July 7, 2012

Applied Mathematics -1

Portion and Syllabus of Applied Mathematics -1 of Semester 1 of F.Y.B.Sc.(I.T.) is as follows:
  • Matrices
    • Minors and Cofactors
    • Adjoint of a Square Matrix
    • Inverse of a Matrix. 
    • Rank of a Matrix
    • Solution of Homogeneous and Non Homogeneous linear Equations using Matrix method.
  • Eigen Values and Eigen Vectors
    • Vectors
    • Linear Combination of Vectors
    • Inner Product of two Vectors
    • Characteristic Equation
    • Eigen Vector
    • Cayley- Hamilton Theorem
    • Similarity of Matrices
    • Derogatory and Non-derogatory Matrices
    • Complex Matrices: Hermitian
    • Skew-Hermitian and Unitary Matrices and their Properties.
  • Vector Calculus
    • Vector Differentiation: Vector Operator Del
    • Gradient
    • Geometrical Meaning of Gradient
    • Divergence and Curl.
  • Differential Equations
    • Differential Equations of 1st order and 1st Degree and Applications.
  • Linear Differential Equations: 
    • Linear Differential Equations with Constant coefficient
    • Differential Equations of Higher Order and Applications.
  • Successive Differentiation
  • Mean Value Theorems
  • Partial Differentiation
  • Euler's Theorem
  • Approximation and Errors
  • Maxima and Minima
Text Books:
  • Engineering Mathematics A tutorial approach by R. R. Singh and Mukul Bhatt
  • TMH 2010 Text Book of Applied Mathematics Vol I and Vol II. P.N. Wartikar & J.N. Wartikar, Pune Vidyarthi Griha Prakashan.
  • Higher Engineering Mathematics by B. V. Ramana, McGrawHill 
  • Differential Calculus by Shanti Narayan. S. Chand. 
  • Higher Engineering Mathematics by B.S. Grewal, Khanna Publications 
  • Vector Analysis by Murray Spiegel, McGrawHill 
  • Matrices by Vashistha, S. Chand


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