syllabus of Engineering Mathematics I

Engineering Mathematics I Syllabus

  1. Differential Calculus

    • Functions of one variable
    • Limits and continuity
    • Differentiation rules
    • Mean Value Theorems
    • Taylor’s and Maclaurin’s Theorems
    • Applications of derivatives (e.g., maxima and minima)

  2. Integral Calculus

    • Definite and indefinite integrals
    • Techniques of integration
    • Applications of integrals (e.g., area under curves, volumes of solids of revolution)
    • Improper integrals

  3. Linear Algebra

    • Matrices and determinants
    • Systems of linear equations
    • Vector spaces
    • Eigenvalues and eigenvectors
    • Diagonalization

  4. Vector Calculus

    • Vector functions
    • Differentiation and integration of vector functions
    • Gradient, divergence, and curl
    • Line and surface integrals
    • Green’s, Stokes’, and Gauss’ theorems

  5. Ordinary Differential Equations (ODEs)

    • First-order ODEs
    • Second-order linear ODEs
    • Higher-order ODEs
    • Series solutions of ODEs

  6. Partial Differential Equations (PDEs)

    • Basic concepts
    • Fourier series and Fourier transforms
    • Applications to engineering problems

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