# Mathematics-1

 Course Code : BMA101 Author : Ulektz University : Bharath University, Tamil Nadu (BU) Regulation : 2015 Categories : Engineering Mathematics Format : ePUB3 (DRM Protected) Type : eBook

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Description :Mathematics-1 of BMA101 covers the latest syllabus prescribed by Bharath University, Tamil Nadu (BU) for regulation 2015. Author: Ulektz, Published by uLektz Learning Solutions Private Limited.

Note : No printed book. Only ebook. Access eBook using uLektz apps for Android, iOS and Windows Desktop PC.

##### Topics
###### UNIT I MATRICES

1.1 Characteristic equation

1.2 Eigenvalues and Eigen vectors of a real matrix

1.3 Properties of eigenvalues and eigen vectors

1.4 Cayley - Hamilton Theorem(Excluding proof)

1.5 Orthogonal transformation of a symmetric matrix to diagonal form

1.7 Reduction of a quadratic form to canonical form by orthogonal transformation

###### UNIT-II Three Dimensional Analytical Geometry

2.1 Equation of a Sphere

2.2 Plane section of a sphere - Tangent plane

2.3 Equation of cone - Right circular cone

2.4 Equation of a cylinder - Right circular cylinder

###### UNIT III APPLICATIONS OF DIFFERENTIAL CALCULUS

3.1 Curvature in Cartesian co-ordinates

3.2 Centre and radius of curvature

3.3 Circle of curvature

3.4 Evolutes

3.5 Envelopes-Applications of Evolutes and Envelopes.

4.1 Partial derivatives

4.2 Euler’s theorem for homogeneous functions

4.3 Total derivatives- Differentiation of implicit functions

4.4 Jacobians

4.5 Taylor’s expansion- Maxima and Minima

4.6 Method of Lagrangian multipliers

###### UNIT V MULTIPLE INTEGRALS

5.1 Double integrals - Cartesian and polar coordinates

5.2 Change of order of integration

5.3 Change of variables between Cartesian and Polar coordinates

5.4 Triple integration in Cartesian coordinates

5.5 Area as double integral

5.6 Volume as triple integral