aim to impart enough mathematical background in matrices and differential calculus for the exact...

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

http://images.google.co.in/imgres?imgurl=http://www.astro.columbia.edu/~archung/labs/fall2001/images/celestial-sphere.jpg&imgrefurl=http://www.astro.columbia.edu/~archung/labs/fall2001/lec02_fall01.html&usg=__6czj3w3jVtLyyRqqkStloPEAifI=&h=440&w=440&sz=106&hl=en&start=12&um=1&tbnid=kTP-saCB32QRZM:&tbnh=127&tbnw=127&prev=/images%3Fq%3DSPHERE%26hl%3Den%26sa%3DN%26um%3D1

http://images.google.co.in/imgres?imgurl=http://thesaurus.maths.org/mmkb/media/png/Cone.png&imgrefurl=http://thesaurus.maths.org/mmkb/entry.html%3Bjsessionid%3DA0786208C64CDF744FF8DAD1810E91FD%3Faction%3DentryByConcept%26id%3D877%26langcode%3Den%26expand%3D4&usg=__xsEiMJBDvJC9uRUqig5e2Rzw8PY=&h=300&w=300&sz=78&hl=en&start=16&um=1&tbnid=Pc42mjrdO6kLIM:&tbnh=116&tbnw=116&prev=/images%3Fq%3Dcone%26hl%3Den%26um%3D1

http://images.google.co.in/imgres?imgurl=http://www.mathworks.com/access/helpdesk/help/techdoc/ref/graphics_ca.gif&imgrefurl=http://www.mathworks.com/access/helpdesk/help/techdoc/ref/cylinder.html&usg=__xk8pobXKVBagBpvh-KeyiztVMxc=&h=365&w=346&sz=8&hl=en&start=14&um=1&tbnid=S6h3BjOdoyatFM:&tbnh=121&tbnw=115&prev=/images%3Fq%3Dcylinder%26hl%3Den%26um%3D1

http://images.google.co.in/imgres?imgurl=http://www.icoachmath.com/Sitemap/images/Coplanar2.jpg&imgrefurl=http://www.icoachmath.com/SiteMap/Coplanar.html&usg=__qL4ewbSOIA8WmZkmGjveqc5OrHo=&h=218&w=277&sz=8&hl=en&start=14&um=1&tbnid=7Ip_FytO16FucM:&tbnh=90&tbnw=114&prev=/images%3Fq%3Dcoplanar%2Bline%26hl%3Den%26um%3D1

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

http://images.google.co.in/imgres?imgurl=http://blog.thepimp.net/public/images/astronomy/m96sqcrop_block.jpg&imgrefurl=http://blog.thepimp.net/archives/Astronomy-picture-of-the-day.html&usg=__x7vcydR6C4_7HxhL5xXcjqvXZUk=&h=1649&w=1723&sz=776&hl=en&start=10&um=1&tbnid=Rbx44CPGvuCheM:&tbnh=144&tbnw=150&prev=/images%3Fq%3Dastronomy%2Bpicture%2Bof%2Bthe%2Bday%26hl%3Den%26sa%3DN%26um%3D1

http://images.google.co.in/imgres?imgurl=http://curvebank.calstatela.edu/index/evoluteparabola.jpg&imgrefurl=http://curvebank.calstatela.edu/index/index.htm&usg=__1RU5Zura7UTtNfvTPBA3EhQh4fE=&h=453&w=500&sz=30&hl=en&start=5&um=1&tbnid=GfSAJ4ly0NjBeM:&tbnh=118&tbnw=130&prev=/images%3Fq%3Devolute%2Bof%2Bparabola%26hl%3Den%26um%3D1

UNIT-IIIDIFFERENTIAL CALCULUS

http://images.google.co.in/imgres?imgurl=http://upload.wikimedia.org/wikipedia/commons/thumb/4/49/Minimal_surface_curvature_planes-fr.svg/800px-Minimal_surface_curvature_planes-fr.svg.png&imgrefurl=http://commons.wikimedia.org/wiki/File:Minimal_surface_curvature_planes-fr.svg&usg=__ZDJn-m2gcKysYmwYoHjd1WeCk6c=&h=546&w=800&sz=141&hl=en&start=14&um=1&tbnid=enlSZ_pJMMbjkM:&tbnh=98&tbnw=143&prev=/images%3Fq%3DCurvature%26hl%3Den%26um%3D1

DIFFERENTIAL CALCULUS

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

http://images.google.co.in/imgres?imgurl=http://mathworld.wolfram.com/images/eps-gif/AstroidInvolute_800.gif&imgrefurl=http://mathworld.wolfram.com/AstroidInvolute.html&usg=__E95xF1drZe1VRYG0Orp3SBiLAP4=&h=226&w=226&sz=3&hl=en&start=23&um=1&tbnid=L_-FXipYqrsrQM:&tbnh=108&tbnw=108&prev=/images%3Fq%3Devolute%2Binvolute%26ndsp%3D18%26hl%3Den%26sa%3DN%26start%3D18%26um%3D1

APPLICATIONS

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

http://images.google.co.in/imgres?imgurl=http://upload.wikimedia.org/wikipedia/commons/thumb/9/91/Electromagnetism.svg/550px-Electromagnetism.svg.png&imgrefurl=http://commons.wikimedia.org/wiki/File:Electromagnetism.svg&usg=__0Ie7JJRaQ9gilWV14YTd9lvQrts=&h=599&w=550&sz=58&hl=en&start=1&um=1&tbnid=EODWQcLNi0OOLM:&tbnh=135&tbnw=124&prev=/images%3Fq%3Delectromagnetism%26hl%3Den%26sa%3DN%26um%3D1

http://images.google.co.in/imgres?imgurl=http://www.photopositives.com/mars/brycecanyon.jpg&imgrefurl=http://www.photopositives.com/mars/brycecanyon.html&usg=__DZ5kxr8q_fyegCZbef3Qgmh1gW0=&h=750&w=500&sz=115&hl=en&start=126&um=1&tbnid=3dEz2PC-_mXh0M:&tbnh=141&tbnw=94&prev=/images%3Fq%3Dgeologic%2Bstructure%26ndsp%3D18%26hl%3Den%26sa%3DN%26start%3D108%26um%3D1

http://images.google.co.in/imgres?imgurl=http://www.damtp.cam.ac.uk/user/ngb23/EM/field_big.gif&imgrefurl=http://www.damtp.cam.ac.uk/user/ngb23/EM/index.html&usg=__akn51zkpfQuHfrRtJeYXiG6Q7j8=&h=423&w=376&sz=108&hl=en&start=42&um=1&tbnid=uER3A61OdHUXfM:&tbnh=126&tbnw=112&prev=/images%3Fq%3Delectromagnetism%26ndsp%3D18%26hl%3Den%26sa%3DN%26start%3D36%26um%3D1

http://images.google.co.in/imgres?imgurl=http://www.ba.infn.it/~zito/museo/figura1.gif&imgrefurl=http://www.ba.infn.it/~zito/museo/leonardoen.html&usg=__yireaO-A0av23nTDbywoYmo03UQ=&h=365&w=564&sz=8&hl=en&start=37&um=1&tbnid=9TZU_P8IyNeXFM:&tbnh=87&tbnw=134&prev=/images%3Fq%3Delectromagnetism%26ndsp%3D18%26hl%3Den%26sa%3DN%26start%3D36%26um%3D1

UNIT – IVFUNCTIONS OF SEVERAL

VARIABLES

http://images.google.co.in/imgres?imgurl=http://www.usd.edu/~jflores/MultiCalc02/WebBook/Chapter_15/Graphics15/Chapter15_1/Html15_1/15.1%2520Functions%2520of%2520Several%2520variables__35.png&imgrefurl=http://www.usd.edu/~jflores/MultiCalc02/WebBook/Chapter_15/Graphics15/Chapter15_1/Html15_1/15.1%2520Functions%2520of%2520Several%2520variables.htm&usg=__3-keRfFMe_QyxXAjamJy5OiR-FU=&h=344&w=317&sz=12&hl=en&start=1&um=1&tbnid=PsHw4dCsd9doWM:&tbnh=120&tbnw=111&prev=/images%3Fq%3DFUNCTIONS%2BOF%2BSEVERAL%2BVARIABLES%26hl%3Den%26um%3D1

http://images.google.co.in/imgres?imgurl=http://archives.math.utk.edu/ICTCM/EP-10/C9/html/lc.gif&imgrefurl=http://www.grossmont.edu/jennyvandeneynden/archive/M281_links.htm&usg=__oxgENnBI7NgZP0eXIS_4SOfm_-k=&h=384&w=403&sz=187&hl=en&start=54&um=1&tbnid=1kEoLV96fzbfIM:&tbnh=118&tbnw=124&prev=/images%3Fq%3DFUNCTIONS%2BOF%2BSEVERAL%2BVARIABLES%26ndsp%3D18%26hl%3Den%26sa%3DN%26start%3D36%26um%3D1

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

http://images.google.co.in/imgres?imgurl=http://www.math.jhu.edu/mathcourses/302/images/LorenzBeads.jpg&imgrefurl=http://www.math.jhu.edu/mathcourses/302/index.html&usg=__D2hhi1z-z3f1XAw-z9V5gBDtA38=&h=575&w=780&sz=29&hl=en&start=3&um=1&tbnid=mWe8XfDhBZHRSM:&tbnh=105&tbnw=142&prev=/images%3Fq%3Ddifferential%2Bequations%26ndsp%3D18%26hl%3Den%26sa%3DN%26um%3D1

http://images.google.co.in/imgres?imgurl=http://www.analyzemath.com/calculus/Differential_Equations/order_linearity_5.gif&imgrefurl=http://www.analyzemath.com/calculus/Differential_Equations/order_linearity.html&usg=__CBqR-UzVYeTo9jrzC7FzCSSpeZY=&h=361&w=349&sz=6&hl=en&start=1&um=1&tbnid=-q_VsGIpY_MvxM:&tbnh=121&tbnw=117&prev=/images%3Fq%3Ddifferential%2Bequations%26ndsp%3D18%26hl%3Den%26sa%3DN%26um%3D1

ORDINARY DIFFERENTIAL EQUATIONS

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

http://www.walterzorn.com/images/grapher/ode_xsin.png

APPLICATIONS

• Aero Dynamics• Missile Technology• Planetary Motion• Circuit Theory• Wave Equation

http://images.google.co.in/imgres?imgurl=http://tellus.ssec.wisc.edu/outreach/space_physics/Cosmology_Tutorial/doppler.gif&imgrefurl=http://tellus.ssec.wisc.edu/outreach/space_physics/Cosmology_Tutorial/redshift.html&usg=__cwwZHKMcoBIp7VBGZqgDX5f1NJ8=&h=387&w=393&sz=6&hl=en&start=55&um=1&tbnid=aEC1TJ1BMuJzrM:&tbnh=122&tbnw=124&prev=/images%3Fq%3Dlight%2Bwaves%26ndsp%3D18%26hl%3Den%26sa%3DN%26start%3D54%26um%3D1

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.

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