 Preface

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
Exercises

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
Exercises

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
Exercises

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
Exercises

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
Exercises

Appendix

 Book DETAILS Book Full Name Advanced Engineering Mathematics Author Name Erwin Kreyszig Publisher Wiley Reprint 2013 Category Prescribed

Write a review

Note: HTML is not translated!