Learning Outcomes#
These are the learning outcomes we will be studying in MTH 142, organized by topic. Also included are the relevant sections from the textbook as well as any applicable assessments.
Integration Rule#
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). |
5.4 |
HW I1, Checkpoint Exam, Midterm Exam 1, Final Exam |
I2 |
Calculate a definite integral using the Fundamental Theorem of Calculus. |
5.3 |
HW I2, Checkpoint Exam, Midterm Exam 1, Final Exam |
I3 |
Calculate an indefinite integral using substitution rule. |
5.5 |
HW I3, Checkpoint Exam, Midterm Exam 1, Final Exam |
I4 |
Calculate a definite integral using substitution rule. |
5.5 |
HW I4, Checkpoint Exam, Midterm Exam 1, Final Exam |
I5 |
Calculate an indefinite integral using integration by parts. |
7.1 |
HW I5, Checkpoint Exam, Midterm Exam 1, Final Exam |
I6 |
Calculate a definite integral using integration by parts. |
7.2 |
HW I6, Checkpoint Exam, Midterm Exam 1, Final Exam |
Advanced Integration Techniques#
Number |
Learning Outcome |
Textbook Sections |
Assessments |
|---|---|---|---|
AI1 |
Evaluate a trigonometric integral involving an odd power of sine or cosine. |
7.2 |
HW AI1, Checkpoint Exam, Midterm Exam 1, Final Exam |
AI2 |
Evaluate a trigonometric integral involving only even powers of sine or cosine. |
7.2 |
HW AI2, Checkpoint Exam, Midterm Exam 1, Final Exam |
AI3 |
Evaluate a trigonometric integral involving powers of secant and tangent. |
7.2 |
HW AI3, Checkpoint Exam, Midterm Exam 1, Final Exam |
AI4 |
Use a trigonometric substitution to convert an integral of \(x\) into an integral of theta. |
7.3 |
HW AI4, Checkpoint Exam, Midterm Exam 1, Final Exam |
AI5 |
Evaluate an integral (indefinite or definite) using a trigonometric substitution. |
7.3 |
HW AI5, Checkpoint Exam, Midterm Exam 1, Final Exam |
AI6 |
Find a partial fraction decomposition of a rational function. |
7.4 |
HW AI6, Checkpoint Exam, Midterm Exam 1, Final Exam |
AI7 |
Evaluate the integral of a rational function using a partial fraction decomposition. |
7.4 |
HW AI7, Checkpoint Exam, Midterm Exam 1, Final Exam |
AI8 |
Determine whether an improper integral is convergent or divergent. If convergent evaluate the integral. |
7.8 |
HW AI8, Checkpoint Exam, Midterm Exam 1, Final Exam |
AI9 |
Determine for which values of \(p\) the improper integral involving \(1/x^p\) is convergent and for which values of \(p\) the integral is divergent. |
7.8 |
HW AI9, Checkpoint Exam, Midterm Exam 1, Final Exam |
Applications of Definite Integrals#
Number |
Learning Outcome |
Textbook Sections |
Assessments |
|---|---|---|---|
AD1 |
Calculate the area of a region bounded by curves, using a definite integral. |
6.1 |
HW AD1, Checkpoint Exam, Midterm Exam 1, Final Exam |
AD2 |
Calculate the volume of a solid of revolution, using a a definite integral. Sketch a typical approximating disk/washer and state the inner radius and outer radius as part of your work. |
6.2 |
HW AD2, Checkpoint Exam, Midterm Exam 1, Final Exam |
AD3 |
Calculate the exact length of a curve over an interval, using a definite integral. |
8.1 |
HW AD3, Checkpoint Exam, Midterm Exam 1, Final Exam |
Parametric Equations#
Number |
Learning Outcome |
Textbook Sections |
Assessments |
|---|---|---|---|
PE1 |
Given parametric equations \(x = f (t)\), \(y = g(t)\) for a curve, sketch the curve using the parametric equations to plot points. Indicate, using an arrow, the direction in which the curve is traced as t increases. |
10.1 |
HW PE1, Checkpoint Exam, Midterm Exam 2, Final Exam |
PE2 |
Given parametric equations \(x = f (t)\), \(y = g(t)\) for a curve, eliminate the parameter to find a Cartesian equation of the curve. |
10.1 |
HW PE2, Checkpoint Exam, Midterm Exam 2, Final Exam |
PE3 |
Given parametric equations \(x=f(t)\), \(y=g(t)\) for a curve, find \(dy/dx\). |
10.2 |
HW PE3, Checkpoint Exam, Midterm Exam 2, Final Exam |
PE4 |
Given parametric equations \(x=f(t)\), \(y=g(t)\) for a curve, find the exact length of the curve. |
10.2 |
HW PE4, Checkpoint Exam, Midterm Exam 2, Final Exam |
Polar Coordinates#
Number |
Learning Outcome |
Textbook Sections |
Assessments |
|---|---|---|---|
PC1 |
Plot points given in polar coordinates. Convert from polar coordinates to Cartesian coordinates. Convert between Cartesian and Polar coordinates. |
10.3 |
HW PC1, Checkpoint Exam, Midterm Exam 2, Final Exam |
PC2 |
Convert a point in Cartesian coordinates to polar coordinates. |
10.3 |
HW PC2, Checkpoint Exam, Midterm Exam 2, Final Exam |
PC3 |
Sketch polar curves and polar regions. |
10.3 |
HW PC3, Checkpoint Exam, Midterm Exam 2, Final Exam |
Introduction to Series#
Number |
Learning Outcome |
Textbook Sections |
Assessments |
|---|---|---|---|
S1 |
List the first few terms of a sequence given the general term \(a_n\). |
11.1 |
HW S1, Checkpoint Exam, Midterm Exam 2, Final Exam |
S2 |
Determine whether a sequence is convergent or divergent. |
11.1 |
HW S2, Checkpoint Exam, Midterm Exam 2, Final Exam |
S3 |
Given an infinite series, find partial sums of the series. |
11.2 |
HW S3, Checkpoint Exam, Midterm Exam 2, Final Exam |
S4 |
Determine whether a geometric series is convergent or divergent. If convergent find the sum. |
11.2 |
HW S4, Checkpoint Exam, Midterm Exam 2, Final Exam |
S5 |
State for which values of parameter \(p\), the \(p\)-series is convergent / divergent. |
11.3 |
HW S5, Checkpoint Exam, Midterm Exam 2, Final Exam |
Series Testing#
Number |
Learning Outcome |
Textbook Sections |
Assessments |
|---|---|---|---|
ST1 |
Use the Test for Divergence to show a series is divergent. |
11.2 |
HW ST1, Checkpoint Exam, Midterm Exam 2, Final Exam |
ST2 |
Use the Integral Test to test the convergence or divergence of an infinite series. |
11.3 |
HW ST2, Checkpoint Exam, Midterm Exam 2, Final Exam |
ST3 |
Use the Comparison Test to test the convergence or divergence of a series with positive terms. |
11.4 |
HW ST3, Checkpoint Exam, Midterm Exam 2, Final Exam |
ST4 |
Use the Limit Comparison Test to test the convergence or divergence of a series with positive terms. |
11.4 |
HW ST4, Checkpoint Exam, Midterm Exam 2, Final Exam |
ST5 |
Use the Alternating Series Test to show an alternating series is convergent. |
11.5 |
HW ST5, Checkpoint Exam, Midterm Exam 2, Final Exam |
ST6 |
Determine if a series is absolutely convergent or conditionally convergent. |
11.6 |
HW ST6, Checkpoint Exam, Midterm Exam 2, Final Exam |
ST7 |
Use the Ratio Test to determine if a series is convergent or divergent. |
11.6 |
HW ST7, Checkpoint Exam, Midterm Exam 2, Final Exam |
ST8 |
Use the Root Test to determine if a series is convergent or divergent. |
11.6 |
HW ST8, Checkpoint Exam, Midterm Exam 2, Final Exam |
Power Series#
Number |
Learning Outcome |
Textbook Sections |
Assessments |
|---|---|---|---|
PS1 |
Find the radius of convergence \(R\) for a power series. |
11.8 |
HW PS1, Checkpoint Exam, Final Exam |
PS2 |
Find the interval of convergence for a power series. |
11.8 |
HW PS2, Checkpoint Exam, Final Exam |
PS3 |
Find a power series expression for a function \(f\) that can be generated from \({1}/{1-x}\) through multiplication by \(x^k\) and/or composition of functions. |
11.9 |
HW PS3, Checkpoint Exam, Final Exam |
PS4 |
Use term-by-term differentiation or integration to express a function as a power series. |
11.9 |
HW PS4, Checkpoint Exam, Final Exam |
PS5 |
Find a Taylor Series of a function \(f\) centered at \(a\). Find the associated radius of convergence. |
11.10 |
HW PS5, Checkpoint Exam, Final Exam |
PS6 |
Find the Maclaurin Series of a function \(f\). Find the associated radius of convergence. |
11.10 |
HW PS6, 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.