Mathematics for Electrical Science and Physical Science-2 (Common to Groups B & C) For KTU B.Tech Second Semester
ISBN: 9789363865457
394 pages
For more information write to us at: acadmktg@wiley.com
Description
This book is a carefully crafted adaptation of the best-selling titles, Advanced Engineering Mathematics, 10th Edition by Erwin Kreyszig, and Calculus: Early Transcendentals, 12th Edition by Howard Anton. Known for its clear expository style and exceptional clarity, this textbook offers a thorough introduction to engineering mathematics and calculus, catering to the evolving needs of modern students in engineering and technical fields. Designed to enhance understanding of key mathematical concepts, it serves as an invaluable resource for students pursuing studies in engineering, mathematics, and related disciplines.
MULTIVARIABLE CALCULUS-DIFFERENTIATION
1.1 Limits and Continuity
Limits Along Curves
Open and Closed Sets
General Limits of Functions of Two Variables
Relationships Between General Limits and Limits Along Smooth Curves
Repeated Limits
Algebra of Limits
Continuity
Limits at Discontinuities
Continuity at Boundary Points
Extensions to Three Variables
Solved Examples
Quick Check Problem 1.1
Problem Set 1.1
Answer Key
1.2 Partial Derivatives 21
Partial Derivatives of Functions of Two Variables
The Partial Derivative Functions
Partial Derivative Notation
Partial Derivatives Viewed as Rates of Change and Slopes
Estimating Partial Derivatives from Tabular Data
Implicit Partial Differentiation
Partial Derivatives and Continuity
Sufficient Conditions for Continuity
Partial Derivatives of Functions With More Than Two Variables
Higher-Order Partial Derivatives
Equality of Mixed Partials
Sufficient Condition for the Equality of fxy and fyx
The Wave Equation
Solved Examples
Quick Check Problem 1.2
Problem Set 1.2
Answer Key
1.3 Differentiability, Differentials, and Local Linearity
Differentiability
Differentiability and Continuity
Differentials
Sufficient Conditions for Differentiability
Differentials of Higher Orders
Local Linear Approximations
Solved Examples
Quick Check Problem 1.3
Problem Set 1.3
Answer Key
1.4 The Chain Rule
Chain Rules for Derivatives
Chain Rules for Partial Derivatives
Other Versions of the Chain Rule
Implicit Differentiation
Solved Examples
Quick Check Problem 1.4
Problem Set 1.4
Answer Key
1.5 Maxima and Minima of Functions of Two Variables
Extrema
Bounded Sets
The Extreme-Value Theorem
Finding Relative Extrema
The Second Partials Test
Solved Examples
Quick Check Problem 1.5
Problem Set 1.5
Answer Key
MULTIPLE INTEGRALS
2.1 Double Integrals
Volume
Definition of a Double Integral
Evaluating Double Integrals
Properties of Double Integrals
Solved Examples
Quick Check Problem 2.1
Problem Set 2.1
Answer Key
2.2 Double Integrals Over Nonrectangular Regions
Iterated Integrals with Nonconstant Limits of Integration
Double Integrals Over Nonrectangular Regions
Setting Up Limits of Integration for Evaluating Double Integrals
Reversing the Order of Integration
Area Calculated as a Double Integral
Solved Examples
Quick Check Problem 2.2
Problem Set 2.2
Answer Key
2.3 Double Integrals in Polar Coordinates
Simple Polar Regions
Double Integrals in Polar Coordinates
Evaluating Polar Double Integrals
Finding Areas Using Polar Double Integrals
Converting Double Integrals from Rectangular to Polar Coordinates
Solved Examples
Quick Check Problem 2.3
Problem Set 2.3
Answer Key
2.4 Triple Integrals
Definition of a Triple Integral
Properties of Triple Integrals
Evaluating Triple Integrals Over Rectangular Boxes
Evaluating Triple Integrals Over More General Regions
Volume Calculated as a Triple Integral
Integration in Other Orders
Solved Examples
Quick Check Problem 2.4
Problem Set 2.4
Answer Key
2.5 Triple Integrals in Cylindrical and Spherical Coordinates
Triple Integrals in Cylindrical Coordinates
Converting Triple Integrals from Rectangular to Cylindrical Coordinates
Triple Integrals in Spherical Coordinates
Converting Triple Integrals from Rectangular to Spherical Coordinates
Solved Examples
Quick Check Problem 2.5
Problem Set 2.5
Answer Key
CALCULUS OF VECTOR FUNCTIONS
3.1 Introduction to Vector-Valued Functions
Parametric Curves in 3-space
Parametric Curves Generated with Technology
Parametric Equations for Intersections of Surfaces
Vector-valued Functions
Graphs of Vector-valued Functions
Vector Form of a Line Segment
Solved Examples
Quick Check Problem 3.1
Problem Set 3.1
Answer Key
3.2 Calculus of Vector-valued Functions
Limits and Continuity
Derivatives
Derivative Rules
Tangent Lines to Graphs of Vector-valued Functions
Derivatives of Dot and Cross Products
Definite Integrals of Vector-valued Functions
Rules of Integration
Antiderivatives of Vector-valued Functions
Solved Examples
Quick Check Problem 3.2
Problem Set 3.2
Answer Key
3.3 Directional Derivatives and Gradients
Directional Derivatives
The Gradient
Properties of the Gradient
Gradients Are Normal to Level Curves
An Application of Gradients
Solved Examples
Quick Check Problem 3.3
Problem Set 3.3
Answer Key
3.4 Vector Fields
Graphical Representations of Vector Fields
A Compact Notation for Vector Fields
Inverse-square Fields
Gradient Fields
Conservative Fields and Potential Functions
Divergence and Curl
The _ Operator
The Laplacian _2
Solved Examples
Quick Check Problem 3.4
Problem Set 3.4
Answer Key
3.5 Line Integrals
Evaluating Line Integrals
Line Integrals with Respect to x, y, and z
Integrating a Vector Field Along a Curve
Work as a Line Integral
Line Integrals Along Piecewise Smooth Curves
Quick Check Problem 3.5
Problem Set 3.5
Answer Key
3.6 Independence of Path; Conservative Vector Fields
Work Integrals
Independence of Path
The Fundamental Theorem of Line Integrals
Line Integrals Along Closed Paths
A Test for Conservative Vector Fields
Conservative Vector Fields in 3-space
Conservation of Energy
Solved Examples
Quick Check Problem 3.6
Problem Set 3.6
Answer Key
VECTOR INTEGRAL THEOREMS
4.1 Green’s Theorem
A Notation for Line Integrals Around Simple Closed Curves
Finding Work Using Green’s Theorem
Finding Areas Using Green’s Theorem
Green’s Theorem for Multiply Connected Regions
Solved Examples
Quick Check Problem 4.1
Problem Set 4.1
Answer Key
4.2 Surface Integrals
Definition of a Surface Integral
Evaluating Surface Integrals
Surface Integrals Over Z = G(x, Y), Y = G(x, Z), and X = G(y, Z)
Solved Examples
Quick Check Problem 4.2
Problem Set 4.2
Answer Key
4.3 Applications of Surface Integrals; Flux
Flow Fields
Oriented Surfaces
Orientation of a Smooth Parametric Surface
Flux
Evaluating Flux Integrals
Orientation of Nonparametric Surfaces
Quick Check Problem 4.3
Problem Set 4.3
Answer Key
Orientation of Piecewise Smooth Closed Surfaces
4.4 The Divergence Theorem
Using the Divergence Theorem to Find Flux
Divergence Viewed as Flux Density
Sources and Sinks
Gauss’s Law for Inverse-square Fields
Gauss’s Law in Electrostatics
Solved Examples
Quick Check Problem 4.4
Problem Set 4.4
Answer Key
4.5 Stoke’s Theorem
Relative Orientation of Curves and Surfaces
Stoke’s Theorem
Using Stoke’s Theorem to Calculate Work
Relationship Between Green’s Theorem and Stokes’ Theorem
Curl Viewed as Circulation
Solved Examples
Quick Check Problem 4.5
Problem Set 4.5
Answer Key