Shivaji University, Kolhapur
First Year B. Tech
ENGINEERING MATHEMATICS - I
Unit 1 Matrix Theory 8 hrs
Rank of a matrix, Normal form of a matrix, Consistency of the system of linear equations, linear dependence and independence of vectors, Eigen values and eigen vectors, Cayley-Hamilton Theorem and its applications.
Unit 2 Differential Calculus 8 hrs
Successive differentiation, Leibnitz’s Theorem and its applications, Taylor's and Maclaurin's series, indeterminate forms.
Unit 3 Partial Differentiation 8 hrs
Partial derivatives of first and higher order, total differentials, differentiation of composite and implicit functions. Euler’s Theorem on Homogeneous functions with two and three independent variables. Deductions from Euler’s Theorem.
Unit 4 Applications of Partial Differentiation 8 hrs
Errors and Approximation, Jacobian, Properties of Jacobian, Jacobian of Implicit function, Maxima and Minima of functions of two variables
Unit 5 Complex Numbers 8 hrs
Complex number, representation of a complex number in Cartesian & Polar co-ordinate systems, Argand’s diagram, De’Moivre’s Theorem and its applications, circular and inverse circular functions, hyperbolic and inverse hyperbolic functions, logarithm of complex numbers.
Unit 6 Curve fitting 8 hrs
Fitting of Curves by method of Least-squares for linear, parabolic, and exponential, Coefficient of correlation, Spearman’s rank correlation, coefficient and lines of regression of bivariate data.
Suggested list of Tutorials/Assignments-
- Teacher: H P Salunkhe