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LECTURE NOTES ON MATHEMATICAL METHODS

LECTURE NOTES ONMATHEMATICAL METHODSM ihir SenJoseph M. PowersDepartment of Aerospace and Mechanical EngineeringUniversity of Notre DameNotre Dame, Indiana 46556-5637 USAupdated29 July 2012, 2:31pm2CC BY-NC-ND. 29 July 2012, Sen & Multi-variable Implicit functions .. Functional dependence .. Coordinate transformations .. Jacobian matrices and metric tensors .. Covariance and contravariance .. Orthogonal curvilinear coordinates .. Maxima and minima .. Derivatives of integral expressions .. Calculus of variations .. Lagrange multipliers .. 50 Problems .. 542 First-order ordinary differential Separation of variables .. Homogeneous equations .. Exact equations .. Integrating factors .. Bernoulli equation .. Riccati equation .. Reduction of order .. Uniqueness and singular solutions .. Clairaut equation .. 73 Problems .. 763 Linear ordinary differential Linearity and linear independence.

4 Series solution methods 103 ... survey topics in applied mathematics, including multidimensional calculus, ordinary differ-ential equations, perturbation methods, vectors and tensors, linear analysis, linear algebra, and non-linear dynamic systems. In short, the course fully explores linear systems and con-

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