Spring Semester Engineering Mathematics'., Lecture notes of Mathematics

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3/14/25, 9:04 PM about:blank MAS 140 151 152 156 Spring Semester Engineering Mathematics University of Sheffield School of Mathematics and Statistics MAS140/151/152/156 Engineering Mathematics Spring Semester Module Leader: Prof. Lucy Wyatt, School of Mathematics and Statistics. Email: mas-engineering@sheffield.ac.uk Outline Syllabus: Spring Semester + Integration: Indefinite integrals of simple functions. Simple substitutions, Standard forms involving inverse trigonometric and inverse hyperbolic functions. Examples using completing the square and partial fractions. Integration by parts. Definite integrals: properties, evaluation, application to area. * Matrices and linear equations: Definition of an mn matrix. Special matrices (identity, zero, square etc.). Matrix algebra. Transpose. Symmetric and skew-symmetric matrices, and the decomposition of square matrices. Determinants. Inverse of a non-singular matrix. Use of matrices to solve systems of linear equations (homogeneous and nonhomogeneous). Gaussian elimination. Eigenvalues and eigenvectors. * Ordinary differential equations: First order differential equations: variables separable, linear with integrating factor, general solution, solution satisfying given initial conditions. Second order linear differential equations with constant coefficients: auxiliary equation, complementary function. Particular integral for polynomials, exponentials, trigonometric functions and products of polynomials and exponential/trigonometric functions on right-hand side. Laplace transforms and application to the solution of ODEs. 1/81