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

Polynomial Functions

Functions in the form

's are called coefficients of the polynomial
The number is called the degree of the polynomial

Interactive Graph

Table Of Contents

Polynomial Functions