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महाराणा प्रताप ट्रेल सज्जनगढ़ उदयपुर

महाराणा प्रताप ट्रेल सज्जनगढ़ उदयपुर में इको ट्रेल 30 नवम्बर को राजस्थान वन विभाग उदयपुर डिविजन तथा WWF-India उदयपुर डिविजन के सानिध्य में महाराणा प्रताप ट्रेल सज्जनगढ़ उदयपुर में इको ट्रेल की गई, जिसमें WWF-India के स्टेट काॅर्डिनेटर श्रीमान अरूण सोनी तथा वन विभाग कीे ओर से डाॅ. सतीश कुमार शर्मा, सेवानिवृत्त अधिकारी मौजूद थे। मुझे भी इस इको ट्रेल में जाने का सुअवसर प्राप्त हुआ, जो गोरीला व्यू पाॅइंट से बड़ी-लेक व्यू पाॅइंट तक की गई इसमें मुझे विज्ञान की एक नई शाखा के बारे में पता चला, जिसे टट्टी विज्ञान कहा जाता है। सुनने में आपको थोड़ा अजीब लगेगा, मुझे भी सुनकर हैरानी हुई, परन्तु वास्तव में एक ऐसा भी विज्ञान है, जिसके बारे में डाॅ. सतीश शर्मा ने बड़े ही विस्तार पूर्वक बताया कि किस प्रकार वनों में जानवरों की टट्टी देखकर यह पता लगाया जा सकता है कि यहां कौनसा जानवर आया था। जानवरों की टट्टी कितनी पुरानी है, वह गीली है या सूखी है। इसी के आधार पर उस विशेष जंगल में कौन-कौनसे जानवर विचरण करते हैं, उसके बारे में वन विज्ञान के कर्मचारी पता लगा लेते हैं। जानवरों की टट्टी का विश्लेषण करके यह पता लगा...
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Advanced Calculus | Mathematics | BSc

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

This book includes the following topics 

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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