Mathematics for Engineers and Scientists

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This Mathematics for Engineers and Scientists study guide covers 6 topics in depth. These include Complex Numbers, Vectors, Linear Algebra and more, with multiple subtopics inside each of the main topic areas (see full list of topics below). It has been tailored to cater for Engineering students of all levels, from any University and has been specifically designed to improve both, the direction of your coursework research and the efficiency of your exam revision.

  • Complex Numbers
    • Number Classification
    • Fundamental Theorem of Algebra
    • Definitions
    • Addition and Subtraction
    • Complex Conjugation
    • Multiplication
    • Modulus
    • Division
    • Polar Coordinates
    • Euler Formula
    • De Moivre's’ Theorem
    • Roots and Powers of Complex Numbers
    • The General Expression
    • Polynomial Expressions
    • Logarithms
    • Some Geometry
    • Application - LCR Circuits
    • Application - Mapping and 2D flow
  • Calculus, Limits and Series
    • Limits Introduction
    • Calculus of Limits
    • Limits of a function
    • The pinching/squeezing theorem
    • Continuity
    • Differentiation and differentiability
    • L'Hopital's Rule
    • Taylor Series
    • Leibnetz’ rule
    • Calculus of Taylor’s Series
    • Integrating and Differentiating
    • Newton-Raphson Method
  • Vectors
    • Notation and definitions of vectors
    • Vector addition
    • Scalar multiplication
    • Laws of addition, subtraction and scalar multiplication
    • Bases and components
    • Scalar (dot) product
    • Equation of a straight line
    • Equation of a plane
    • Parametric equation of a plane
    • Work done
    • Intersecting planes
    • Vector (cross) product
    • Scalar triple product
    • Vector equation of a straight line
    • Distance between 2 lines
    • Differentiation of vectors
    • Vector mechanisms
  • Functions of Several Variables
    • Partial differentiation
    • Chain rule
    • Higher dimensions
    • Directional derivatives
    • Tangent planes and normals to surfaces
    • Div and Curl
    • Critical Points
    • Differential Equations
    • General solutions and particular solutions
    • 1st order ODE’s
    • Homogeneous ODE’s
    • Linear ODE’s
    • Exact ODE’s
    • Second order linear constant coefficient ODE’s
  • Linear Algebra
    • Matrices and Vectors Introduction
    • Using matrices for linear algebra
    • Gaussian elimination
    • Determinants and inverses
    • LU factorisation
    • Application to electrical circuits
  • Vector Spaces
    • Vector spaces introduction
    • Eigenvectors and eigenvalues
    • Linear system of ODE’s
    • Numerical Linear Algebra

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