Engineering mathematics/ (Record no. 163599)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 00380nam a2200145Ia 4500 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9788120341005 |
| 040 ## - CATALOGING SOURCE | |
| Transcribing agency | CUS |
| 082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 510.2462 |
| Item number | SAS/E |
| 100 ## - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Sastry, S.S. |
| 245 #0 - TITLE STATEMENT | |
| Title | Engineering mathematics/ |
| Statement of responsibility, etc. | S.S.Sastry |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |
| Place of publication, distribution, etc. | New Delhi: |
| Name of publisher, distributor, etc. | PHI Learning Private Limited, |
| Date of publication, distribution, etc. | 2010. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 649 p. |
| Other physical details | ill. |
| Dimensions | 24 cm. |
| 505 ## - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 1. Differentiation (Review) 3-11<br/>1.1 Differential Coefficient 3<br/>1.2 Formulae for Differentiation 3<br/>1.2.1 Other Useful Formulae 4<br/>Exercise 1.1 10<br/>2. Successive Differentiation 12-23<br/>2.1 Higher Derivatives of Functions 12<br/>Exercise 2.1 16<br/>2.2 Leibnitz's Theorem 17<br/>Exercise 2.2 22<br/>3. Partial Differentiation 24-40<br/>3.1 Introduction 24<br/>3.1.1 Partial Derivatives 24<br/>3.1.2 Geometrical Interpretation of dzJ^x and dzl^y 26<br/>3.1.3 Partial Derivatives of Higher Orders 27<br/>Exercise 3.1 30<br/>iii<br/>iv Contents<br/>3.2 Homogeneous Functions 31<br/>3.2.1 Euler's Theorem 32<br/>3.2.2 Deductions from Euler's Theorem 33<br/>Exercise 3.2 38<br/>4. Total Differentiation 41-58<br/>4.1 Total Differential Coefficient 41<br/>4.1.1 Important Deductions 42<br/>Exercise 4.1 51<br/>4.2 Change of Variables 52<br/>4.2.1 Change of Independent Variable to the Dependent<br/>Variable 53<br/>4.2.2 Change to Another Variable 53<br/>4.2.3 Change of Both Dependent and Independent<br/>Variables 54<br/>4.2.4 Change of Two Independent Variables 54<br/>Exercise 4.2 57<br/>5. Expansion of Functions of Several Variables 59-66<br/>5.1 Taylor's Series 59<br/>Exercise 5.1 65<br/>6. Curve Tracing 67-87<br/>6.1 Introduction 67<br/>6.1.1 Definitions 67<br/>6.1.2 Asymptotes of a Curve 69<br/>6.1.3 Tracing of Cartesian Curves 71<br/>6.1.4 Sketches of Some Important Curves 75<br/>Exercise 6.1 76<br/>6.2 Tracing of Polar Curves 76<br/>6.2.1 Sketches of Some Important Polar Curves 81<br/>Exercise 6.2 81<br/>6.3 Tracing of Curves Given in Parametric Form 81<br/>Unit n Differential Calculus H<br/>7. Jacobians 91-101<br/>7.1 Definition 91<br/>7.1.1 Properties of Jacobians 92<br/>7.1.2 Jacobians of Implicit Functions 97<br/>Exercise 7.1 100<br/>8. Approximation of Errors 102-109<br/>8.1 Differentials 102<br/>8.1.1 Definitions 103<br/>Exercise 8.1 108<br/>9. Extrema of Functions of Several Variables 110-124<br/>9.1 Maxima and Minima 110<br/>9.1.1 Criteria for Maxima or Minima 110<br/>Exercise 9.1 117<br/>9.2 Lagrange's Method of Undetermined Multipliers 118<br/>Exercise 9.2 123<br/>Unit III Matrices<br/>10. Algebra of Matrices 127-189<br/>10.1 Introduction 127<br/>10.1.1 Basic Definitions 127<br/>10.1.2 Matrix Operations 129<br/>10.1.3 Determinants 132<br/>10.1.4 Transpose, Adjoint and Inverse of a Matrix 134<br/>10.1.5 Some Special Matrices 138<br/>Exercise 10.1 143<br/>10.2 Elementary Transformations 145<br/>10.2.1 Elementary Matrices 145<br/>10.2.2 Rank of the Matrix 146<br/>Exercise 10.2 152<br/>10.3 Linear Dependence and Linear Independence of<br/>Vectors 153<br/>Exercise 10.3 155<br/>10.4 Solution of a System of Linear Equations 156<br/>10.4.1 Consistency of a Nonhomogenous Linear<br/>System 156<br/>10.4.2 Solution of Homogeneous Systems 160<br/>10.4.3 Solution of AX = 5 when Ais Nonsingular 162<br/>Exercise 10.4 165<br/>10.5 Eigenvalues and Eigenvectors of Matrices 166<br/>10.5.1 Eigenvalues of Some Important Matrices * 167<br/>10.5.2 Properties of Eigenvalues and Eigenvectors 174<br/>10.5.3 Cayley-Hamilton Theorem 177<br/>10.5.4 Diagonalization of a Matrix 179<br/>Contents V<br/>10.5.5 Diagonalization by Orthogonal Transformation 183<br/>Exercise 10.5 186<br/>Unit IV Multiple Integrals<br/>11. Double Integration 193-215<br/>11.1 Double Integral 193<br/>11.1.1 Evaluation of a Double Integral 194<br/>11.1.2 Change of Order of Integration 199<br/>vi Contents<br/>11.1.3 Double Integral in Polar Coordinates 205<br/>Exercise 11.1 208<br/>11.2 Applications of Double Integrals 209<br/>11.2.1 Moments and Centroid of Area 210<br/>11.2.2 Moments of Inertia 210<br/>11.2.3 Volume of a Solid of Revolution 212<br/>11.2.4 Volume of a Solid as a Double Integral 212<br/>Exercise 11.2 214<br/>12. Triple Integrals 216-231<br/>12.1 Volume as a Triple Integral 216<br/>12.1.1 Cylindrical Coordinates 220<br/>12.1.2 Spherical Polar Coordinates 221<br/>12.1.3 Applications of Triple Integrals 222<br/>12.1.4 Change of Variables 225<br/>Exercise 12.1 229<br/>13. Beta and Gamma Functions Ihl-IAl<br/>13.1 Introduction 252<br/>13.1.1 A Formula for r(n) 233<br/>13.1.2 Transformations of Gamma Function 235<br/>13.1.3 Transformations of Beta Function 236<br/>13.1.4 Relation between Beta and Ganrmia Functions 237<br/>13.1.5 Deductions 239<br/>Exercise 13.1 246<br/>Unit V Vector Calculus '<br/>14. Vector Differential Calculus 251-278<br/>14.1 Introduction 251<br/>14,1.1 Scalar and Vector Fields 251<br/>•14.1.2 Derivatives of Vectors 251<br/>14.1.3 The Directional Derivative 255<br/>Exercise 14.1 261<br/>14.2 Divergence and Curl of a Vector Point Function 263<br/>14.2.1 Divergence of a Vector Point Function 263<br/>14.2.2 The Curl of a Vector 267<br/>14.2.3 Second-Order Expressions 272<br/>Exercise 14.2 275<br/>15. Vector Integration 279-304<br/>15.1 Introduction 279<br/>15.1.1 Line Integrals 279<br/>15.1.2 Surface and Volume Integrals 284<br/>. Exercise 15.1 287<br/>15.2 Integral Theorems 289<br/>15.2.1 Green's Theorem for a Plane 289<br/>15.2.2 Stoke's Theorem 292<br/>15.2.3 Divergence Theorem of Gauss 296<br/>Exercise 15.2 301<br/>UPTU Examination Paper 305-307<br/>PART II (SECOND SEMESTER)<br/>Unit I Differential Equations<br/>1. Differential Equations (Revision) 311-324<br/>1.1 Introduction 311<br/>1.1.1 Variables Separable 311<br/>1.1.2 Exact Differential Equations 313<br/>1.1.3 Homogeneous Equations 314<br/>1.1.4 First-Order Linear Differential Equations 316<br/>1.1.5 Bernoulli's Differential Equation 318<br/>1.2 Differential Equations of First Order and Higher<br/>Degree 319<br/>Exercise 1.1 322<br/>2. Linear Differential Equations 325-370<br/>2.1 Differential Equations of Higher Order 325<br/>2.1.1 Homogeneous Linear Equations 327<br/>2.1.2 Nonhomogeneous Linear Differential Equations 331<br/>2.1.3 Method of Variation of Parameters 332<br/>2.1.4 The Operator Method for Particular Integrals 336<br/>Exercise 2.1 344<br/>2.2 Simultaneous Linear Differential Equations 345<br/>Exercise 2.2 350<br/>2.3 Solution of Certain Types of Differential Equations 351<br/>Exercise 2.3 358<br/>2.4 Linear Equations with Variable Coefficients 359<br/>2.4.1 Change of Independent Variable 359<br/>2.4.2 Method of Variation of Parameters 363<br/>Exercise 2.4 367<br/>3. Applications of Differential Equations 371-402<br/>3.1 Introduction 371<br/>3.1.1 Electrical Circuits 371<br/>3.1.2 Motion under Gravity 380<br/>3.1.3 Elastic Strings 384<br/>Contents Vii<br/>viii Contents<br/>3.1.4 Vibration of a Particle<br/>3.1.5 Elastic Curves 391<br/>3.1.6 Motion of a Particle in a Plane 397<br/>Exercise 3.1 399<br/>Unit II Series Solutions and Special Functions<br/>4. Solution in Series of Differential Equations 405-420<br/>4.1 Ordinary Points of a Differential Equation 405<br/>4.1.1 Solution of Differential Equations with Ordinary<br/>Points 405<br/>4.2 Singular Points of a Differential Equation 408<br/>4.2.1 Roots Distinct and do not Differ by an<br/>Integer 408<br/>4.2.2 The Roots C| and C2 are Equal 412<br/>4.2.3 Roots Distinct and Differ by an Integer 416<br/>Exercise 4.1 419<br/>5. Bessel Functions 421-440<br/>5.1 Introduction 421<br/>5.2 Bessel's Differential Equation and Bessel Functions 421<br/>5.3 Recurrence Formulae for y„(jc) 426<br/>5.4 Generating Function for Jn{x) 430<br/>5.5 Integral Relations Involving Bessel Functions 435<br/>5.6 Bessel Functions of the Second Kind 435<br/>Exercise 5.1 439<br/>6. Legendre Polynomials 441-460<br/>6.1 Legendre's Equation and Its Solutions 441<br/>6.1.1 Solution of Legendre's Equation 441<br/>6.2 Rodrigue's Formula 444<br/>6.3 Generating Function 447<br/>6.4 Orthogonal Properties 448<br/>6.5 Recurrence Formulae 452<br/>6.6 Legendre's Polynomials as Integrals 454<br/>Exercise 6.1 458<br/>Unit III Laplace Transforms<br/>7. Laplace Transforms 463-509<br/>7.1 Introduction 463<br/>7.1.1 Definition and Conditions for Existence 463<br/>7.1.2 Laplace Transforms of Some Elenientary<br/>Functions 465<br/>7.1.3 Table of Laplace Transforms 470<br/>7.1.4 Properties of Laplace Transforms 470<br/>7.1.5 Transforms of Derivatives 484<br/>Exercise 7.1 486<br/>7.2 The Inverse Laplace Transform 487<br/>1.2.1 Definition and Uniqueness 487<br/>7.2.2 Properties of Inverse Transforms 489<br/>7.2.3 Use of Partial Fractions 496<br/>Exercise 7.2 499<br/>7.3 Applications to Differential Equations 500<br/>7.3.1 Linear Differential Equations with Constant<br/>Coefficients 500<br/>7.3.2 Linear Differential Equations with Variable<br/>Coefficients 503<br/>7.3.3 Simultaneous Differential Equations 504<br/>Exercise 7.3 506<br/>Unit IV Fourier Series and Partial Differential Equations<br/>8. Fourier Series 513-556<br/>9.<br/>8.1 Introduction 513<br/>8.1.1 Definitions and Derivations 513<br/>8.1.2 Odd and Even Functions 523<br/>Exercise 8.1 530<br/>8.2 Half-Range Series from 0 to ;r 531<br/>Exercise 8.2 535<br/>8.3 Change of Scale 536<br/>8.3.1 Parseval's Equalities 542<br/>Exercise 8.3 548<br/>8.4 Numerical Harmonic Analysis 550<br/>Exercise 8.4 552<br/>Contents ix<br/>Partial Differential Equations 557-586<br/>9.1 Introduction 557<br/>9.1.1 Formation of Partial Differential Equations 559<br/>9.1.2 Solution of a Partial Differential Equation 562<br/>Exercise 9.1 564<br/>9.2 Partial Differential Equations of the First Order 565<br/>9.2.1 Solutions of Some Standard Types 565<br/>9.2.2 Lagrange's Linear Equation 570<br/>Exercise 9.2 575<br/>9.3 Nonlinear First-Order Partial Differential Equations 576<br/>9.3.1 Some Standard Types 576<br/>9.3.2 Charpit's Method 580<br/>Exercise 9.3 585<br/>X Contents<br/>10. Partial Differential Equations of the Second Order 587-608<br/>10.1 Introduction 587<br/>10.1.1 Classification of Second-Order Linear<br/>Equations 587<br/>10.1.2 Homogeneous Linear Partial Differential<br/>Equations 589<br/>10.1.3 Linear Non-homogeneous Equations 591<br/>Exercise 10.1 592<br/>10.2 Evaluation of Particular Integrals 593<br/>10.2.1 Method of Separation of Variables 603<br/>Exercise 10.2 606<br/>Unit V Applications of Partial Differential Equations<br/>11. Initial Boundary-Value Problems 611-639<br/>11.1 Introduction 611<br/>11.1.1 One-Dimensional Wave Equation (Vibrations<br/>of a String) 611<br/>11.1.2 One-Dimensional Heat Flow 620<br/>11.1.3 Two-Dimensional Heat Flow 626<br/>11.1.4 Laplace's Equation in Polar Coordinates 632<br/>11.1.5 Equations of Transmission Lines 634<br/> |
| 650 ## - SUBJECT | |
| Keyword | Engineering mathematics. |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Koha item type | General Books |
| Withdrawn status | Lost status | Damaged status | Not for loan | Home library | Current library | Shelving location | Date acquired | Full call number | Accession number | Date last seen | Koha item type |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Central Library, Sikkim University | Central Library, Sikkim University | General Book Section | 29/08/2016 | 510.2462 SAS/E | P18509 | 29/08/2016 | General Books |