This book is a compilation of all basic topics on functions of Several Variables and is primarily meant for undergraduate and post graduate students.

    Topics covered are:

    • Limits, continuities and differentiabilities of functions of several variables.
    • Properties of Implicit functions and Jacobians.
    • Extreme values of multivariate functions.
    • Various types of integrals in planes and surfaces and their related theorems including Dirichlet and Liouville’s extension to Dirichlet.

    Print edition not for sale in South Asia (India, Sri Lanka, Nepal, Bangladesh, Pakistan or Bhutan)



    1. Functions of Several Variables: Limits & Continuity

    2. Functions of Several Variables: Differentiation – I

    3. Functions of Several Variables: Differentiation – II

    4. Jacobians, Functional Dependence and Implicit Functions

    5. Extrema of Functions of Several Variables

    6. Multiple Integrals

    7. Line, Surface and Volume Integrals

    8. Dirichlet’s Theorem and Liouville’s Extension




    Samiran Karmakar is Assistant Professor in Mathematics, Bankura Sammilani College, Bankura, West Bengal and is actively engaged in research in the field of Optimization Theory and Operational Research. Formerly, he was Assistant Professor in Mathematics, St. Xavier’s College, Kolkata.

    Sibdas Karmakar was former Associate Professor in Mathematics, Ramananda College, Bankura, West Bengal and has been associated with the teaching of honors in Mathematics for decades. He has also taught in Achhruram Memorial College, Purulia.