TY  - BOOK
AU  - Sastry, S. S.
TI  - Engineering mathematics. Vol.1
SN  - 812033616X
U1  - 510 
PY  - 2009///
CY  - New Delhi
PB  - PHI Learning Pvt Ltd
N1  - CONTENTS Preface  ix Preface to the First Edition xi 1. HIGHER ALGEBRA 1-174 1.1 Partial Fractions7 1.1.1 Linear Factors  3 1.1.2 Repeated Linear Factors  4 1.1.3 Nonlinear Factors6 1.1.4 Repeated Nonlinear Factors7 Exercise 1.18 1.2 Infinite Series9 1.2.1 Comparison Tests  12 1.2.2 D'Alembert's Ratio Test16 1.2.3 Cauchy's Root Test19 1.2.4 Absolute and Conditional Convergence  20 1.2.5 Alternating Series  22 Exercise 1.2  24 1.3 Binomial, Exponential and Logarithmic Series  26 1.3.1 The Binomial Theorem  26 1.3.2 Applications of Binomial Theorem to Approximation and Interpolation 37 1.3.3 The Exponential Series  37 1.3.4 The Logarithmic Series  44 Exercise 1.3  49 1.4 Continued Fractions52 1.4.1 Convergents of a Continued Fraction  53 1.4.2 Estimation of Error  57 1.4.3 Application to Interpolation  59 Exercise 1.462 1.5 Theory of Equations63 1.5.1 The Fundamental Theorem of Algebra  64 1.5.2 Relations between the Roots and Coefficients  65 1.5.3 Imaginary and Irrational Roots  67 1.5.4 Symmetric Functions of the Roots  69 1.5.5 Reciprocal Equations73 1.5.6 Transformation of Equations76 1.5.7 Descartes' Rule of Signs79 1.5.8 Homer's Method for Finding a Real Root  80 Exercise 1.5 83 1.6 Matrices  85 1.6.1 Basic Definitions  85 1.6.2 Matrix Operations  87 1.6.3 Transpose, Adjoint and Inverse of a Matrix  91 1.6.4 Some Special Matrices101 1.6.5 Rank of a Matrix and Linear Dependence of Vectors109 1.6.6 Linear Algebraic Systems118 1.6.7 Eigenvalues and Eigenvectors  130 1.6.8 Diagonalization by Orthogonal Transformation150 1.6.9 Quadratic Forms153 Exercise 1.6164 Answers to Selected Exercises170 2. GEOMETRY, VECTORS AND  COMPLEX NUMBERS 175-370 2.1 Coordinate Systems  175 2.1.1 Rectangular Coordinates in a Plane  175 2.1.2 Distance between Two Points  176 2.1.3 Polar Coordinates178 2.1.4 Equation for a Line in Polar Coordinates179 2.1.5 Rectangular Coordinates in Space180 2.1.6 Cylindrical Polar Coordinates  182 2.1.7 Spherical Polar Coordinates183 Exercise 2.1184 2.2 Elementary Coordinate Geometry  185 2.2.1 The Straight Line  185 2.2.2 The Circle197 2.2.3 The Conic Sections  205 2.2.4 Translation of Axes  235 2.2.5 Equation of a Conic in Polar Coordinates  239 Exercise 2.2  241 2.3 Analytical Geometry of Three Dimensions  247 2.3.1 Direction Cosines and Angle between Two Lines  247 2.3.2 Equation of a Plane  255 2.3.3 The Straight Line  265 2.3.4 Shortest Distance between Two Skew Lines  277 2.3.5 The Sphere  282 2.3.6 The Cylinder  288 2.3.7 The Cone  293 2.3.8 Quadric Surfaces  299 Exercise 2.3304 2.4 Vector Algebra  306 2.4.1 The Concept of a Vector  307 2.4.2 Addition and Subtraction of Vectors  307 2.4.3 Resolution of Vectors  309 2.4.4 Scalar or Dot Product of Two Vectors  376 2.4.5  Vector or Cross Product of Two Vectors  320 2.4.6 Equations of Lines and Planes  324 2.4.7 Products of Three or More Vectors  337 Exercise 2.4  335 2.5 Complex Numbers  338 2.5.1 The Argand Diagram  342 2.5.2 Multiplication and Division in Polar Forms  344 2.5.3 De Moivre's Theorem  344 2.5.4 Roots of a Complex Number  346 2.5.5 Expansions for Powers of sine and cosine  348 2.5.6 Expansion of cos no and sin no in Powers of cos o and sin o 352 2.5.7 Relation to Exponential Series  353 2.5.8 Inverse Hyperbolic Functions  357 2.5.9 The Logarithm of a Negative Quantity  367 2.5.10 Complex Numbers and Matrices  361 Exercise 2.5  362 Answers to Selected Exercises366 3. APPLICATIONS OF DIFFERENTIAL CALCULUS  371-459 3.1 Introduction377 3.1.1 Geometrical Applications  377 3.1.2 Related Rates and Indeterminate Forms  394 Exercise 3.1406 3.2 Maxima, Minima and Points of Inflexion411 Exercise 3.2 421 3.3 Expansions of Functions  422 Exercise 3.3431 3.4 Curvature, Envelopes and Evolutes  432 3.4.1 Curvature  432 3.4.2 Envelopes442 3.4.3 Evolutes and Involutes  448 Exercise 3.4455 Answers to Selected Exercises457 4. INTEGRATION 460-523 4.1 Introduction460 4.1.1 Theory of the Integral460 4.1.2 Properties of the Definite Integral465 4.1.3 Methods of Integration471 4.1.4 Reduction Formulae and Definite Integrals  480 Exercise 4.1 490 4.2 Applications of the Definite Integral492 4.2.1 Volumes and Surfaces of Solids of Revolution499 4.2.2 Length of an Arc of a Curve  505 4.2.3 Centroid of Area and Volume of Revolution  508 4.2.4 Theorems of Pappus  570 4.2.5 Areas and Volumes in Polar Coordinates  514 4.2.6 Mean Values and Root-mean-square Values  577 Exercise 4.2518 Answers to Selected Exercises521 5. ORDINARY DIFFERENTIAL EQUATIONS OF THE  FIRST  ORDER  524-583 5.1 Introduction524 5.1.1 Analytical Methods of Solution  529 5.1.2 Method of Variation of Parameters  540 5.1.3 Equations of Higher Degree  543 Exercise 5.1549 5.2 Applications involving First-Order Equations  552 5.2.1 Trajectories  552 5.2.2 Flow of Electricity  556 5.2.3 Newton's Law of Cooling  560 5.2.4 Laws of Decay and Growth  562 5.2.5 Hooke's Law  564 5.2.6 Body Falling in a Resisting Medium  567 5.2.7 Satellite Launch Vehicles  575 Exercise 5.2  579 Answers to Selected Exercises581 6. NUMERICAL METHODS  584-669 6.1  Interpolation and Least Squares  584 6.1.1 Lagrange Interpolation  584 6.1.2 Newton's Divided Difference Formula  593 6.1.3 Finite Differences: Newton's Formulae  597 6.1.4 Central Differences: Stirling's, Bessel's and Everett's Formulae 603 6.1.5 Empirical Laws and Least Squares Curve Fitting  608 Exercise 6.1613 6.2 Solution of Nonlinear Equations  616 6.2.1 The Bisection Method617 6.2.2 The Regula-falsi Method  677 6.2.3 Newton-Raphson Method  619 6.2.4 Generalized Newton's Method622 6.2.5 Muller's Method623 6.2.6 Solution of Systems of Nonlinear Equations  625 Exercise 6.2  626 6.3 Numerical Differentiation627 6.3.1 Numerical Differentiation Formulae628 6.3.2 Maximum and Minimum Values of a Tabulated Function  633 Exercise 6.3  635 6.4 Numerical Integration  636 6.4.1Trapezoidal Rule637 6.4.2 Simpson's 1/3-rule638 6.4.3 Simpson's 3/8-rule  638 6.4.4 Romberg Integration  639 Exercise 6.4  644 6.5 Numerical Methods for First-Order Differential Equations  646 6.5.1 Solution by Taylor's Series647 6.5.2 Picard's Iterative Method  649 6.5.3 Euler's Method652 6.5.4 Runge-Kutta Methods 656 6.5.5 Milne's Method 662 Exercise 6.5 665 Answers to Selected Exercises 668 BIBLIOGRAPHY 671 INDEX 673-676
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