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Specifications of Engineering Mathematics-I

Book Details

  • 978-93-83644-25-4
  • English
  • 2017
  • Paper Back
  • -

Contents

  • S.No. Chapter
    1. Asymptotes 
    1.1 Introduction
    1.2 Equation of an Asymptote
    1.3 Asymptotes of General Algebraic Curve
    1.4 Parallel Asymptotes 
    1.5 Asymptotes Parallel to the Coordinate Axes
    Illustrative Examples 
    Exercise 1 (A)
    1.6 Total Number of Asymptotes
    1.7 Alternative Methods for Finding Asymptotes of Algebraic Curves
    1.8 Intersection of the Curve and its Asymptotes
    Illustrative Examples 
    Exercise 1 (B)
    2. Curve Tracing
    2.1 Introduction 
    2.2 Basic Prerequisites for Curve Tracing 
    2.2.1 Concavity and Convexity 
    2.2.2 Point of Inflexion
    Exercise 2 (A)
    2.2.3 Multiple Point
    2.2.4 Double Point
    2.2.5 Tangent at Origin
    2.2.6 Tangent at Any Point
    2.3 Curve Tracing: Cartesian Curves 
    Illustrative Examples
    Exercise 2 (B)
    2.4 Curve Tracing: Polar Curves
    Illustrative Examples
    Exercise 2 (C)
    2.5 Curve Tracing: Parametric Curves
    Illustrative Examples
    Exercise 2 (D) 
    3. Partial Differentiation
    3.1 Introduction 
    3.2 Limit 
    3.3 Continuity
    3.4 Partial Differentiation 
    3.5 Higher Order Derivatives 
    3.5 Homogeneous Function.
    3.6 Euler’s Theorem
    Illustrative Examples
    Exercise 3 (A)
    3.7 Total Derivative 
    3.8 Change of Variable
    3.9 Directional Derivative 
    3.10 Gradient
    3.11 Tangent Plane and Normal 
    3.12 Taylor’s Theorem
    3.13 Errors and Approximations 
    3.14 Jacobian
    Illustrative Examples
    Exercise 3 (B)
    4. Maxima and Minima of Functions
    of two or More Variables
    4.1 Introduction 
    4.2 Maxima and Minima of Function of a Single Variable 
    4.3 Maxima and Minima of Function of two or More Variables
    4.4 Maxima and Minima of a Multivariable
    Function with Equality Constraints 
    4.4.1 Solution by Direct Substitution 
    4.4.2 Lagrange’s Multipliers Method 
    Illustrative Examples 
    Exercise 4 (A)
    5. Multiple Integration and its Applications
    5.1 Introduction
    5.2 Double Integrals 
    5.3 Evaluation of Double Integrals in Cartesian Coordinates 
    5.4 Evaluation of Double Integrals in Polar Coordinates 
    5.5 Change of Variables: Cartesian to Polar Form
    Illustrative Examples 
    Exercise 5 (A)
    5.6 Area by Double Integration: Cartesian Coordinates .
    5.7 Area by Double Integration: Polar Coordinates
    5.8 Volume by Double Integration
    Illustrative Examples
    Exercise 5 (B)
    5.9 Change of Order of Integration
    5.10 Triple Integral
    Illustrative Examples
    Exercise 5 (C)
    6. Beta and Gamma Functions
    6.1 Introduction 
    6.2 Beta Functions
    6.2.1 Properties of Beta Function 
    6.3 Gamma Function 
    6.3.1 Properties of Gamma Function
    6.3.2 Improved Form of Gamma Function
    6.4 Relation Between Beta and Gamma Function 
    6.5 Duplication Formula .
    Illustrative Examples
    Exercise 6 (A)
    7. Vector Calculus
    7.1 Introduction
    7.2 Vector Function
    7.3 Limit and Continuity of a Vector Function 
    7.4 Differentiation of a Vector Function 
    7.5 Geometrical Interpretation of
    7.6 Velocity and Acceleration 
    Exercise 7 (A)
    7.7 Scalar and Vector Point Functions
    7.8 Uniform Continuity and Level Surfaces 
    7.9 Vector Differential Operator  (del)
    7.10 Gradient 
    7.11 Directional Derivative 
    7.12 Divergence 
    7.13 Curl .
    7.14 Expansion Formulae Involving the Operator 
    7.15 Second Order Differential Operators
    Exercise 7 (B) 
    8. Application of Vector Calculus .
    8.1 Integration of Vector Function 
    8.2 Line Integral 
    8.3 Applications of Line Integral .
    Exercise 8 (A)
    8.4 Surface Integral
    8.5 Volume Integral
    Exercise 8 (B)
    8.6 Integral Theorems 
    Exercise 8 (C)