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Engineering Mathematics-I

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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
3.11 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)
7.11 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)