Chapter 1: Differential Calculus I

  • Learning Objectives
  • Introduction
  • Successive Differentiation: nth Derivative of Standard Functions
  • Leibnitz’s Theorem
  • Partial Derivatives
  • Homogeneous Function
  • Total Derivatives
  • Variables Treated as Constant
  • Asymptotes
  • Tracing the Curve in Cartesian Form
  • Tracing of Curves in Parametric Form
  • Tracing the Curves in Polar Form

 Important Points and Formulas
 True and False Questions

Chapter 2: Differential Calculus II

  • Learning Objectives
  • Introduction
  • Taylor’s and Maclaurin’s Theorems and Expansion of Functions
  • Expansion of Functions
  • Jacobians
  • Functionally Dependent Functions
  • Errors and Approximations
  • Maxima and Minima of Function of Two Variables
  • Constrained Maxima and Minima (Lagrange’s Method of Undetermined Multipliers)

 Important Points and Formulas
 True and False Questions
 Match the Following

Chapter 3: Linear Algebra

  • Learning Objectives
  • Introduction
  • Basic Concepts: Matrices
  • Determinants
  • Real Matrices: Symmetric, Skew-Symmetric and Orthogonal
  • Complex Matrices
  • Adjoint and Inverse of a Matrix
  • Inverse of a Matrix by Elementary Transformations (or Gauss-Jordan Method)
  • Rank of a Matrix
  • System of Linear Equations
  • Vectors: Linear Dependence and Independence
  • System of Linear Equations: Triangular Systems
  • Characteristic Equation
  • Eigenvalues and Eigenvectors
  • Cayley-Hamilton Theorem
  • Diagonalization and Powers of a Matrix
  • Applications of Matrices to Engineering Problems
  • Vector Spaces: Subspaces, Rank and Nullity

Linear Transformations

  • Kernel of a Linear Transformation

 Important Points and Formulas
 Multiple-Choice Questions
 True and False Questions

Chapter 4: Multiple Integrals

  • Learning Objectives
  • Introduction
  • Double Integrals
  • Triple Integrals
  • Change of Order of Integration in a Double Integral
  • Change of Variables
  • Rectification of Standard Curves
  • Area as a Double Integral (Area Enclosed by Plane Curves)
  • Volume as a Triple Integral
  • Volume of Solids
  • Area of a Curved Surface
  • Beta and Gamma Functions
  • Dirichlet’s Integrals and Applications
  •  Important Points and Formulas
     Multiple-Choice Questions
     Match the Following

    Chapter 5: Vector Calculus

    • Learning Objectives
    • Introduction
    • Vector Algebra
    • Differentiation of a Vector
    • Gradient of a Scalar Point Function
    • Directional Derivative
    • Angle of Intersection of Two Surfaces
    • Divergence and Curl
    • Solenoidal and Irrotational Vectors
    • Vector Integration
    • Surface and Volume Integrals
    • Green’s Theorem in the Plane
    • Gauss Divergence Theorem
    • Stokes’ Theorem

     Important Points and Formulas
     Fill in the Blanks


Book Full NameAdvanced Engineering Mathematics
Author NameErwin Kreyszig

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Advanced Engineering Mathematics (VOL 1) |Erwin Kreyszig | Wiley | 2013

  • Product Code: 1EMP2
  • Availability: In Stock
  • Rs. 809.00
  • Rs. 567.00
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Tags: advanced, engineering, mathematics, |erwin, kreyszig, wiley, 2013, (m)