jQuery and jQuery UI

Cover......Page 1
Contents......Page 8
Preface to the Revised Edition......Page 12
Symbols and Basic Formulae......Page 14
 1.2 Convergence of Sequences......Page 18
 1.3 The Upper and Lower Limits of a Sequence......Page 20
 1.4 Cauchy’s Principle of Convergence......Page 21
 1.5 Monotonic Sequence......Page 23
 1.6 Theorems on Limits......Page 25
 1.7 Subsequences......Page 28
 1.8 Series......Page 29
 1.9 Comparison Tests......Page 32
 1.10 D’alemberi’s Ratio Test......Page 37
 1.11 Cauchy’s Root Test......Page 42
 1.12 Raabe’s Test......Page 44
 1.13 Logarithmic Test......Page 48
 1.14 De Morgan–Berirand Test......Page 50
 1.15 Gauss’s Test......Page 51
 1.16 Cauchy’s Integral Test......Page 53
 1.17 Cauchy’s Condensation Test......Page 55
 1.18 Kummer’s Test......Page 57
 1.19 Alternating Series......Page 58
 1.20 Absolute Convergence of a Series......Page 60
 1.21 Convergence of the Series of the Type......Page 65
 1.22 Derangement of Series......Page 67
 1.23 Nature of Non-Absolutely Convergent Series......Page 68
 1.24 Effect of Derangement of Non-Absolutely Convergent Series......Page 69
 1.25 Uniform Convergence......Page 71
 1.26 Uniform Convergence of a Series of Functions......Page 73
 1.27 Properties of Uniformly Convergent Series......Page 74
 1.28 Power Series......Page 75
 Exercises......Page 76
 2.1 Successive Differentiation......Page 80
 2.2 Leibnitz’s Theorem and its Applications......Page 84
 2.3 General Theorems......Page 88
 2.4 Taylor’s Infinite Series and Power Series Expansion......Page 95
 2.6 Expansion of Functions......Page 96
 2.7 Indeterminate Forms......Page 106
 Exercises......Page 115
 3.1 Radius of Curvature of Intrinsic  Curves......Page 120
 3.2 Radius of Curvature for Cartesian Curves......Page 121
 3.3 Radius of Curvature for Parametric Curves......Page 125
 3.4 Radius of Curvature for Pedal Curves......Page 127
 3.5 Radius of Curvature for Polar Curves......Page 128
 3.6 Radius of Curvature at the Origin......Page 131
 3.7 Center of Curvature......Page 133
 3.9 Equation of the Circle of Curvature......Page 134
 3.10 Chords of Curvature Parallel to the Coordinate Axes......Page 137
 3.11 Chord of Curvature in Polar Coordinates......Page 138
 3.12 Miscellaneous Examples......Page 140
 Exercises......Page 145
 4.1 Determination of Asymptotes When the Equation of the Curve in Cartesian form is Givens......Page 148
 4.2 The Asymptotes of the General Rational Algebraic Curve......Page 149
 4.3 Asymptotes Parallel to Coordinate Axes......Page 150
 4.4 Working Rule for Finding Asymptotes of Rational Algebraic Curve......Page 151
 4.5 Intersection of a Curve and its Asymptotes......Page 154
 4.6 Asymptotes by Expansion......Page 156
 4.7 Asymptotes of the Polar Curves......Page 157
 4.9 Concavity, Convexity and Singular Points......Page 159
 4.10 Curve Tracing (Cartesian Equations)......Page 163
 4.11 Curve Tracing (Polar Equations)......Page 168
 4.12 Curve Tracing (Parametric Equations)......Page 170
 Exercises......Page 171
Chapter 5: Functions of Several Variables......Page 176
 5.3 The Differential Coefficients......Page 177
 5.5 Higher-Order Partial Derivatives......Page 178
 5.6 Envelopes and Evolutes......Page 183
 5.7 Homogeneous Functions and Euler’s Theorem......Page 185
 5.8 Differentiation of Composite Functions......Page 190
 5.9 Transformation from Cartesian to Polar Coordinates and Vice Versa......Page 194
 5.10 Taylor’s Theorem for Functions of Several Variables......Page 196
 5.11 Approximation of Errors......Page 199
 5.12 General Formula for Errors......Page 200
 5.13 Tangent Plane and Normal to a Surface......Page 203
 5.15 Properties of Jacobian......Page 205
 5.16 Necessary and Sufficient Conditions for Jacobian to Vanish......Page 208
 5.17 Differentiation Under the Integral Sign......Page 209
 5.18 Miscellaneous Examples......Page 212
 5.19 Extreme Values......Page 216
 5.20 Lagrange’s Method of Undetermined Multipliers......Page 223
 Exercises......Page 228
 6.3 Equation of the Normal at a Point of a Curve......Page 232
 6.4 Lengths of Tangent, Normal, Sub-Tangent and Subnormal at any Point of a Curve......Page 236
 Exercises......Page 237
 7.2 Properties of Beta Function......Page 238
 7.4 Properties of Gamma Function......Page 241
 7.5 Relation Between Beta and Gamma Functions......Page 242
 7.6 Dirichlet’s and Liouville’s Theorems......Page 247
 7.7 Miscellaneous Examples......Page 249
 Exercises......Page 250
 8.1 Reduction Formulas for sinn x dx and cosn x dx......Page 252
 8.2 Reduction Formula for sinm x cosn x dx 8.3......Page 254
 8.3 Reduction Formulas for tann x dx and  secn x dx 8.5......Page 256
 8.4 Reduction Formulas for xn sinmx dx and xn cosmx dx......Page 257
 8.5 Reduction Formulas for x n eaxdx and xm (log x)n dx......Page 258
 8.7 Reduction Formula For......Page 259
 Exercises......Page 260
  9.1.1 Area of a Curve Given by the Cartesian Equation......Page 262
  9.1.2 Area of a Curve Given by Polar Equation......Page 267
  9.2.1 Length of a Curve......Page 270
 Exercises......Page 275
 10.1 Centre of Gravity......Page 278
 10.2 Moment of Inertia......Page 281
 10.3 Mean Values of a Function......Page 282
 Exercises......Page 283
 11.1 Volume of the Solid of Revolution (Cartesian Equations)......Page 284
 11.2 Volume of the Solid of Revolution (Parametric Equations)......Page 289
 11.3 Volume of the Solid of Revolution (Polar Curves)......Page 291
 11.4 Surface of the Solid of Revolution (Cartesian Equations)......Page 292
 11.5 Surface of the Solid of Revolution (Parametric Equations)......Page 294
 11.6 Surface of the Solid of Revolution (Polar Curves)......Page 296
 Exercises......Page 297
 12.1 Double Integrals......Page 300
 12.3 Evaluation of Double Integrals (Cartesian Coordinates)......Page 301
 12.4 Evaluation of Double Integrals (Polar Coordinates)......Page 305
 12.5 Change of Variables in a Double Integral......Page 307
 12.6 Change of Order of Integration......Page 311
 12.7 Area Enclosed by Plane Curves (Cartesian and Polar Coordinates)......Page 315
 12.8 Volume and Surface Area as Double Integrals......Page 318
 12.9 Triple Integrals and their Evaluation......Page 325
 12.10 Change to Spherical Polar Coordinates from Cartesian Coordinates in a Triple Integral......Page 329
 12.11 Volume as a Triple Integral......Page 332
 12.12 Miscellaneous Examples......Page 336
 Exercises......Page 338
Chapter 13: Vector Calculus......Page 344
 13.1 Differentiation of a Vector......Page 354
 13.2 Partial Derivatives of a Vector Function......Page 361
 13.3 Gradient of a Scalar Field......Page 362
 13.5 Properties of a Gradient......Page 363
  13.6.1 Directional Derivatives along Coordinate Axes......Page 364
 13.8 Physical Interpretation of Divergence......Page 369
 13.11 The Laplacian Operator......Page 371
 13.12 Properties of Divergence and Curl......Page 375
 13.14 Line Integral......Page 380
 13.15 Work Done by a Force......Page 384
 13.16 Surface Integral......Page 386
 13.17 Volume Integral......Page 390
 13.18 Gauss’s Divergence Theorem......Page 392
 13.19 Green’s Theorem in a Plane......Page 398
 13.20 Stoke’s Theorem......Page 402
 13.21 Miscellaneous Examples......Page 407
 Exercises......Page 415
 14.3 Direction Ratios and Direction Cosines of a Line......Page 424
 14.4 Section Formulae—Internal Division of a Line by a Point on the Line......Page 425
  14.4.1 External Division of a Line by a Point on the Extended Line......Page 426
 14.5 Straight Line in Three Dimensions......Page 429
 14.6 Angle Between Two Lines......Page 432
 14.7 Shortest Distance Between Two Skew Lines......Page 434
 14.8 Equation of a Plane......Page 441
 14.10 Equation of a Plane Passing through Three Points......Page 442
 14.12 Equation of a Plane Passing through Two Point and Parallel to a Line......Page 443
 14.13 Angle Between Two Planes......Page 447
 14.15 Perpendicular Distance of a Point From a Plane......Page 449
 14.16 Planes Bisecting the Angles Between Two Planes......Page 450
 14.18 Planes Passing through the Intersection of Two Given Planes......Page 452
 14.19 Sphere......Page 454
 14.20 Equation of a Sphere Whose Diameter is the Line Joining Two Given Points......Page 457
 14.21 Equation of a Sphere Passing through Four Points......Page 456
 14.24 Angle of Intersection of Two Spheres......Page 459
 14.25 Condition of Orthogonality of Two Spheres......Page 460
 14.27 Equation of a Cylinder with Given Axis and Guiding Curves......Page 463
 14.28 Right Circular Cylinder......Page 464
 14.31 Equation of a Cone with Given Vertex and Guiding Curve......Page 466
 14.32 Right Circular Cone......Page 468
 14.33 Right Circular Cone with Vertex (α, β, γ), Semi-Vertical Angle and the (l, m, n) Direction Cosines of the Axis.......Page 469
 14.34 Conicoids......Page 470
 14.36 Shape of the Hyperboloid of One Sheet......Page 471
 14.38 Shape of the Elliptic Cone......Page 472
 14.40 Tangent Plane at a Point of Central Conicoid......Page 473
 14.42 Equation of Normal to the Central Conicoid at any Point (α, β, γ) on  it......Page 474
 14.43 Miscellaneous Examples......Page 477
 Exercises......Page 479
 15.1 Propositions......Page 490
 15.2 Basic Logical Operations......Page 491
  15.2.1 Translating from English to Symbols......Page 492
  15.2.2 Truth Table for Exclusive OR......Page 493
 15.3 Logical Equivalence Involving Tautologies and Contradictions......Page 495
 15.4 Conditional Propositions......Page 496
 Exercises......Page 507
 16.1 Fuzzy Set......Page 510
 16.2 Standard Operations on a Fuzzy Set......Page 512
 16.3 Many Valued Logic......Page 514
 Exercises......Page 515
 17.1 Definitions and Basic Concepts......Page 518
 17.2 Special Graphs......Page 520
 17.3 Subgraphs......Page 523
 17.4 Isomorphisms of Graphs......Page 525
 17.5 Walks, Paths and Circuits......Page 527
 17.6 Eulerian Paths and Circuits......Page 531
  17.6.1 Methods for Finding Euler Circuit......Page 536
 17.7 Hamiltonian Circuits......Page 538
  17.7.1 Travelling Salesperson Problem......Page 543
 17.8 Matrix Representation of Graphs......Page 544
 17.9 Planar Graphs......Page 546
 17.10 Colouring of Graph......Page 553
 17.11 Directed Graphs......Page 556
 17.12 Trees......Page 560
 17.13 Isomorphism of Trees......Page 565
 17.14 Representation of Algebraic Expressions by Binary Trees......Page 568
 17.15 Spanning Tree of a Graph......Page 571
  17.16.1 Dijkstra’s Shortest Path Algorithm......Page 573
  17.16.2 Shortest Path if All Edges Have Length 1......Page 576
  17.17.1 Prim Algorithm......Page 577
  17.17.2 Kruskal’s Algorithm......Page 580
 17.18 Cut Sets......Page 582
  17.18.1 Relation Between Spanning Trees, Circuits and Cut Sets......Page 584
 17.19 Tree Searching......Page 586
  17.19.1 Procedure to Evaluate an Expression Given in Polish Form......Page 587
 17.20 Transport Networks......Page 588
 Exercises......Page 595
Index......Page 602