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MATH 33B
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UCLA  MATH 33  Class Notes  
UCLA  MATH 33  Class Notes  
Description
Reviews
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
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
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 NonExact 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
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
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
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 NonExact 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
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
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
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 NonExact 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
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
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