Learning Outcomes#
These are the learning outcomes we will be studying in MTH 121, organized by topic. Also included are the relevant sections from the textbook as well as any applicable assessments.
Tangent Lines and Limits#
Number |
Learning Outcome |
Textbook Sections |
Assessments |
|---|---|---|---|
TL-1 |
Find the equation of a line. |
1.1 |
HW TL-1, Checkpoint Exam, Midterm Exam |
TL-2 |
Graphically estimate the slope of a curve at a point. |
1.2 |
HW TL-2, Checkpoint Exam, Midterm Exam |
TL-3 |
Calculate the derivative of a function using power rule. |
1.3 |
HW TL-3, Checkpoint Exam, Midterm Exam |
TL-4 |
Find the equation of a tangent line. |
1.3 |
HW TL-4, Checkpoint Exam, Midterm Exam |
TL-5 |
Compute the value of a limit graphically. |
1.4 |
HW TL-5, Checkpoint Exam, Midterm Exam |
TL-6 |
Compute the value of a limit algebraically. |
1.4 |
HW TL-6, Checkpoint Exam, Midterm Exam |
TL-7 |
Find the derivative of a function using the limit definition of derivative. |
1.4 |
HW TL-7, Checkpoint Exam, Midterm Exam |
TL-8 |
Determine if a function is continuous and / or differentiable at a number. |
1.5 |
HW TL-8, Checkpoint Exam, Midterm Exam |
Basic Derivative Rules#
Number |
Learning Outcome |
Textbook Sections |
Assessments |
|---|---|---|---|
BD-1 |
Calculate the first derivative of a function using basic derivative rules. |
1.6 |
HW BD-1, Checkpoint Exam, Midterm Exam |
BD-2 |
Find the second derivative of a function. |
1.7 |
HW BD-2, Checkpoint Exam, Midterm Exam |
BD-3 |
Calculate the average rate of change of a function over an interval. |
1.7 |
HW BD-3, Checkpoint Exam, Midterm Exam |
BD-4 |
Calculate the instantaneous rate of change of a function including units. |
1.8 |
HW BD-4, Checkpoint Exam, Midterm Exam |
BD-5 |
Use derivatives to solve problems related to motion in a straight line. |
1.8 |
HW BD-5, Checkpoint Exam, Midterm Exam |
Derivatives and Graphs#
Number |
Learning Outcome |
Textbook Sections |
Assessments |
|---|---|---|---|
DG-1 |
Determine, graphically, where a function is increasing / decreasing / concave up / concave down. |
2.1 |
HW DG-1, Checkpoint Exam, Midterm Exam |
DG-2 |
Determine, graphically, the intervals where \(f'\) and \(f''\) are postive and negative. |
2.2 |
HW DG-2, Checkpoint Exam, Midterm Exam |
DG-3 |
Find the intervals of increase / decrease for a function using its first derivative. |
2.3 |
HW DG-3, Checkpoint Exam, Midterm Exam |
DG-4 |
Find the intervals of concavity and any inflection points for a function using its second derivative. |
2.3 |
HW DG-4, Checkpoint Exam, Midterm Exam |
DG-5 |
Find and then classify the critical numbers of a function using the First and Second Derivative Tests. |
2.3 |
HW DG-5, Checkpoint Exam, Midterm Exam |
DG-6 |
Sketch a graph using information about the intervals of increase / decrease / concave up / concave down / extreme points / inflection points. |
2.4 |
HW DG-6, Checkpoint Exam, Midterm Exam |
Derivatives and Optimization#
Number |
Learning Outcome |
Textbook Sections |
Assessments |
|---|---|---|---|
DO-1 |
Solve a constrained optimization problem. |
2.5 |
HW DO-1, Checkpoint Exam, Midterm Exam |
DO-2 |
Solve an applied optimization problem. |
2.5 & 2.6 |
HW DO-2, Checkpoint Exam, Midterm Exam |
DO-3 |
Solve problems related to marginal profit, revenue, cost. |
1.7 |
HW DO-3, Checkpoint Exam, Midterm Exam |
DO-4 |
Use calculus to optimize a profit, revenue, or cost function. |
2.7 |
HW DO-4, Checkpoint Exam, Midterm Exam |
DO-5 |
Solve an applied optimization problem involving inventory control. |
2.6 |
HW DO-5, Checkpoint Exam, Midterm Exam |
Advanced Differentiation Rules#
Number |
Learning Outcome |
Textbook Sections |
Assessments |
|---|---|---|---|
AD-1 |
Use the product rule to differentiate a function. |
3.1 |
HW AD-1, Checkpoint Exam, Midterm Exam |
AD-2 |
Use the quotient rule to differentiate a function. |
3.1 |
HW AD-2, Checkpoint Exam, Midterm Exam |
AD-3 |
Differentiate a composite function using chain rule. |
3.2 |
HW AD-3, Checkpoint Exam, Midterm Exam |
AD-4 |
Use implicit differentiation to find an expression for the derivative. |
3.3 |
HW AD-4, Checkpoint Exam, Midterm Exam |
AD-5 |
Use implicit differentiation to solve related rates problems. |
3.3 |
HW AD-5, Checkpoint Exam, Midterm Exam |
Exponential and Logarithmic Functions#
Number |
Learning Outcome |
Textbook Sections |
Assessments |
|---|---|---|---|
EL-1 |
Simplify and solve basic exponential equations. |
4.1 and 4.2 |
HW EL-1, Checkpoint Exam, Midterm Exam |
EL-2 |
Simplify and solve general exponential and logarithmic equations. |
4.4 |
HW EL-2, Checkpoint Exam, Midterm Exam |
EL-3 |
Differentiate a function involving \(e^x\) and \(\ln x\). |
4.2 and 4.5 |
HW EL-3, Checkpoint Exam, Midterm Exam |
EL-4 |
Differentiate a function involving \(e^{u({x})}.\) |
4.3 |
HW EL-4, Checkpoint Exam, Midterm Exam |
EL-5 |
Differentiate a function involving \(\ln\big({u({x})}\big)\). |
4.5 |
HW EL-5, Checkpoint Exam, Midterm Exam |
EL-6 |
Use logarithmic properties to help differentiate a complicated function. |
4.6 |
HW EL-6, Checkpoint Exam, Midterm Exam |
Applications of Exponential and Logarithmic Functions#
Number |
Learning Outcome |
Textbook Sections |
Assessments |
|---|---|---|---|
AEL-1 |
Model exponential growth and decay. |
5.1 |
HW AEL-1, Checkpoint Exam, Midterm Exam |
AEL-2 |
Model continuously compounded interest. |
5.2 |
HW AEL-2, Checkpoint Exam, Midterm Exam |
AEL-3 |
Find the relative rate of change of a function. |
5.3 |
HW AEL-3, Checkpoint Exam, Midterm Exam |
AEL-4 |
Model diffusion using an exponential model. |
5.4 |
HW AEL-4, Checkpoint Exam, Midterm Exam |
Integration#
Number |
Learning Outcome |
Textbook Sections |
Assessments |
|---|---|---|---|
I-1 |
Calculate an indefinite integral using basic antiderivative rules. |
6.1 |
HW I-1, Checkpoint Exam, Midterm Exam |
I-2 |
Find a particular antiderivative in applied problems. |
6.1 |
HW I-2, Checkpoint Exam, Midterm Exam |
I-3 |
Calculate a definite integral using the Fundamental Theorem of Calculus. |
6.2 |
HW I-3, Checkpoint Exam, Midterm Exam |
I-4 |
Calculate the area under the graph of a non-negative function using definite integrals. |
6.3 |
HW I-4, Checkpoint Exam, Midterm Exam |
I-5 |
Calculate the area under the graph of a general function using definite integrals. |
6.4 |
HW I-5, Checkpoint Exam, Midterm Exam |
I-6 |
Calculate the area between two curves using definite integrals. |
6.4 |
HW I-6, Checkpoint Exam, Midterm Exam |
I-7 |
Find the average value of a function over a given interval. |
6.5 |
HW I-7, Checkpoint Exam, Midterm 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.