Engineering Mathematics Tutorial
COURSE OBJECTIVE:
The objective of this course is to familiarize the graduate engineers with techniques in calculus,
multivariate analysis, vector calculus and linear algebra. It aims to equip the students with
standard concepts and tools from intermediate to advanced level that will enable them to tackle
more advanced level of mathematics and applications that they would find useful in their
disciplines.
The students will learn:
To apply the knowledge of differential calculus in the field of engineering.
To deal with functions of several variables that is essential in optimizing the results of real
life problems.
Multiple integral tools to deal with engineering problems involving centre of gravity,
volume etc.
To deal with vector calculus that is required in different branches of Engineering to
graduate engineers.
The essential tools of matrices and linear algebra, Eigen values and diagonalization in a
Comprehensive manner are required.
- Common For All B.Tech Students 1st year
- Basics of class 11th & 12th are required
- Classes are available in group as well as One-To-One
- Highly Experienced faculties from colleges and corporates
- Individual attention with free test series and doubt session
- 100% Passing Results
- Timing are flexible and adjustable
- Classes are available in online as well as offline mode
Details Syllabus Of Engineering Mathematics
- Matrices: Types of Matrices: Symmetric, Skew-symmetric and
Orthogonal Matrices; Complex Matrices, Inverse and Rank of matrix
using elementary transformations, Rank-Nullity theorem; System of linear
equations, Characteristic equation, Cayley-Hamilton Theorem and its
application, Eigen values and eigenvectors; Diagonalisation of a Matrix - Differential Calculus- I: Introduction to limits, continuity and differentiability, Rolle’s Theorem, Lagrange’s Mean value theorem and Cauchy mean value theorem, Successive Differentiation (nth order derivatives), Leibnitz theorem and its application, Envelope of family of one and two parameter, Curve tracing: Cartesian and Polar co-ordinates
- Differential Calculus-II: Partial derivatives, Total derivative, Euler’s
Theorem for homogeneous functions, Taylor and Maclaurin’s theorems for
a function of two variables, Maxima and Minima of functions of several
variables, Lagrange Method of Multipliers, Jacobians, Approximation of
errors - Multivariable Calculus-I: Multiple integration: Double integral, Triple
integral, Change of order of integration, Change of variables, Application:
Areas and volumes, Center of mass and center of gravity (Constant and
variable densities) - Vector Calculus: Vector identities (without proof), Vector differentiation:
Gradient, Curl and Divergence and their Physical interpretation, Directional
derivatives.
Vector Integration: Line integral, Surface integral, Volume integral, Gauss’s
Divergence theorem, Green’s theorem and Stoke’s theorem (without proof)
and their applications
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