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.

References: 

• 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