MathNotes

basic

algebra

completing-the-square

system-of-equations

complex-numbers

complex-conjugate

complex-numbers

imaginary-numbers

coordinate-systems

polar-coords

cylindrical-coordinates

polar-coordinates

rectangular-coords

cartesian-coordinates

spherical-coords

spherical-coordinates

data

data-definition

dependent-variable

independent-variable

qualitative-data

quantitative-data

function

function-definition

horizontal-line-test

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shifts-transitions

stretches-reflections

x-equal-y-on-2d-graph

xyz-on-3d-graph

geometry

2d-space

point-definition

3d-space

3d-graph-x-times-y

equation-of-a-plane

parametric-equations

plane-definition

solid-definition

line-definition

parallel-definition

perpendicular-definition

projection-light

pythagorean-theorem

graphs

graph-definition

log-rules

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natural-logarithm

summation-notation

summation-labeled

summation-notation

trigonometry

common-triangles

trig-identities

domain-and-range

equation-definition

euclidean-space

evaluate-definition

exponential-function

interval-notation

polynomial-definition

quadratic-formula

right-hand-rule

trivial-solution

unit-step-function

calculus

applications

finding-centroids

finding-moments

basic

critical-points

fundamental-theorem

calc3-notes

2204_Ch12_Sect1-2-3

2204_Ch12_Sect4-5

2204_Ch12_Sect6

2204_Ch13_Sect1-2

2204_Ch13_Sect3-4

2204_Ch14_Sect1-2

2204_Ch14_Sect3-4

2204_Ch14_Sect5-6

2204_Ch14_Sect7-8

2204_Ch15_Sect1-2

2204_Ch15_Sect3-4

2204_Ch15_Sect6-8

2204-ApplicationsVectors

graphsOfQuadricSurfaces

difference-types

difference-types

differential-equations

2ndClassNotes

class-notes-index

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W1-Ch2.1.2-PhaseDiagrams

W1-Ch2.2-SeparatingVariablesExample

W1-Ch2.2-SeparatingVariablesIdea

W1L1 - Checking solutions in Diffeq

W1L2 - Intro To IVPs

W1L3 - Slope fields and isoclines example

W1L4 - Intro to slope fields

W1L5 - Applications of Slope Fields

W1L6 - Phase Lines

W1L7 - Separable Differential Equations

W1L8 - Separable Equations with Initial Values

W1L9 - Intro to Linear Differential Equations and Integrating Factors

W1L10 - Solving Linear Differential Equations with an Integrating Factor

W2L1 - First Order Linear Models

W2L2 - Applications with Separable Equations

W2L3 - Non-linear Models

W2L4 - Higher Order Linear ODEs

W2L5 - Reduction of Order

W2L6 - Homogeneous Linear ODEs

W3L1 - Method of Undetermined Coefficients

W3L2 - Cauchy-Euler Differential Equations

W3L3 - Introduction to Free Undamped Motion (Spring System)

W3L4 - Intro to Boundary Value Problems

W3L5 - Power Series Solutions of Differential Equations

W3L6 - Power Series Solution about Singular Points

W4L1 - Intro to Laplace Transforms

W4L2 - Calculating the Laplace Transform

W4L3 - Calculating the Laplace Transform of a Function using Tables

W4L4 - Basic Inverse Laplace Transforms

W4L5 - Inverse Laplace Transform

W4L6 - Laplace Transform Basic Properties

W4L7 - Translation Theorems and Derivatives of Laplace Transforms

approximation-methods

classifying

cauchy-euler-differential-equations

higher-order-linear-differential-equations

homogeneous-linear-differential-equations

definitions

boundary-value-problem

characteristic-polynomial

derivative-order

fundamental-set-of-solutions

linear-dependance

logistic-equation

superposition-principle

models

first-order-linear-models

first-order-non-linear-models

powerSeries

frobenius-method

power-series-about-singular-points

power-series-ordinary-points

SlopeFieldsDiffeq

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slope-fields-diffeq

solutionTypes

explicit-solution

general-solution

implicit-solution

particular-solution

solving

laplace-transforms

laplace-transform

laplace-transform-table

LaplaceTransforms

integrating-factor

power-series-differential-equations

reduction-of-order

separable-variables

undetermined-coefficients

variation-of-parameters

zzz_old

applications

mixing-problems

approximation-methods

diffeq-notes

1- Introduction Sect 4.6 Complex Eigenvalues Part 1

1- Review from Week 6 and Fundamental Set of Solutions, Fundamental Matrix and Abel's Formula (sect 4.3 and 4.4)

1-Euler's Method Part 1

1-Mixing Problems Part 1

1-Review of Matrix Algebra

1-Second Order Scalar DE (Sect 3-1 to 3-5)

1-Sect 4.8 Method of Variation of Parameters

1-Sects 6.2 and 6.6 Stability

1-Week 1 sect 1.1 and 1.2 Introduction to Differential Equations

2- Undetermined Coefficients Try Functions (Sect4-8)

2-Euler's Method (4.9 Systems)_Part2

2-Mixing Problem Part 2- A 2 tank system

3- Method of Undetermined Coefficients Sect4-8 Part 1

3-Existence and Uniqueness Theorems for systems and 2nd order DE

4- Method of Undetermined Coefficients Sect4-8 Part 3

4-Sect 4.7 Defective Matrix

4-Solving a constant coefficient system of DE_Part1

5-Linearization Sect 6.2-6.4-6.5

How to find Solutions Part1 Calculations

numerical-methods-notes

9_ODEs_Numerical

AppliedEngineeringMathematics

scalar-equations

solution-types

general-solution-scalar-equations

solving-methods

undetermined-coefficients-scalar-equations

solution-types

complementary-solution

general-solutions

particular-solution

solving-methods

integrating-factor

separation-of-variables

undetermined-coefficients

variation-of-parameters

systems-of-equations

linear-systems

solution-types

complementary-solutions-linear-systems

general-solutions-for-linear-systems

particular-solutions-linear-systems

linear-systems-diffeq

nonhomogeneous-linear-system-diffeq

nonlinear-systems

nonlinear-systems-diffeq

solving-methods

undetermined-coefficients-systems

variation-of-parameters-systems

differential-equ-matrix-ops

systems-of-equ-diffeq

two-dimensional-autonomous

characteristic-equation

defective-matrices

differential-equation-notation

differential-equations

equilibrium-solutions

existence-and-uniqueness-linear-IVP

fundamental-matrix

initial-value-problem

reduction-of-order

differential-equations

differentiation

differentiation

differentiation-notation

differentiation-rules

leibnez-labeled

integration

approximation-methods

Trapezoidal_rule_illustration.svg

trapezoidal-rule

average-value-of-function

constant-of-integration

definite-integral

improper-integral

indefinite-integral

integral-python

integration-bounds

integration-notation

integration-rules

region-of-integration

limits

limit-definition

proving-limit-DNE

proving-limit-exists

multi-var

min-max

extreme-value-theorem

lagrange-multipliers

second-derivative-test

multivar-integrals

double-integral

double-integral-area

double-integral-python

multiple-integral-notation

multiple-integrals

triple-integral

partial derivative

partial-deriv-geometric-idea

partial-derivative-notation

partial-derivatives

space-curves

arc-length-of-space-curve

unit-tangent-vector-space-curve

velocity-tangent-vectors

directional-derivative-max

directional-derivatives

jacobian-matrix

multivariable-calculus

region-definition-calc

tangent-plane-to-level-surface

rules

series

single-var

finding-derivatives

sympy-diff-example

vector-calculus

direction-fields

direction-field

gradient-notation

vector-calculus

mat266notes_written

mat1225notes_written

position-vs-velocity

linear

1-3

1-3-dot_products

1-4

1-basic_matrix_operations

2-matrix_vector_products

identity-matrix

2-1

1-augmented_row_echelon

2-elementary_row_operations

3-elementary_row_operations_2

4-curve_fitting_example

5-inconsistent_linear_system

elementary-row-operations

2-2

3-reduced_row_echelon_form

4-general_solution_ex1

5-general_solution_ex2

6-general_solution_ex3

7-homogeneous_linear_systems

homogeneous-systems

nonhomogeneous-linear-systems

reduced-row-echelon

2-3

1-introduction_span

2-visualizing_span

3-matrix_rank_span

4-redundant_vectors

5-redundant_vector_examples

6-elementary_row_redundant

span-definition

3-1

1-intro_matrix_inverses

2-matrix_inverses_solve

3-intro_matrix_invertibility

4-fundamental_theorem_invertible

5-matrix_inverse_calculation

6-matrix_inverse_calculation_ex1

7-matrix_inverse_calculation_ex2

3-4

1-column_space_matrix

2-matrix_rank_column_space

3-null_space_matrix

4-basis_null_space

5-rank_nullity_theorem

6-rank_nullity_application

7-more_rank_nullity

4-3

1-intro_eigenvalues_eigenvectors

2-invertibility_2x2_matrices

3-calculating_eigenvalues_2x2

4-finding_eigenvectors

5-intro_eigenspaces

6-geometric_interp_eigen

complex-eigenpairs

eigenvalues-eigenvectors

5-1

1-definition_determinant

2-fast_determinant_calculation

3-fast_determinant_calculation_2

4-properties_determinant

5-determinants_invertibility

6-invertibility_examples

triangular-matrix

gauss-seidel

glossary

Kent-linear-glossary

linear-glossary

UMBC-linear-glossary

lu-decomposition

lu-decomposition

matrices

basic-matrix-operations

matrix-definition

miscellaneous

PartialFractionDecompositionExamples

scalar-definition

multiplicity

algebraic-multiplicity

geometric-multiplicity

multiplicity-definition

vectors

cross-product-ti84-program

sympy-cross-product

vector-definition

vector-notation

vector-operations

5_Linear_Algebra_post

characteristic-polynomial

mat2114notes_written

matrix-function

vector-function

python

variables

symbolic-vars-link

sympy-online-interpreter

statistics

M1

data-types

continuous-data

CH1 Lecture Notes

data-collection

M2

CH2 Lecture Notes

M3A

M3B

binomial-distribution

CH3B Lecture Notes

difference-factor

discrete-distributions

discrete-random-variables

poisson-distribution

standard-deviation

M3C

CH3C Lecture Notes

continuous-random-variables

cumulative-distribution-function

normal-distribution

probability-density-function

M3D

central-limit-theorem

CH3D Lecture Notes

random-behavior-of-means

M4A

CH4A Lecture Notes

confidence-intervals

critical-values

estimation-and-testing

hypothesis-tests

point-estimation

M4B

proportions

population-proportion

proportion-definition

sample-proportion

categorical-variables

CH4B Lecture Notes

M4C

CH4C Lecture Notes

difference-in-two-proportions

independent-samples

M6

scatterplot

scatterplot-shape-examples-from-class

scatterplot-strength-example-from-class

scatterplot-trend-examples-from-class

variables

confounding-variable

explanatory-variable

response-variable

variables-stats

analysis-of-variance-table

CH6 Lecture Notes

coefficient-of-determination

regression-line

M7

one-way-analysis-of-variance

common-definitions

Helpful Math Notes

Differential Equation Notation

It is common to use a uppercase letters to designate solutions to a function within a differential equation?

Sources:

Paul's Math Notes

Interactive Graph

Table Of Contents

Differential Equation Notation