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UCLA - MATH 33 - Class Notes - --

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School: University of California - Los Angeles
Department: Mathematics
Course: Differential Equations
Professor: Omer neria
Term: Fall 2016
Tags: Math, Differential Equations, and Linear Equations
Name: Math 33B, Differential Equations - Linear Equations
Description: Covers the following: Linear Equations How to solve Linear Equations Homogeneous Equations How to solve Homogeneous Equations Variation of Parameters
Uploaded: 10/21/2016
MATH 33B - Class Notes - Week 1
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

MATH 33B - Class Notes - Week 2
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

MATH 33B - Class Notes - Week 3
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

MATH 33B - Class Notes - Week 2
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

MATH 33B - Class Notes - Week 3
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

MATH 33B - Class Notes - Week 3
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

MATH 33B - Class Notes - Week 4
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

MATH 33B - Class Notes - Week 5
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)

MATH 33B - Class Notes - Week 6
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

MATH 33B - Class Notes - Week 6
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

MATH 33B - Class Notes - Week 6
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

MATH 33B - Class Notes - Week 6
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

MATH 33B - Class Notes - Week 6
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

MATH 33B - Class Notes - Week 7
3 pages

Math 33B, Differential Equations - Planar Systems

Fall 2016

Omer neria

MATH 33B

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

MATH 33B - Class Notes - Week 7
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

MATH 33B - Class Notes - Week 8
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

MATH 33B - Class Notes - Week 8
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

MATH 33B - Class Notes - Week 9
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

MATH 33B - Class Notes - Week 9
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


MATH 33B - Class Notes - Week 1
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

MATH 33B - Class Notes - Week 2
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

MATH 33B - Class Notes - Week 3
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

MATH 33B - Class Notes - Week 2
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

MATH 33B - Class Notes - Week 3
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

MATH 33B - Class Notes - Week 3
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

MATH 33B - Class Notes - Week 4
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

MATH 33B - Class Notes - Week 5
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)

MATH 33B - Class Notes - Week 6
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

MATH 33B - Class Notes - Week 6
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

MATH 33B - Class Notes - Week 6
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

MATH 33B - Class Notes - Week 6
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

MATH 33B - Class Notes - Week 6
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

MATH 33B - Class Notes - Week 7
3 pages

Math 33B, Differential Equations - Planar Systems

Fall 2016

Omer neria

MATH 33B

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

MATH 33B - Class Notes - Week 7
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

MATH 33B - Class Notes - Week 8
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

MATH 33B - Class Notes - Week 8
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

MATH 33B - Class Notes - Week 9
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

MATH 33B - Class Notes - Week 9
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

MATH 33B - Class Notes - Week 1
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

MATH 33B - Class Notes - Week 2
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

MATH 33B - Class Notes - Week 3
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

MATH 33B - Class Notes - Week 2
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

MATH 33B - Class Notes - Week 3
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

MATH 33B - Class Notes - Week 3
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

MATH 33B - Class Notes - Week 4
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

MATH 33B - Class Notes - Week 5
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)

MATH 33B - Class Notes - Week 6
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

MATH 33B - Class Notes - Week 6
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

MATH 33B - Class Notes - Week 6
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

MATH 33B - Class Notes - Week 6
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

MATH 33B - Class Notes - Week 6
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

MATH 33B - Class Notes - Week 7
3 pages

Math 33B, Differential Equations - Planar Systems

Fall 2016

Omer neria

MATH 33B

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

MATH 33B - Class Notes - Week 7
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

MATH 33B - Class Notes - Week 8
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

MATH 33B - Class Notes - Week 8
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

MATH 33B - Class Notes - Week 9
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

MATH 33B - Class Notes - Week 9
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