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AIM
To impart enough Mathematical background in Matrices and Differential Calculus for the exact understanding of the Engineering subjects.
UNIT-IMATRICES
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-IITHREE 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
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 – IVFUNCTIONS 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(x2+y2)(1/2)-t
Z=sin(x2+y2)(1/2)-t
(texture)
UNIT – VORDINARY 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 BOOKs• Grewal, B.S, “Higher Engineering Mathematics”, Thirty eighth Edition, Khanna Publishers,
New Delhi, 2005.• Venkataraman. M. K., “Engineering Mathematics”, Volume I and II Revised enlarged Fourth
Edition, The National Publishing Company, Chennai, 2004.
REFERENCE BOOKS• Glyn James., “Advanced Modern Engineering Mathematics”, Third Edition, Pearson Education
Ltd, New Delhi, 2004.• Veerarajan. T., “Engineering Mathematics (for first year)”, Fourth Edition, Tata McGraw – Hill
Publishing Company Limited, New Delhi, 2005.• Bali N. P and Manish Goyal, “Text book of Engineering Mathematics”, Third edition, Laxmi
Publications (P) Ltd., 2008.