MathematicalMethodsinEngineeringandScience 1, Mathematical Methods in Engineering and Science [http://home.iitk.ac.in/˜dasgupta/MathCourse] Bhaskar Dasgupta [email protected] AnAppliedMathematicscoursefor graduateandseniorundergraduate students andalsofor risingresearchers. MathematicalMethodsinEngineeringandScience 2, Textbook: Dasgupta B., App. Math. Meth. (Pearson Education 2006, 2007). http://home.iitk.ac.in/˜dasgupta/MathBook MathematicalMethodsinEngineeringandScience 3, Contents I Preliminary Background Matrices and Linear Transformations Operational Fundamentals of Linear Algebra Systems of Linear Equations Gauss Elimination Family of Methods Special Systems and Special Methods Numerical Aspects in Linear Systems MathematicalMethodsinEngineeringandScience 4, Contents II Eigenvalues and Eigenvectors Diagonalization and Similarity Transformations Jacobi and Givens Rotation Methods Householder Transformation and Tridiagonal Matrices QR Decomposition Method Eigenvalue Problem of General Matrices Singular Value Decomposition Vector Spaces: Fundamental Concepts* MathematicalMethodsinEngineeringandScience 5, Contents III Topics in Multivariate Calculus Vector Analysis: Curves and Surfaces Scalar and Vector Fields Polynomial Equations Solution of Nonlinear Equations and Systems Optimization: Introduction Multivariate Optimization Methods of Nonlinear Optimization* MathematicalMethodsinEngineeringandScience 6, Contents IV Constrained Optimization Linear and Quadratic Programming Problems* Interpolation and Approximation Basic Methods of Numerical Integration Advanced Topics in Numerical Integration* Numerical Solution of Ordinary Differential Equations ODE Solutions: Advanced Issues Existence and Uniqueness Theory MathematicalMethodsinEngineeringandScience 7, Contents V First Order Ordinary Differential Equations Second Order Linear Homogeneous ODE’s Second Order Linear Non-Homogeneous ODE’s Higher Order Linear ODE’s Laplace Transforms ODE Systems Stability of Dynamic Systems Series Solutions and Special Functions MathematicalMethodsinEngineeringandScience 8, Contents VI Sturm-Liouville Theory Fourier Series and Integrals Fourier Transforms Minimax Approximation* Partial Differential Equations Analytic Functions Integrals in the Complex Plane Singularities of Complex Functions MathematicalMethodsinEngineeringandScience 9, Contents VII Variational Calculus* Epilogue Selected References MathematicalMethodsinEngineeringandScience PreliminaryBackground 10, Outline ThemeoftheCourse CourseContents SourcesforMoreDetailedStudy LogisticStrategy ExpectedBackground Preliminary Background Theme of the Course Course Contents Sources for More Detailed Study Logistic Strategy Expected Background