चार महीने का बच्चा कैसे बना अरब़पति? जन्म के सिर्फ चार माह बाद यदि कोई बच्चा अरबपति बन जाए तो इसे उसकी किस्मत ही कहेंगे। भारत के एकाग्रह रोहन मूर्ति नाम के बच्चे की किस्मत कुछ इसी प्रकार चमकी है। देश की दूसरी सबसे बड़ी आइटी कम्पनी इंफोसिस के फाउंडर नारायण मूर्ति ने सोमवार अपने चार महीने के पोते एकाग्रह मूर्ति को 240 करोड़ रूपए के शेयरों की हिस्सेदारी का तोहफा देकर उसे शायद देश का सबसे कम उम्र का अरबपति बना दिया है। BSE की फाइलिंग के अनुसार इंफोसिस में अब एकाग्रह रोहन की 15 लाख शेयरों की हिस्सेदारी हो गई है। इसका मतलब अब एकाग्रह रोहन इंफोसिस का 0.04% का हिस्सेदार है। शेयरों के स्थानान्तरण के बाद नारायण मूर्ति के पास कम्पनी के कुल शेयरों का 0.36% हिस्सा बचा है। जिस समय नारायण मूर्ति द्वारा अपने पोते को शेयर देने की खबर बाई उस समय इंफोसिस के शेयरों में गिरावट देखने को मिल रही थी। एकाग्रह रोहन, नारायण मूर्ति तथा सुधा मूर्ति के बेट रोहन मूर्ति और उनकी पत्नि अर्पणा कृष्णन का बेटा है। आपको यह पता होगा कि नोरायण मूर्ति ने अपनी पत्नि सुधा मूर्ति से 10 हजार रूपए उधार लेकर 1981 में इंफोसिस क
Advanced Calculus
Advanced Differential Calculus, Integral Calculus and Vector Calculus
Authors: Dr. Vimal Saraswat, Dr. Anil Kumar Menaria
ISBN :978-81-7906-950-9
Price: Rs. 375.00
Publisher: Himanshu Publications, Hiran Magri Udaipur; Himanshu Publications Prakash House, Ansari Road, New Delhi
E-mail : info@sacademy.co.in
Phone: +91 9664392614
To buy this book click on the link Advanced Calculus by Saraswat
Continuity
- Introduction
- Limit
- Left and right limit
- To find the R.H.L. and L.H.L. of a function
- Existence of limit)/li>
- Distinction between the value and limit of a function
- Some theorems based on limits
- Methods of finding the limit of functions
- Some standard limits
- Cauchy’s definition of continuity
- Continuity from left and right
- Continuity of a function in an interval Continuity in the open interval); Continuity in the closed interval
- Continuous function
- Heine's definition of continuity or sequential continuity
- Discontinuity and its types Removable discontinuity; Discontinuity of first kind or ordinary discontinuity; Discontinuity of the second kind; Mixed discontinuity
- Properties of continuous functions
- Uniform continuity
- Function of two variables
- Limit of function of two variables
- Continuity of function of two variables
Derivability
- Differentiable or derivable function
- Right hand and left hand derivative
- Differentiability of a function in an interval
- Some standard results on differentiability
- Necessary condition for the existence of a finite derivative
- Algebraic properties of derivatives
- Chain rule or derivative of function of a function
- Derivative of the inverse function
- Properties of derivative
- Darboux intermediate value theorem for derivatives
- Differentiability of functions of two variables
- Necessary and sufficient condition for differentiability
- Total derivative
- Algebraic property of differentiability of real valued functions of two variables
- Condition for differentiability in polar coordinates
Partial Differentiation
- Introduction
- Partial differential coefficients
- Partial derivatives of higher order
- Homogeneous functions
- Euler's theorem for homogeneous functions
- Total differential coefficient
- Differentiation of implicit functions
Maxima and Minima
- Introduction
- Extreme values of functions of two variables
- Criteria for extreme value of f (x, y)
- Working method of finding extreme values
- Lagrange's method for undetermined multipliers
Envelopes and Evolutes
- Family of curves
- Envelope
- Method of finding the envelope
- Working method for finding envelope
- Relation between envelope and each member of the family of curves
- To find the envelope, when two parameters are connected by a relation
- Evolute
Jacobians
- Introduction
- Definition
- Jacobians of functions of functions
- Jacobians of implicit functions
- Dependence of functions
Double Integrals
- Introduction
- Double integration
- Method of finding double integral
- Double integral in polar coordinates
- Change of double integral from cartesian to polar coordinates
- Change of order of integration
- Applications of double integrals Area; Mass
Triple Integrals
- Introduction
- Evaluation of triple integral
- Dirichlet's integral
- Liouville's extension of Dirichlet's integral
- Dirichlet's general theorem
- Applications of triple integral
Volume and Surface of Solids of Revolution
- Introduction
- Volume of solids of revolution of cartesian curves
- Volume generated by revolution about any line
- Volume of solids of revolution of polar curves
- Prolate and oblate spheroid
- Surface area of solids of revolution of cartesian curves
Differential Operators
- Introduction
- Differential formulae for vectors
- Partial derivatives of vectors
- Vector differential operator ▽
- Scalar point function and scalar field
- Vector point function and vector field
- Gradient of scalar point function
- Theorem based on gradient
- a ⋅ ▽ operator
- Directional derivative
- Theorems based on directional derivatives
- Vector equation of tangent plane
- Vctor equation of the normal
- Divergence of a vector point function
- Solenoidal vector
- Theorem based on divergence
- Curl of a vector point function
- Irrotational vector
- Theorem based on curl
- Some important vector identities
- Second order differential function and its properties
Vector integrationn
- Introduction
- Vector constant of integration
- Some important integral result
- Linear integral or line integral
- Irrotational vector
- Work
Integral theorems
- Introduction
- Surface integral
- Volume integral
- Gauss's divergence theorem
- Stoke's theorem
- Green's theorem
- Cartesian form of Green's theorem
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