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MATHEMATICS FOR ENGINEERS AND SCIENTISTS 4

The Laplace Transform, Definition and Properties, First Shift Theorem. The Inverse Laplace Transform, Using partial fractions. Finding inverses using the first shift theorem, Method of completing the square. Solution of Differential Equations Using Laplace Transforms. Laplace Transforms of Derivatives. Constant-Coefficient Linear Differential Equations. Differential Equations and the Dirac Delta Function. Systems of Differential Equations. Geometry, Revision of Vector Operations. Lines in Three Dimensions, Equations of a Plane. Vector Differentiation, Gradient of a Scalar Function. Introduction to div and curl (divergence operator) Systems of Linear Equations, Gaussian Elimination: General Case. Matrices, Vectors and Matrices, Inverse Matrices, Determinants. Eigenvalues and Eigenvectors, Diagonalisation. Systems of Linear Differential Equations.