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Specifications of Engineering Mathematics II

Book Details

  • 978-81-88870-43-1
  • English
  • 2008, 2009, 2010, 2011, 2012, 2013
  • Paper Back
  • 572

Contents

  • 1. Preliminaries
    Introduction, Coordinates of a Point in Space, Some Important Formulae and Results.
     
    2. The Sphere
    Sphere, Equation of a Sphere (When Centre and Radius of Sphere are Known), General Equation of Sphere, Equation of Sphere Passing Through Four Non-coplanar Points, Diameter Form of a Sphere, Exercise 2.1, Intersection of a Sphere and a Plane, Intersection of Two Spheres, Exercise 2.2, Intersection of a Sphere and a Line, Tangent Line and Plane, Equation of Tangent Plane, Condition of Tangency, Length of Tangent, Angle of Intersection of Two Spheres, Condition of Orthogonality of Two Spheres, Exercise 2.3.
     
    3. Cone and Cylinder
    Cone, Equation of a Cone Whose Vertex and Guiding Curve are Given, Cone with Vertex at Origin, The Right Circular Cone, Equation of a Right Circular Cone, Exercise 3.1, The Cylinder, Equation of a Cylinder, The Right Circular Cylinder, Equation of a Right Circular Cylinder, Exercise 3.2.
     
    4. Matrices
    Introduction, Definition of a Matrix, Types of Matrices, Algebra of Matrices, Addition of Matrices, Properties of Matrix Addition, Subtraction of Matrices, Scalar Multiple of a Matrix, Product of Two Matrices, Properties of Matrix Multiplication, Positive Integral Powers of Matrices, Determinants, Minors and Cofactors, Properties of Determinants, Adjoint of a Square Matrix, Property of Adjoint Matrix, Singular and Non-Singular Matrices, Inverse of a Matrix, Submatrix of a Matrix, Excercise 4.1, Rank of a Matrix, Elementary Transformation, Echelon Form of a Matrix, Normal Form of a Matrix, Inverse of a Matrix by Elementary Transformations, System of Linear Simultaneous Equations, Solution of System of n Simultaneous Non-Homogeneous Linear Equations in n Unknowns, System of Linear Homogeneous Equations, Vectors: Linearly Dependent and Linearly Independent, Exercise 4.2, Eigenvalues and Eigenvectors, Eigenvalues or Characteristic Roots, Eigenvectors or Characteristic Vectors, Cayley-Hamilton Theorem, Inverse by Cayley-Hamilton Theorem, Diagonalization of a Matrix, Powers of a Matrix A, Exercise 4.3.
     
    5. Vector Calculus
    Introduction, Vector Function, Limit and Continuity of a Vector Function, Differentiation of a Vector Function, Geometrical Interpretation of dr dt, Velocity and Acceleration, Exercise 5.1, Scalar and Vector Point Functions, Uniform Continuity and Level Surfaces, Vector Differential Operator  (del), Gradient, Directional Derivative, Divergence, Curl, Expansion Formulae Involving the Operator, Second Order Differential Operators, Excercise 5.2.
     
    6. Application of Vector Calculus
    Integration of Vector Function, Line Integral, Applications of Line Integral, Exercise 6.1, Surface Integral, Volume Integral, Exercise 6.2, Integral Theorems, Exercise 6.3.
     
    7. Fourier Series
    Introduction, Fourier Series, Dirichlet’s Conditions, Even and Odd Functions, Fourier Series for Even and Odd Functions, Illustrative Examples, Exercise 7.1, Fourier Series in Arbitrary Interval (0, 2l) or (–l, l), Half-range Series, Illustrative Examples, Exercise 7.2, Harmonic Analysis, Exercise 7.3.
     
    8. Series Solution of Differential Equations
    Introduction, Method of Solution in Series, Exercise 8.1.
     
    9. Partial Differential Equations
    Introduction, Formation of Partial Differential Equations, Definitions, Linear Partial Differential Equations of First Order, Exercise 9.1, Special Methods of Solution to First Order P.D.E., Exercise 9.2, Charpit’s Method for Solving General P.D.E., Exercise 9.3.
     
    P. Papers