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Specifications of Engineering Mathematics 1

Book Details

  • 978-81-88870-65-3
  • English
  • 2008, 2009, 2010, 2011, 2012, 2013, 2014
  • Paper Back
  • 584

Contents

  • 1. Asymptotes
    Introduction, Equation of an Asymptote, Asymptotes of General Algebraic Curve, Parallel Asymptotes, Asymptotes Parallel to the Coordinate Axes, Illustrative Examples, Exercise 1 (A), Total Number of Asymptotes, Alternative Methods for Finding Asymptotes of Algebraic Curves, Intersection of the Curve and its Asymptotes, Illustrative Examples, Exercise 1 (B).
     
    2. Curvature
    Introduction, Curvature, Intrinsic Formula for the Radius of Curvature, Cartesian Formula for Radius of Curvature, Formula for Radius of Curvature when x and y are Functions of s, Radius of Curvature for the Parametric Curves, Illustrative Examples, Exercise 2 (A), Curvature at the Origin, Tangents at the Origin, Centre of Curvature, Chord of Curvature Through the Origin, Chord of Curvature Perpendicular to Radius Vector, Chords of Curvature Parallel to Coordinate Axes, Illustrative Examples, Exercise 2 (B), Concavity and Convexity, Point of Inflexion, Exercise 2 (C).
     
    3. Curve Tracing
    Introduction, Basic Prerequisites for Curve Tracing, Multiple Point, Double Point, Tangent at Origin, Tangent at Any Point, Curve Tracing: Cartesian Curves, Illustrative Examples, Exercise 3 (A), Curve Tracing: Polar Curves, Illustrative Examples, Exercise 3 (B), Curve Tracing: Parametric Curves, Illustrative Examples, Exercise 3 (C).
     
    4. Partial Differentiation
    Introduction, Partial Differentiation, Higher Order Derivatives, Homogeneous Function, Euler’s Theorem, Illustrative Examples, Exercise 4 (A), Total Derivative, Change of Variable, Errors and Approximations, Illustrative Examples, Exercise 4 (B).
     
    5. Maxima and Minima of Functions of two or More Variables
    Introduction, Maxima and Minima of Function of a Single Variable, Maxima and Minima of Function of two or More Variables, Maxima and Minima of a Multivariable Function with Equality Constraints, Solution by Direct Substitution, Lagrange’s Multipliers Method, Illustrative Examples, Exercise 5 (A).
     
    6. Surfaces and Volumes of Solids of Revolution
    Introduction, Basic Definitions, Surfaces of Solids of Revolution, Cartesian Form, Parametric Form, Polar Form, Volumes of Solids of Revolution, Cartesian Form, Parametric Form, Polar Form, Illustrative Examples, Exercise 6 (A).
     
    7. Double Integration and its Applications
    Introduction, Double Integrals, Evaluation of Double Integrals in Cartesian Coordinates, Evaluation of Double Integrals in Polar Coordinates, Change of Variables: Cartesian to Polar Form, Illustrative Examples, Exercise 7 (A), Area by Double Integration: Cartesian Coordinates, Area by Double Integration: Polar Coordinates, Volume by Double Integration, Illustrative Examples, Exercise 7 (B), Change of Order of Integration, Illustrative Examples, Exercise 7 (C).
     
    8. Beta and Gamma Functions
    Introduction, Beta Functions, Properties of Beta Function, Gamma Function, Properties of Gamma Function, Improved Form of Gamma Function, Relation Between Beta and Gamma Function, Duplication Formula, Illustrative Examples, Exercise 8 (A).
     
    9. Differential Equations
    Introduction, Differential Equations, Differential Equation of First Order and First Degree, Variables Separable Form, Homogeneous Equations, Equation Reducible to Homogeneous Form, Linear Differential Equation, Exercise 9 (A), Equation Reducible to Linear Form, Exercise 9 (B), Exact Differential Equations, Illustrative Examples, Exercise 9 (C), Equations Reducible to Exact Form, Illustrative Examples, Exercise 9 (D), Change of Variables, Illustrative Examples, Exercise 9 (E).
     
    10. Differential Equation of Higher Order with Constant Coefficients
    Introduction, Obtaining C.F. of f(D)y= Q or General Solution of f(D)y = 0, Exercise 10 (A), Particular Integral of f(D)y = Q, To find P.I. when Q = eax, where ‘a’ is any Constant and f(a) ? 0, To Find P.I. when Q = eax and f (a)= 0, To Find P.I. when Q = sinax or cosax and f(–a2) ? 0, To Find P.I. when Q = sinax or cosax and f(–a2) = 0, To Find P.I. when Q = xm, where m is a Positive Integer, Illustrative Examples, Exercise 10 (B), To Find P.I. when Q = eaxV, where V is any function of x, To Find P.I. when Q = xv, where v is any Function of x, Illustrative Examples, Exercise 10 (C).
     
    11. Second Order Differential Equation
    Introduction, Homogeneous Differential Equation, Illustrative Examples, Exercise 11 (A), Exact Differential Equation, Integrating Factor, Illustrative Examples, Exercise 11 (B), When a Part of C.F is Known, Rules for Finding the Complementary Function, Exercise 11 (C), Reduction to Normal Form (Removal of first Derivative or Change of Dependent Variable), Exercise 11 (D), Finding the Solution of Differential Equation by Changing the Independent Variable, Exercise 11 (E), Method of Variation of Parameters, Exercise 11 (F).