Engineering Mathematics I

Course Outline

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Welcome to Engineering Mathematics I. This course introduces foundational mathematical tools required throughout engineering: differential calculus, linear algebra, differential equations, and Laplace transforms.

Module I: Differential Calculus (One Variable)

  • Rolle's theorem and Cauchy's mean value theorem
  • Taylor's and Maclaurin's theorems with remainders
  • Indeterminate forms
  • Concavity, convexity, and points of inflexion
  • Asymptotes and curvature

Module II: Linear Algebra (Matrix Theory)

  • Algebra of matrices, rank and inverse
  • Hermitian, skew Hermitian and unitary matrices
  • Eigenvalues and eigenvectors
  • Systems of linear equations and consistency
  • Homogeneous systems and linear dependence of vectors
  • Numerical solutions: Gauss, Gauss Jordan and Gauss Seidel
  • Vector spaces, basis and linear transformations

Module III: Ordinary Differential Equations

  • First order equations: exact, linear and Bernoulli
  • Second order equations with constant coefficients
  • Method of variation of parameters
  • General linear ODE with constant coefficients
  • Euler equations and systems of differential equations

Module IV: Laplace Transforms

  • Laplace transforms and inverse transforms
  • Properties of Laplace transform
  • Solution of ODEs using Laplace transform

This course builds the essential mathematical foundation for advanced engineering subjects. Each module includes clearly structured concepts suited for exam preparation.

Differential Calculus