202301041101

Type :Note Tags : Differential Equations

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Diff Eq - Nice Info

People that contributed

Euler, (Jacob and Daniel) Bernoulli, Lagrange, Laplace, Fourier, Cauchy, Maxwell, Poincare$\dots$

Differential Equations greatly contributes to the predictive powers of maths. Connected Fields

• Linear Algebra
• Number Theory
  • Elliptic curves - $({\wp }^{\prime }(z){)}^2=4\wp (z{)}^3-g_2\wp (z)-g_3$
  • Transcendence
• Cauchy-Reimann Equations
• Calaby-Yau spaces $⇝$ Calabi Flow
• Poincare Conjecture $⇝$ Ricci Flow

Grading

4 quizzes (best 3) each 10 % mid term exam - 30 % final exam - 40 %

Homework is given but not graded

References

1. ODE- V.I. Arnold(sometimes it gets unmotivaed and its a little terse)
2. Theory of ODE- Coddington and levinson
3. • GF Simmons
4. ODE - Birkhoff and rota (not entirely aligned w the course)
5. Prof. Pramadh Sastry’s notes

Syllabus

Hopefully will get by the end of the course roughly-

• first and Nth order ODE
• IVP problems (autonomous and non autonomous)
• Lipschitz conditions important for existance and uniqueness theorems
• Systems of linear differential equations
• One parameter group of transformations, etc etc etc

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Related Problems

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References