notes

commit 10c26a58c929d70b033c4404732181407ae48f6b
parent 0b5b264fce70248a7c112b6da87a3b93ed258748
Author: Andrew <andrewlaack1@gmail.com>
Date:   Thu,  3 Oct 2024 08:56:18 -0500

Took some discrete nots

Diffstat:
A
CharacteristicEquation.md
 | 
14
++++++++++++++
A
CharacteristicRoots.md
 | 
8
++++++++
M
DiscreteMath.md
 | 
7
+++++++
A
LinearHomogeneousRecurrenceRelation.md
 | 
14
++++++++++++++

4 files changed, 43 insertions(+), 0 deletions(-)
diff --git a/CharacteristicEquation.md b/CharacteristicEquation.md
@@ -0,0 +1,14 @@
+:discrete:
+# Characteristic Equation
+
+Ch 8.2
+
+## Notes
+
+**Definition:** A characteristic equation is an equation for a linear homogeneous recurrence relation that uses a_n = r^n to substitute into the equation.
+
+Original:
+$a_n = c_1a_{n-1}+c_2a_{n-2}+...+c_ka_{n-k}$
+
+Characteristic Equation:
+$r^k-c_1r^{k-1}-c_2r^{k-2}-...-c_k=0$
diff --git a/CharacteristicRoots.md b/CharacteristicRoots.md
@@ -0,0 +1,8 @@
+:discrete:
+# Characteristic Roots
+
+Ch 8.2
+
+## Notes
+
+**Definition:** A characteristic root in discrete math are values that satisfy a [CharacteristicEquation](CharacteristicEquation.md).
diff --git a/DiscreteMath.md b/DiscreteMath.md
@@ -141,3 +141,10 @@ Unit 6.4 (Binomial Coefficient & Identities)
 Unit 6.5 (Generalized Permutations & Combinations)
 	- [Distinguishable](Distinguishable.md)
 	- [Indistinguishable](Indistinguishable.md)
+
+Unit 8.2 (Solving Linear Recurrence Relations)
+	- [RecurrenceRelation](RecurrenceRelation.md)
+	- [LinearCombination](LinearCombination.md)
+	- [LinearHomogeneousRecurrenceRelation](LinearHomogeneousRecurrenceRelation.md)
+	- [CharacteristicEquation](CharacteristicEquation.md)
+	- [CharacteristicRoots](CharacteristicRoots.md)
diff --git a/LinearHomogeneousRecurrenceRelation.md b/LinearHomogeneousRecurrenceRelation.md
@@ -0,0 +1,14 @@
+:discrete: 
+# Linear Homogeneous Recurrence Relation
+
+Ch 8.2
+
+## Notes
+
+**Definition:** A linear homogeneous recurrence relation is a recurrence relation where each element is a linear combination of k prior elements (degree k).
+
+Example of k degree LHRR:
+
+$a_n = c_1a_{n-1} + c_2a_{n-2} + ... + c_ka_{n-k}$
+
+Assume all c terms are coefficients and c_k is non-zero.