Mathematics - Ordinary Differential Equations and Applications (English)

   Thursday, April 24, 2025   

Starting a new Lecture Notes Series on Mathematics - Ordinary Differential Equations and Applications

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Mathematics - Ordinary Differential Equations and Applications By Lecture Notes together!

Lecture 1: Mod-01 Lec-01 General Introduction

Lecture 2: Mod-01 Lec-02 Examples

Lecture 3: Mod-01 Lec-03 Examples Continued I

Lecture 4: Mod-01 Lec-04 Examples Continued II

Lecture 5: Mod-02 Lec-05 Linear Algebra

Lecture 6: Mod-02 Lec-06 Linear Algebra Continued I

Lecture 7: Mod-02 Lec-07 Linear Algebra Continued II

Lecture 8: Mod-02 Lec-08 Analysis

Lecture 9: Mod-02 Lec-09 Analysis Continued

Lecture 10: Mod-03 Lec-10 First Order Linear Equations

Lecture 11: Mod-03 Lec-11 Exact Equations

Lecture 12: Mod-03 Lec-12 Second Order Linear Equations

Lecture 13: Mod-03 Lec-13 Second Order Linear Equations Continued I

Lecture 14: Mod-03 Lec-14 Second Order Linear Equations Continued II

Lecture 15: Mod-04 Lec-15 Well-posedness and Examples of IVP

Lecture 16: Mod-04 Lec-16 Gronwall's Lemma

Lecture 17: Mod-04 Lec-17 Basic Lemma and Uniqueness Theorem

Lecture 18: Mod-04 Lec-18 Picard's Existence and Uniqueness Theorem

Lecture 19: Mod-04 Lec-19 Picard's Existence and Uniqueness Continued

Lecture 20: Mod-04 Lec-20 Cauchy Peano Existence Theorem

Lecture 21: Mod-04 Lec-21 Existence using Fixed Point Theorem

Lecture 22: Mod-04 Lec-22 Continuation of Solutions

Lecture 23: Mod-04 Lec-23 Series Solution

Lecture 24: Mod-05 Lec-24 General System and Diagonalizability

Lecture 25: Mod-05 Lec-25 2 by 2 systems and Phase Plane Analysis

Lecture 26: Mod-05 Lec-26 2 by 2 systems and Phase Plane Analysis Continued

Lecture 27: Mod-05 Lec-27 General Systems

Lecture 28: Mod-05 Lec-28 General Systems Continued and Non-homogeneous Systems

Lecture 29: Mod-06 Lec-29 Basic Definitions and Examples

Lecture 30: Mod-06 Lec-30 Stability Equilibrium Points

Lecture 31: Mod-06 Lec-31 Stability Equilibrium Points Continued I

Lecture 32: Mod-06 Lec-32 Stability Equilibrium Points Continued II

Lecture 33: Mod-06 Lec-33 Second Order Linear Equations Continued III

Lecture 34: Mod-06 Lec-34 Lyapunov Function

Lecture 35: Mod-06 Lec-35 Lyapunov Function Continued

Lecture 36: Mod-06 Lec-36 Periodic Orbits and Poincare Bendixon Theory

Lecture 37: Mod-06 Lec-37 Periodic Orbits and Poincare Bendixon Theory Continued

Lecture 38: Mod-07 Lec-38 Linear Second Order Equations

Lecture 39: Mod-07 Lec-39 General Second Order Equations

Lecture 40: Mod-07 Lec-40 General Second Order Equations Continued