Differential Equation - 2nd Order A Complete Overview (English)

   Wednesday, December 02, 2020   

Starting a new Lecture Notes Series on Differential Equation - 2nd Order A Complete Overview 

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Differential Equation - 2nd Order A Complete Overview
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Lecture Description of this above Topic:

Lecture 1: Overview

Lecture 2: The Characteristic Equation

Lecture 3: The Harmonic Oscillator

Lecture 4: The Mechanical - Electrical Equivalence

Lecture 5: Linear vs NON-Linear 2nd Order Diff. Eqn.

Lecture 6: The Superposition Principle

Lecture 7: The Superposition Principle: Example

Lecture 8: The Initial Value Problem

Lecture 9: The Initial Value Problem: Example 1

Lecture 10: The Initial Value Problem: Example 2

Lecture 11: The Linearly Independent Solution

Lecture 12: The Linearly Independent Sol.: Checked with Wronskian

Lecture 13: Wronskian Test for Independence

Lecture 14: The Characteristic Eqn. - 2 Real Roots: Ex. 1

Lecture 15: The Characteristic Eqn. - 2 Real Roots: Ex. 2

Lecture 16: The Characteristic Eqn. - 2 Real Roots: Ex. 3

Lecture 17: The Characteristic Eqn. - Real Repeated Roots

Lecture 18: The Chara. Eqn. - Real Repeated Roots: Initial Cond.

Lecture 19: Find the Original Diff. Eqn. Given General Sol.: 1

Lecture 20: Find the Original Diff. Eqn. Given General Sol.: 2

Lecture 21: Constant Coeff. w/ Complex Roots: Another Look

Lecture 22: Constant Coeff. w/ Complex Roots: Example 1

Lecture 23: Constant Coeff. w/ Complex Roots: Example 2

Lecture 24: Constant Coeff. w/ Complex Roots: Example 3

Lecture 25: Constant Coeff. w/ Complex Roots: Example 4

Lecture 26: General Solution y(t)=? When y-term is Missing

Lecture 27: General Solution y(t)=? When y-term is Missing Ex.

Lecture 28: y(t)=? When y-term is Missing; Summary

Lecture 29: Initial Value Problem vs Boundary Value Problem

Lecture 30: Initial Value Problem

Lecture 31: General Approach to Find y(t)=? (Missing y-term)

Lecture 32: Abel's Theorem

Lecture 33: Abel's Theorem: Example

Lecture 34: Summary of Solution (2nd Order Homogen D. E.)

Lecture 35: Summary of Solution: Ex. Case 1

Lecture 36: Summary of Solution: Ex. Case 2 B^2-4ac=0

Lecture 37: Summary of Solution: Ex. Case 3

Lecture 38: Sovling Non-Homog. 2nd Ord. Diff. Eqn. Overview

Lecture 39: Method of Undetermined Coefficient

Lecture 40: Method of Undetermined Coefficient: Ex. 1

Lecture 41: Method of Undetermined Coefficient: Ex. 2

Lecture 42: Method of Undetermined Coefficient: Ex. 3

Lecture 43: General Principle of Superposition

Lecture 44: Method of Undetermined Coefficients

Lecture 45: Method of Undetermined Coefficients: g(t)=Sums

Lecture 46: Method of Undetermined Coefficients: Part 1

Lecture 47: Method of Undetermined Coefficients: Part 2

Lecture 48: Method of Undetermined Coefficients: g(t)=Prod.

Lecture 49: Method of Variation of Parameters

Lecture 50: Method of Variation of Parameters: Part 1/4

Lecture 51: Method of Variation of Parameters: Part 2/4

Lecture 52: Method of Variation of Parameters: Part 3/4

Lecture 53: Method of Variation of Parameters: Part 4/4

Lecture 54: Method of Variation of Parameters: Ex. 1

Lecture 55: Method of Undetermine Coeff.: Ex.

Lecture 56: Method of Variation of Parameters: Ex. 2

Lecture 57: Method of Variation of Parameters: Ex. 3

Lecture 58: Method of Variation of Parameters: Ex. 4

Lecture 59: Laplace Transform (Homog. Eqn.)

Lecture 60: Laplace Transform (NON-Homog. Eqn.)

Lecture 61: Methods to Solve Diff. Eqn. w/ Variable Coeff.

Lecture 62: Missing y-Term w/ Variable Coeff. (Homog. Eq)

Lecture 63: Missing y-Term w/ Variable Coeff (NON-Homog)

Lecture 64: Reduction Method - General Method

Lecture 65: Reduction Method: Example

Lecture 66: Euler Eqn. (Cauchy Eqn.) General Case

Lecture 67: Euler Eqn. (Cauchy Eqn.): Ex. 1

Lecture 68: Euler Eqn. (Cauchy Eqn.): Ex. 2

Lecture 69: Euler Eqn. (Cauchy Eqn.): Ex. 3***