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Math 244 Online Resources

Previous Material Integration Techniques Integration summary
Chapter 1 Classification of Differential equations Linear vs. Nonlinear Differential Equations
SLOPe Fields

Introduction to Slope Fields

Slope Field Example 2 (Section 1.3, Problem 21)

Separable Equations

Separation of Variables Example 1 with u sub (Section 1.4 Problem 4)

Separation of Variables Example 2 with Trig Functions (Section 1.4 Problem 8)

Separation of Variables Example 3 with Partial Fraction Decomposition (Section 1.4, Problem 9)

Separation of Variables Example 4 with Integration By Parts

Integrating Factor Integrating Factor Example
Newton's Law of Cooling

Newton's Law of Cooling Example 1 (Section 1.4 Problem 26)

Newton's Law of Cooling Example 2 (Section 1.6 Problem 24)

Mixing Problems

Mixing Problem Example 1 - Separation of Variable (Section 1.7 Problem 5)

Double Tank Problem (Section 1.7, #8, Part A)

Double Tank Problem (Section 1.7, #8, Part B)

RLC Circuits

RC Circuit - Integrating Factor (Section 1.7 Problem 13)

RL Circuit - Separation of Variable (Section 1.7 Problem 16)

Chapter 2 Row Operations

Row Echelon/Rank Example

Reduced Row Echelon/Rank Example

Gauss Jordan Elimination

Gauss Jordan Elimination - One Solution (Section 2.5 Section 1)

Gauss Jordan Elimination - No Solutions (Section 2.5 Problem 3)

Matrix inverse

Matrix Inverse Using Gauss Jordan Technique (Section 2.6 Problem 8)

Chapter 3 Determinants

Adjoint Method to find Matrix Inverse (Section 3.4 Problem 9)

Cramer's Rule to find Solutions (Section 3.4 Problem 13)

Properties of Determinants

Chapter 4 Vector/Subspaces

Vector Space Axioms 1-4 (Section 4.2 Problem16)

Vector Space Axioms 5-10 (Section 4.2 Problem 16)

Subspace Example 1 (Section 4.3 Problem 5)

Subspace Example 2 (Section 4.3 Problem 16)

Spanning Sets

"Show that the set spans..." with n-tuples (Section 4.4 Problem 9)

"Determine if it lies in the span..." with Polynomials (Section 4.4 Problem 25)

"Find the span..." with Matrices (Section 4.4 Problem 26)

Bases Extending a Basis from Subspace to Vector Space (Section 4.6 Problem 32)
Nullspace

Finding the Basis and Dimension of a Nullspace (Section 4.6 Problem 11)

Nullspace, Basis, and Nullity (Section 4.9 Problem 4)

Chapter 5 Eigenvalue/Eigenvectors Eigenvalues and Eigenvectors (Section 5.6 Problem 16)
Diagonalization

Intro to Diagonalization

Diagonalization Example (Section 5.8 Problem 15)

Chapter 6 Homogeneous Equations

Intro to Linear, Constant Coeff, Homogeneous Equations

Example 1 (Repeated Roots, Section 6.2)

Example 2 (Distinct, Real Roots and Complex Roots)

NonHomogeneous Equations

Intro to Method of Undetermined Coefficients (MOUC)

MOUC Example 1 (F(x) = exponential, need to modify)

MOUC Example 2 (F(x) = trig function)

MOUC Example 3 (F(x) = polynomial)

MOUC Example 4 (F(x) = product of exponential and trig function)

Spring Mass Systems

Overdamped, Free Oscillation (Section 6.5 Problem 5)

Critically damped, Free Oscillation (Section 6.5 Problem 7)

Underdamped, Forced Oscillation (Section 6.5 Problem 23)

Chapter 7 First order linear Systems of differential equations

Using Differential Operators and Substitution (Homogeneous - Section 7.1 Problem 2)

Using Differential Operators and Substitution (Nonhomogeneous - Section 7.1 Problem 13)

Vector Differential Equations with Nondefective Matrices (Section 7.4 Problem 12)

Vector Differential Equations with Nondefective Matrices IVP (Section 7.4 Problem 16)