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MATH 33B
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UCLA - MATH 33 - Class Notes - Week 7
UCLA - MATH 33 - Class Notes - Week 7
Description
Reviews
School: University of California - Los Angeles
Department: Mathematics
Course: Differential Equations
Professor: Omer neria
Term: Fall 2016
Tags: Differential Equations, Linear Algebra, and Calculus
Name: Math 33B, Differential Equations - Planar Systems
Description: This covers the following: -How to solve planar systems of differential equations with a 2x2 matrix -How to solve for real eigenvalues and their corresponding eigenvectors
Uploaded: 11/26/2016

6 pages
Math 33B, Differential Equations - Introduction to Differential Equations
Fall 2016
Omer neria
MATH 33B
Covers the following: Introduction to Differentials Order of a Differential Ordinary and Partial Differential Equations How to Solve ODEs (General Solutions) How to Solve Initial Value Problems (Particular Solutions) Slope Fields

2 pages
Math 33B, Differential Equations - Separable Equations
Fall 2016
Omer neria
MATH 33B
Covers the following: How to Solve Separable Equations Newton's Law of Cooling

5 pages
Math 33B, Differential Equations - Linear Equations
Fall 2016
Omer neria
MATH 33B
Covers the following: Linear Equations How to solve Linear Equations Homogeneous Equations How to solve Homogeneous Equations Variation of Parameters

3 pages
Math 33B, Differential Equations - Mixing Problems and Population Growth
Fall 2016
Omer neria
MATH 33B
Covers the following: Mixing problems (tanks with solutions) Population Growth Models

5 pages
Math 33B, Differential Equations - Exact Differential Equations
Fall 2016
Omer neria
MATH 33B
This covers the following topics: -Exact Differential Equations -How to solve EDEs -Using Integrating Factors for Non-Exact Differentials

5 pages
Math 33B, Differential Equations - Autonomous Equations and Stability
Fall 2016
Omer neria
MATH 33B
This covers the following: -Autonomous Differential Equations -Stability of Autonomous Differential Equations

6 pages
Math 33B, Differential Equations - Uniqueness of Solutions
Fall 2016
Omer neria
MATH 33B
This covers the following: -Uniqueness of Solutions -Existence of Solutions

6 pages
Math 33B, Differential Equations - Second Order ODEs
Fall 2016
Omer neria
MATH 33B
This covers the following: -Introduction to Second Order Ordinary Differential Equations -Form of the General Solution to Second Order ODEs -Complex Numbers and Imaginary Solutions -Form of the General Imaginary Solution to Second Order ODEs -Repeated Solutions

8 pages
Math 33B, Differential Equations - Modeling the Motion of a Vibrating Spring
Fall 2016
Omer neria
MATH 33B
This covers the following: -1st type of motion - no mass, no motion -2nd type of motion - mass, no motion -3rd type of motion - undamped motion -4th type of motion - damped motion -5th type of motion - forced motion (external force)

7 pages
Math 33B, Differential Equations - Inhomogeneous Linear Equations
Fall 2016
Omer neria
MATH 33B
This covers the following: -Inhomegenous Linear Equations -Undetermined Coefficients Method to Solving Inhomogeneous Linear Equations

2 pages
Math 33B, Differential Equations - Homogeneous Euler Equations
Fall 2016
Omer neria
MATH 33B
This covers the following: -Euler Equations, specifically Homogeneous ones -How to Solve Euler Equations

3 pages
Math 33B, Differential Equations - Variation of Parameters
Fall 2016
Omer neria
MATH 33B
This covers the following: -Using the Variation of Parameters method to solve Second Order Inhomogeneous Linear Equations

1 pages
Math 33B, Differential Equations - Uniqueness and Existence for Second Order ODEs
Fall 2016
Omer neria
MATH 33B
This covers the following: -Uniqueness and existence for Second Order ODEs

6 pages
Math 33B, Differential Equations - Review of Linear Algebra
Fall 2016
Omer neria
MATH 33B
This covers the following: -Review of Matrices -System of Equations using Matrices -Multiplying Matrices -Linear Independence of Vectors of Matrices -Determinants of Matrices This section prepares for the Planar Systems section

3 pages
Math 33B, Differential Equations - Planar Systems, Complex Eigenvalues
Fall 2016
Omer neria
MATH 33B
This covers the following: -Complex eigenvalues of 2x2 planar systems -How to find the solution to a complex 2x2 system

3 pages
Math 33B, Differential Equations - Planar Systems, Repeated Eigenvalues
Fall 2016
Omer neria
MATH 33B
This covers the following: -Repeated eigenvalues of a 2x2 planar system -How to find the solution to a 2x2 planar system with repeated eigenvalues

6 pages
Math 33B, Differential Equations - Phase Plane Portraits
Fall 2016
Omer neria
MATH 33B
This covers the following: -Sketching solutions on a phase plane -Using linear form, exponential form, and trigonometric form -Drawing saddle points, nodal sinks, and nodal sources

3 pages
Math 33B, Differential Equations - Complex Roots and Phase Plane Portraits
Fall 2016
Omer neria
MATH 33B
This covers the following: -Drawing center cases, spiral sinks, and spiral sources

6 pages
Math 33B, Differential Equations - Higher Systems
Fall 2016
Omer neria
MATH 33B
This covers the following: -Solving nxn systems -Using the p/q method of polynomials to find roots of characteristic polynomial

6 pages
Math 33B, Differential Equations - Introduction to Differential Equations
Fall 2016
Omer neria
MATH 33B
Covers the following: Introduction to Differentials Order of a Differential Ordinary and Partial Differential Equations How to Solve ODEs (General Solutions) How to Solve Initial Value Problems (Particular Solutions) Slope Fields

2 pages
Math 33B, Differential Equations - Separable Equations
Fall 2016
Omer neria
MATH 33B
Covers the following: How to Solve Separable Equations Newton's Law of Cooling

5 pages
Math 33B, Differential Equations - Linear Equations
Fall 2016
Omer neria
MATH 33B
Covers the following: Linear Equations How to solve Linear Equations Homogeneous Equations How to solve Homogeneous Equations Variation of Parameters

3 pages
Math 33B, Differential Equations - Mixing Problems and Population Growth
Fall 2016
Omer neria
MATH 33B
Covers the following: Mixing problems (tanks with solutions) Population Growth Models

5 pages
Math 33B, Differential Equations - Exact Differential Equations
Fall 2016
Omer neria
MATH 33B
This covers the following topics: -Exact Differential Equations -How to solve EDEs -Using Integrating Factors for Non-Exact Differentials

5 pages
Math 33B, Differential Equations - Autonomous Equations and Stability
Fall 2016
Omer neria
MATH 33B
This covers the following: -Autonomous Differential Equations -Stability of Autonomous Differential Equations

6 pages
Math 33B, Differential Equations - Uniqueness of Solutions
Fall 2016
Omer neria
MATH 33B
This covers the following: -Uniqueness of Solutions -Existence of Solutions

6 pages
Math 33B, Differential Equations - Second Order ODEs
Fall 2016
Omer neria
MATH 33B
This covers the following: -Introduction to Second Order Ordinary Differential Equations -Form of the General Solution to Second Order ODEs -Complex Numbers and Imaginary Solutions -Form of the General Imaginary Solution to Second Order ODEs -Repeated Solutions

8 pages
Math 33B, Differential Equations - Modeling the Motion of a Vibrating Spring
Fall 2016
Omer neria
MATH 33B
This covers the following: -1st type of motion - no mass, no motion -2nd type of motion - mass, no motion -3rd type of motion - undamped motion -4th type of motion - damped motion -5th type of motion - forced motion (external force)

7 pages
Math 33B, Differential Equations - Inhomogeneous Linear Equations
Fall 2016
Omer neria
MATH 33B
This covers the following: -Inhomegenous Linear Equations -Undetermined Coefficients Method to Solving Inhomogeneous Linear Equations

2 pages
Math 33B, Differential Equations - Homogeneous Euler Equations
Fall 2016
Omer neria
MATH 33B
This covers the following: -Euler Equations, specifically Homogeneous ones -How to Solve Euler Equations

3 pages
Math 33B, Differential Equations - Variation of Parameters
Fall 2016
Omer neria
MATH 33B
This covers the following: -Using the Variation of Parameters method to solve Second Order Inhomogeneous Linear Equations

1 pages
Math 33B, Differential Equations - Uniqueness and Existence for Second Order ODEs
Fall 2016
Omer neria
MATH 33B
This covers the following: -Uniqueness and existence for Second Order ODEs

6 pages
Math 33B, Differential Equations - Review of Linear Algebra
Fall 2016
Omer neria
MATH 33B
This covers the following: -Review of Matrices -System of Equations using Matrices -Multiplying Matrices -Linear Independence of Vectors of Matrices -Determinants of Matrices This section prepares for the Planar Systems section

3 pages
Math 33B, Differential Equations - Planar Systems, Complex Eigenvalues
Fall 2016
Omer neria
MATH 33B
This covers the following: -Complex eigenvalues of 2x2 planar systems -How to find the solution to a complex 2x2 system

3 pages
Math 33B, Differential Equations - Planar Systems, Repeated Eigenvalues
Fall 2016
Omer neria
MATH 33B
This covers the following: -Repeated eigenvalues of a 2x2 planar system -How to find the solution to a 2x2 planar system with repeated eigenvalues

6 pages
Math 33B, Differential Equations - Phase Plane Portraits
Fall 2016
Omer neria
MATH 33B
This covers the following: -Sketching solutions on a phase plane -Using linear form, exponential form, and trigonometric form -Drawing saddle points, nodal sinks, and nodal sources

3 pages
Math 33B, Differential Equations - Complex Roots and Phase Plane Portraits
Fall 2016
Omer neria
MATH 33B
This covers the following: -Drawing center cases, spiral sinks, and spiral sources

6 pages
Math 33B, Differential Equations - Higher Systems
Fall 2016
Omer neria
MATH 33B
This covers the following: -Solving nxn systems -Using the p/q method of polynomials to find roots of characteristic polynomial

6 pages
Math 33B, Differential Equations - Introduction to Differential Equations
Fall 2016
Omer neria
MATH 33B
Covers the following: Introduction to Differentials Order of a Differential Ordinary and Partial Differential Equations How to Solve ODEs (General Solutions) How to Solve Initial Value Problems (Particular Solutions) Slope Fields

2 pages
Math 33B, Differential Equations - Separable Equations
Fall 2016
Omer neria
MATH 33B
Covers the following: How to Solve Separable Equations Newton's Law of Cooling

5 pages
Math 33B, Differential Equations - Linear Equations
Fall 2016
Omer neria
MATH 33B
Covers the following: Linear Equations How to solve Linear Equations Homogeneous Equations How to solve Homogeneous Equations Variation of Parameters

3 pages
Math 33B, Differential Equations - Mixing Problems and Population Growth
Fall 2016
Omer neria
MATH 33B
Covers the following: Mixing problems (tanks with solutions) Population Growth Models

5 pages
Math 33B, Differential Equations - Exact Differential Equations
Fall 2016
Omer neria
MATH 33B
This covers the following topics: -Exact Differential Equations -How to solve EDEs -Using Integrating Factors for Non-Exact Differentials

5 pages
Math 33B, Differential Equations - Autonomous Equations and Stability
Fall 2016
Omer neria
MATH 33B
This covers the following: -Autonomous Differential Equations -Stability of Autonomous Differential Equations

6 pages
Math 33B, Differential Equations - Uniqueness of Solutions
Fall 2016
Omer neria
MATH 33B
This covers the following: -Uniqueness of Solutions -Existence of Solutions

6 pages
Math 33B, Differential Equations - Second Order ODEs
Fall 2016
Omer neria
MATH 33B
This covers the following: -Introduction to Second Order Ordinary Differential Equations -Form of the General Solution to Second Order ODEs -Complex Numbers and Imaginary Solutions -Form of the General Imaginary Solution to Second Order ODEs -Repeated Solutions

8 pages
Math 33B, Differential Equations - Modeling the Motion of a Vibrating Spring
Fall 2016
Omer neria
MATH 33B
This covers the following: -1st type of motion - no mass, no motion -2nd type of motion - mass, no motion -3rd type of motion - undamped motion -4th type of motion - damped motion -5th type of motion - forced motion (external force)

7 pages
Math 33B, Differential Equations - Inhomogeneous Linear Equations
Fall 2016
Omer neria
MATH 33B
This covers the following: -Inhomegenous Linear Equations -Undetermined Coefficients Method to Solving Inhomogeneous Linear Equations

2 pages
Math 33B, Differential Equations - Homogeneous Euler Equations
Fall 2016
Omer neria
MATH 33B
This covers the following: -Euler Equations, specifically Homogeneous ones -How to Solve Euler Equations

3 pages
Math 33B, Differential Equations - Variation of Parameters
Fall 2016
Omer neria
MATH 33B
This covers the following: -Using the Variation of Parameters method to solve Second Order Inhomogeneous Linear Equations

1 pages
Math 33B, Differential Equations - Uniqueness and Existence for Second Order ODEs
Fall 2016
Omer neria
MATH 33B
This covers the following: -Uniqueness and existence for Second Order ODEs

6 pages
Math 33B, Differential Equations - Review of Linear Algebra
Fall 2016
Omer neria
MATH 33B
This covers the following: -Review of Matrices -System of Equations using Matrices -Multiplying Matrices -Linear Independence of Vectors of Matrices -Determinants of Matrices This section prepares for the Planar Systems section

3 pages
Math 33B, Differential Equations - Planar Systems, Complex Eigenvalues
Fall 2016
Omer neria
MATH 33B
This covers the following: -Complex eigenvalues of 2x2 planar systems -How to find the solution to a complex 2x2 system

3 pages
Math 33B, Differential Equations - Planar Systems, Repeated Eigenvalues
Fall 2016
Omer neria
MATH 33B
This covers the following: -Repeated eigenvalues of a 2x2 planar system -How to find the solution to a 2x2 planar system with repeated eigenvalues

6 pages
Math 33B, Differential Equations - Phase Plane Portraits
Fall 2016
Omer neria
MATH 33B
This covers the following: -Sketching solutions on a phase plane -Using linear form, exponential form, and trigonometric form -Drawing saddle points, nodal sinks, and nodal sources

3 pages
Math 33B, Differential Equations - Complex Roots and Phase Plane Portraits
Fall 2016
Omer neria
MATH 33B
This covers the following: -Drawing center cases, spiral sinks, and spiral sources

6 pages
Math 33B, Differential Equations - Higher Systems
Fall 2016
Omer neria
MATH 33B
This covers the following: -Solving nxn systems -Using the p/q method of polynomials to find roots of characteristic polynomial