Maths for Engineers and Scientists (MATH1551)

This set of Year 1 notes from Durham University's "Maths for Engineers" module provides a comprehensive overview of Vectors. It covers key topics including coordinates and bases, dot product, projections, lines and planes in 3D, distances, vector product, applications to mechanics, and eigenvalues and eigenvectors. The notes are packed with clear examples and detailed explanations, making complex concepts accessible and easy to understand. Ideal for engineering students seeking to excel in th...

This comprehensive set of Year 1 notes from Durham University's "Maths for Engineers" module provides a thorough introduction to Linear Algebra. Topics covered include gaussian elimination, determinants, matrices and iterative methods all explained with clear examples and step-by-step solutions. These notes are meticulously organised, making them an essential resource for mastering core concepts and excelling in exams. Ideal for engineering students looking to solidify their understanding of ...

This set of Year 1 notes from Durham University's "Maths for Engineers" module offers a comprehensive guide to Limits and Series. It covers crucial topics such as limits of functions, continuous and differentiable functions, intermediate and extreme values, L'Hôpital's rule, Leibniz's rule, the Newton-Raphson method, Taylor series, convergence, and Taylor's Theorem. The notes are meticulously organized with clear examples and step-by-step explanations, making complex concep...

This set of Year 1 notes from Durham University's "Maths for Engineers" module offers a clear and concise introduction to Complex Numbers. Covering solving polynomials, complex logarithms, De Moivre's Theorem, Trigonometric functions, and applications to geometry and AC circuits; these notes are packed with examples and step-by-step explanations. They are meticulously organised to help students grasp challenging concepts and perform well in exams. Perfect for engineering students aiming to m...

This set of Year 1 notes from Durham University's "Maths for Engineers" module offers an in-depth exploration of Differential Equations. It covers a wide range of topics including first-order ODEs (Separable, Homogeneous, Linear, Bernoulli, and Exact), second-order ODEs (Homogeneous and Inhomogeneous), applications, damped and forced oscillations, and systems of linear ODEs. The notes are detailed and methodically structured, with clear examples and step-by-step solutions to help students mas...

This set of Year 1 notes from Durham University's "Maths for Engineers" module provides a thorough introduction to Functions of Several Variables. It covers essential topics such as the chain rule, changes of variables, directional derivatives and gradients, tangent planes, normal lines to surfaces, vector fields (Grad, Div, and Curl), and critical points with extreme values. The notes are well-organised and filled with clear examples and detailed explanations, making complex topics mor...