AIM To impart enough Mathematical background in Matrices and Differential Calculus for the exact understanding of the Engineering subjects.

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Presentation transcript:

AIM To impart enough Mathematical background in Matrices and Differential Calculus for the exact understanding of the Engineering subjects.

UNIT-I MATRICES

MATRICES Characteristic equation Eigen Value & Eigen Vectors Properties of Eigen Values Cayley Hamilton Theorem Similarity Transformation Orthogonal Transformation Quadratic form Canonical form

APPLICATIONS Computer Applications Graph Theory Coding and Decoding Nuclear Physics Signal Processing Digital Image Processing Communication Analysis Bio Medical Engineering

UNIT-II THREE DIMENSIONAL ANALYTICAL GEOMETRY

THREE DIMENSIONAL ANALYTICAL GEOMETRY Angle between two lines Coplanar lines Skew lines Sphere Orthogonal Spheres Cone - Right circular cone Cylinder – Right circular Cylinder

APPLICATIONS Multimedia & Animations Analysis of Forces Engineering Graphics Astronomy

UNIT-III DIFFERENTIAL CALCULUS

DIFFERENTIAL CALCULUS Curvature Cartesian co-ordinates Centre & Radius of curvature Circle of curvature Envelopes Evolutes

APPLICATIONS Digital signal processing Study of electromagnetism To analyze and describe geologic structure To analyze shapes

UNIT – IV FUNCTIONS OF SEVERAL VARIABLES

FUNCTIONS OF SEVERAL VARIABLES Partial derivatives Euler’s Theorem Total derivative Implicit functions Jacobians Maxima & Minima – Two variables Lagrange’s Multipliers Taylor’s expansion

APPLICATIONS Rocket Propulsion optimization & its trajectory optimization Velocity & Acceleration Mathematical modeling Thermodynamics Fluid Dynamics

Z=sin(x 2 +y 2 ) (1/2)-t (texture)

UNIT – V ORDINARY DIFFERENTIAL EQUATIONS

ORDINARY DIFFERENTIAL EQUATIONS Second & higher order linear ODE Simultaneous first order linear equations Cauchy’s & Legendre’s linear equations Method of variation of parameter

APPLICATIONS Aero Dynamics Missile Technology Planetary Motion Circuit Theory Wave Equation

TEXT & REFERENCE BOOKS

TEXT BOOK s Grewal, B.S, “Higher Engineering Mathematics”, Thirty eighth Edition, Khanna Publishers, New Delhi, Venkataraman. M. K., “Engineering Mathematics”, Volume I and II Revised enlarged Fourth Edition, The National Publishing Company, Chennai, REFERENCE BOOKS Glyn James., “Advanced Modern Engineering Mathematics”, Third Edition, Pearson Education Ltd, New Delhi, Veerarajan. T., “Engineering Mathematics (for first year)”, Fourth Edition, Tata McGraw – Hill Publishing Company Limited, New Delhi, Bali N. P and Manish Goyal, “Text book of Engineering Mathematics”, Third edition, Laxmi Publications (P) Ltd., 2008.