Differentiation, Integration, Maxima and Minima, Determinants and Matrices
To make the students familiarize with concepts and techniques in Calculus, Fourier series and
Matrices. The aim is to equip them with the techniques to understand advanced level
mathematics and its applications that would enhance analytical thinking power, useful in their
Mean value theorems and its generalizations leading to Taylors and Maclaurin’s series
useful in the analysis of engineering problems.
The Fourier series representation and harmonic analysis for design and analysis of periodic
continuous and discrete systems.
To deal withderivative of functions of several variables that are essential in various
branches of Engineering.
To apply the concept of Jacobian to find partial derivative of implicit function and
functional dependence. Use of partial derivatives in estimating error and approximation and
finding extreme values of the function.
The essential tool of matrices and linear algebra in a comprehensive manner for analysis of
system of linear equations, finding linear and orthogonal transformations, Eigen values and
Eigen vectors applicable to engineering problems
Syllabus and Notes
Rolle’s Theorem, Mean Value Theorems, Taylor's Series and Maclaurin's Series, Expansion of
functions using standard expansions, Indeterminate Forms, L' Hospital's Rule, Evaluation of
Limits and Applications.
Definition, Dirichlet’s conditions, Full range Fourier series, Half range Fourier series, Harmonic
analysis, Parseval’s identity and Applications to problems in Engineering.
Introduction to functions of several variables, Partial Derivatives, Euler's Theorem on
Homogeneous functions, Partial derivative of Composite Function, Total Derivative, Change of
Applications of Partial Differentiation
Jacobian and its applications, Errors and Approximations, Maxima and Minima of functions of
two variables, Lagrange's method of undetermined multipliers.
Linear Algebra-Matrices, System of Linear Equations
Rank of a Matrix, System of Linear Equations, Linear Dependence and Independence, Linear
and Orthogonal Transformations, Application to problems in Engineering.
Linear Algebra-Eigen Values and Eigen Vectors, Diagonaliztion
Eigen Values and Eigen Vectors, Cayley Hamilton theorem, Diagonaliztion of a matrix,
Reduction of Quadratic forms to Canonical form by Linear and Orthogonal transformations.