<?xml version='1.0' encoding='UTF-8'?>
<bank xmlns="https://checkit.clontz.org" version="0.1">
<title>Differential Equations</title>
<url>https://github.com/StevenClontz/checkit-clontz-diff-eq</url>
<outcomes>
<outcome>
<title>Structure of an IVP and Verifying Solutions</title>
<slug>AA1</slug>
<description>
Identify the structure of an initial value problem and its solution.
</description>
<alignment>
Fundamentals of Differential Equations and Boundary Value Problems, 7th ed; 1.1 and 1.2
</alignment>
</outcome>
<outcome>
<title>Direction Fields</title>
<slug>AA2</slug>
<description>
Use technology to generate a direction/slope field for a first-order ODE,
and interpret this field to approximate
the value of an IVP solution at a point.
</description>
<alignment>
Fundamentals of Differential Equations and Boundary Value Problems, 7th ed; 1.3
</alignment>
</outcome>
<outcome>
<title>Euler's Method</title>
<slug>AA3</slug>
<description>
Implement Euler's Method for a first-order IVP to approximate
the value of an IVP solution at a point.
</description>
<alignment>
Fundamentals of Differential Equations and Boundary Value Problems, 7th ed; 1.4
</alignment>
</outcome>
<outcome>
<title>Existence/uniqueness IVP Theorems</title>
<slug>AA4</slug>
<description>
Apply appropriate theorems to determine the largest possible domain for which an IVP
is guaranteed a unique solution.
</description>
<alignment>
Fundamentals of Differential Equations and Boundary Value Problems, 7th ed; 1.2 and 6.1
</alignment>
</outcome>
<outcome>
<title>Constant-Coefficient Linear Homogeneous First-Order IVPs</title>
<slug>CC1</slug>
<description>
Find general and particular solutions for constant-coefficient linear homogeneous first-order IVPs.
</description>
<alignment>
Fundamentals of Differential Equations and Boundary Value Problems, 7th ed; 4.2
</alignment>
</outcome>
<outcome>
<title>Constant-Coefficient Linear Non-Homogeneous First-Order IVPs</title>
<slug>CC2</slug>
<description>
Find particular solutions for constant-coefficient linear non-homogeneous first-order IVPs.
</description>
<alignment>
Fundamentals of Differential Equations and Boundary Value Problems, 7th ed; 4.6 and 6.4
</alignment>
</outcome>
<outcome>
<title>Constant-Coefficient Linear Homogeneous Higher-Order ODEs</title>
<slug>CC3</slug>
<description>
Find general solutions for constant-coefficient linear homogeneous higher-order ODEs.
</description>
<alignment>
Fundamentals of Differential Equations and Boundary Value Problems, 7th ed; 4.2 and 4.3
</alignment>
</outcome>
<outcome>
<title>Constant-Coefficient Linear Homogeneous Second-Order IVPs</title>
<slug>CC4</slug>
<description>
Find particular solutions for constant-coefficient linear homogeneous second-order ODEs.
</description>
<alignment>
Fundamentals of Differential Equations and Boundary Value Problems, 7th ed; 4.2 and 4.3
</alignment>
</outcome>
<outcome>
<title>Constant-Coefficient Linear Non-Homogeneous Second-Order IVPs</title>
<slug>CC5</slug>
<description>
Find particular solutions for constant-coefficient linear homogeneous second-order ODEs.
</description>
<alignment>
Fundamentals of Differential Equations and Boundary Value Problems, 7th ed; 4.4, 4.5, 6.2, and 6.3
</alignment>
</outcome>
<outcome>
<title>Autonomous Linear First-Order IVP Systems</title>
<slug>CC6</slug>
<description>
Find particular solutions for autonomous linear first-order IVP systems.
</description>
<alignment>
Fundamentals of Differential Equations and Boundary Value Problems, 7th ed; 5.2 and 7.10
</alignment>
</outcome>
<outcome>
<title>Discontinuous Functions and Distributions</title>
<slug>DL1</slug>
<description>
Illustrate and compute integrals involving the unit step function and Dirac-delta distribution.
</description>
<alignment>
Fundamentals of Differential Equations and Boundary Value Problems, 7th ed; 7.6 and 7.9
</alignment>
</outcome>
<outcome>
<title>Laplace Transforms from Definition and Formulas</title>
<slug>DL2</slug>
<description>
Use a table of transforms to find Laplace transformations, and verify a given Laplace transformation from
its integral definition.
</description>
<alignment>
Fundamentals of Differential Equations and Boundary Value Problems, 7th ed; 7.2 and 7.3
</alignment>
</outcome>
<outcome>
<title>Inverse Laplace Transforms and Convolution</title>
<slug>DL3</slug>
<description>
Compute inverse Laplace transforms using the convolution theorem.
</description>
<alignment>
Fundamentals of Differential Equations and Boundary Value Problems, 7th ed; 7.4 and 7.8
</alignment>
</outcome>
<outcome>
<title>Using Laplace Transforms to Solve IVPs</title>
<slug>DL4</slug>
<description>
Solve a second-order constant-coefficient linear IVP involving a discontinuous function by
applying Laplace transforms.
</description>
<alignment>
Fundamentals of Differential Equations and Boundary Value Problems, 7th ed; 7.5
</alignment>
</outcome>
<outcome>
<title>Linear Homogeneous First-Order IVPs</title>
<slug>FO1</slug>
<description>
Find particular solutions for constant-coefficient linear homogeneous first-order IVPs.
</description>
<alignment>
Fundamentals of Differential Equations and Boundary Value Problems, 7th ed; 2.2
</alignment>
</outcome>
<outcome>
<title>Linear Non-Homogeneous First-Order IVPs</title>
<slug>FO2</slug>
<description>
Find particular solutions for constant-coefficient linear non-homogeneous first-order IVPs.
</description>
<alignment>
Fundamentals of Differential Equations and Boundary Value Problems, 7th ed; 2.3 and 4.6
</alignment>
</outcome>
<outcome>
<title>Substitution for First-Order IVPs</title>
<slug>FO3</slug>
<description>
Find particular solutions for constant-coefficient linear non-homogeneous first-order IVPs.
</description>
<alignment>
Fundamentals of Differential Equations and Boundary Value Problems, 7th ed; 2.6
</alignment>
</outcome>
<outcome>
<title>Exact First-Order IVPs</title>
<slug>FO4</slug>
<description>
Identify exact ODEs, and find their implicit solutions.
</description>
<alignment>
Fundamentals of Differential Equations and Boundary Value Problems, 7th ed; 2.4
</alignment>
</outcome>
<outcome>
<title>Strategies for Solving IVPs</title>
<slug>AA5</slug>
<description>
Identify appropriate techniques for solving IVPs based on their structure.
</description>
<alignment>
Fundamentals of Differential Equations and Boundary Value Problems, 7th ed; various sections
</alignment>
</outcome>
<outcome>
<title>Wronskian</title>
<slug>Extra1</slug>
<description>
Use the Wronskian to prove linear independence of particular solutions.
</description>
<alignment>
</alignment>
</outcome>
</outcomes>
</bank>
