Midterm Outline

1. Lagrange Interpolation
   • Order of Accuracy.
   • Degree of Precision.
2. Quadrature
   • Open and Closed Newton-Cotes Quadratures.
   • Gaussian Quadratures.
3. ODEs
   • Sufficient conditions for well-posedness.
   • Method of integrating factor.
   • Separation of variables.
4. One-step Numerical Methods
   • Euler's Method : Forward and Backward.
   • Taylor's Methods.
   • Runge-Kutta Methods.
   • Order of Accuracy of above methods.
5. Multistep Numerical Methods
   • Adams-Bashforth Methods
   • Adams-Moulten Methods
   • Order of accuracy of above methods.
   • Criteria for stability of general multistep methods.

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