Transcription of LECTURE NOTES ON MATHEMATICAL METHODS
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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.
These are lecture notes for AME 60611 Mathematical Methods I, the first of a pair of courses on applied mathematics taught in the Department of Aerospace and Mechanical Engineering of the University of Notre Dame. Most of the students in this course are beginning graduate students in engineering coming from a variety of backgrounds.
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