a function in a \(0/0\) form using algebraic methods. |
2.3 |
HW L5, Checkpoint Exam, Midterm Exam 1, Final Exam |
L6 |
Determine and explain why a function is continuous (or not). |
2.5 |
HW L6, Checkpoint Exam, Midterm Exam 1, Final Exam |
L7 |
Find the limit of a function at infinity. Find any horizontal asymptotes |
2.6 |
HW L7, Checkpoint Exam, Midterm Exam 1, Final Exam |
L8 |
Identify limits in indeterminate form and apply L’Hospital’s Rule to evaluate them. |
4.4 |
HW L8, Checkpoint Exam, Midterm Exam 1, Final Exam |
Derivatives - Conceptual#
Number |
Learning Outcome |
Textbook Sections |
Assessments |
|---|---|---|---|
DC1 |
Find the slope of a secant line. Use limits to then find the slope of the tangent line. |
2.1, 2.7 |
HW DC1, Checkpoint Exam, Midterm Exam 1, Final Exam |
DC2 |
Find the average velocity on a time interval. Use limits to then find the instantaneous velocity. |
2.1, 2.7 |
HW DC2, Checkpoint Exam, Midterm Exam 1, Final Exam |
DC3 |
Find the derivative of a function, both at a point and as a function, using the limit definition of the derivative. |
2.7, 2.8 |
HW DC3, Checkpoint Exam, Midterm Exam 1, Final Exam |
DC4 |
Determine where a function is differentiable given a graph or formula of the function and explain why. |
2.5, 2.8 |
HW DC4, Checkpoint Exam, Midterm Exam 1, Final Exam |
DC5 |
Estimate the value of a derivative graphically. |
2.7, 2.8 |
HW DC5, Checkpoint Exam, Midterm Exam 1, Final Exam |
DC6 |
Estimate the value of a derivative using difference quotients. Interpret the meaning of a derivative in context and state the units. |
2.7, 2.8 |
HW DC6, Checkpoint Exam, Midterm Exam 1, Final Exam |
DC7 |
Use the derivative to help find the equation of the tangent line. |
2.1, 2.7 |
HW DC7, Checkpoint Exam, Midterm Exam 1, Final Exam |
Derivative Rules#
Number |
Learning Outcome |
Textbook Sections |
Assessments |
|---|---|---|---|
D1 |
Compute derivatives using sum, difference, or constant multiple rules in conjunction with our list of elementary forms. |
3.1, 3.3, 3.6 |
HW D1, Checkpoint Exam, Midterm Exam 1, Final Exam |
D2 |
Compute derivatives of products of functions. |
3.2 |
HW D2, Checkpoint Exam, Midterm Exam 1, Final Exam |
D3 |
Compute derivatives of quotients of functions. |
3.3 |
HW D3, Checkpoint Exam, Midterm Exam 1, Final Exam |
D4 |
Compute derivatives of composite power functions. |
3.4 |
HW D4, Checkpoint Exam, Midterm Exam 1, Final Exam |
D5 |
Compute derivatives of composite trigonometric or inverse trigonometric functions. |
3.4, 3.6 |
HW D5, Checkpoint Exam, Midterm Exam 1, Final Exam |
D6 |
Compute derivatives of composite exponential or logarithmic functions. |
3.4, 3.6 |
HW D6, Checkpoint Exam, Midterm Exam 1, Final Exam |
D7 |
Compute derivatives using multiple rules in combination. |
3.5 |
HW D7, Checkpoint Exam, Midterm Exam 2, Final Exam |
D8 |
Compute derivatives of implicitly-defined functions and find the slope of the tangent line to an implicit curve. |
3.6 |
HW D8, Checkpoint Exam, Midterm Exam 2, Final Exam |
Derivatives and Graphs#
Number |
Learning Outcome |
Textbook Sections |
Assessments |
|---|---|---|---|
DG1 |
Use the graph of \(f\) to find the intervals of increase / decrease for a function \(f\). |
4.1 |
HW DG1, Checkpoint Exam, Midterm Exam 2, Final Exam |
DG2 |
Use the derivative \(f'\) to find the intervals of increase / decrease for a function \(f\). |
4.3 |
HW DG2, Checkpoint Exam, Midterm Exam 2, Final Exam |
DG3 |
Use the graph of \(f\) to find the intervals of concavity and inflection points for a function \(f\). |
4.1 |
HW DG3, Checkpoint Exam, Midterm Exam 2, Final Exam |
DG4 |
Use the second derivative \(f''\) to find the intervals of concavity and inflection points for a function \(f\). |
4.3 |
HW DG4, Checkpoint Exam, Midterm Exam 2, Final Exam |
DG5 |
Given information about \(f\), \(f'\), or \(f''\) determine the behavior of \(f\), \(f'\), or \(f''\) as related to increasing/decreasing, concavity, and extrema. |
2.8, 4.1, 4.3 |
HW DG5, 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. |
4.3, 4.5 |
HW O1, Checkpoint Exam, Midterm Exam 2, Final Exam |
O2 |
Find and classify any critical numbers using the Second Derivative Test. |
4.3. 4.5 |
HW O2, Checkpoint Exam, Midterm Exam 2, Final Exam |
O3 |
Use the Extreme Value Theorem to find and classify the absolute extrema on a closed interval. |
4.1 |
HW O3, Checkpoint Exam, Midterm Exam 2, Final Exam |
O4 |
Solve a basic applied optimization problem using derivatives. |
4.7 |
HW O4, Checkpoint Exam, Midterm Exam 2, Final Exam |
O5 |
Solve a more complicated applied optimization problem using derivatives. |
4.7 |
HW O5, Checkpoint Exam, Midterm Exam 2, Final Exam |
Integration Rules#
Number |
Learning Outcome |
Textbook Sections |
Assessments |
|---|---|---|---|
I1 |
Calculate the indefinite integral of basic functions (integrals that can ultimately be solved by using the sum, difference, or constant multiple rules in conjunction with our list of the elementary forms). |
4.9, 5.4 |
HW I1, Checkpoint Exam, Midterm Exam 2, Final Exam |
I2 |
Calculate a definite integral using the Fundamental Theorem of Calculus. |
5.3 |
HW I2, Checkpoint Exam, Final Exam |
I3 |
Calculate an indefinite integral using the substitution rule. |
5.5 |
HW I3, Checkpoint Exam, Final Exam |
I4 |
Calculate a definite integral using the substitution rule. |
5.5 |
HW I4, Checkpoint Exam, Final Exam |
Integration - Conceptual#
Number |
Learning Outcome |
Textbook Sections |
Assessments |
|---|---|---|---|
IC1 |
Find an antiderivative of a function that passes through a specific point. Given s(t), v(t), or a(t) calculate s(t), v(t), or a(t) using either differentiation or integration as needed. |
4.9, 5.4 |
HW IC1, Checkpoint Exam, Midterm Exam 2, Final Exam |
IC2 |
Use definite integrals to calculate the net area between a curve and the x-axis. |
5.1, 5.2, 5.3 |
HW IC2, Checkpoint Exam, Final Exam |
IC3 |
Use definite integrals to calculate the total area between a curve and the x-axis. |
5.1, 5.2, 5.3 |
HW IC3, Checkpoint Exam, Final Exam |
IC4 |
Use definite integrals to calculate the displacement and total distance traveled by an object moving in a straight line. More generally, use definite integrals to calculate net change. |
5.1, 5.2, 5.3 |
HW IC4, Checkpoint Exam, Final Exam |
IC5 |
Explain the definition of the definite integral using approximating rectangles. Calculate a Riemann Sum for a function over a given interval. |
5.3 |
HW IC5, 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.