Book description
Engineering Mathematics Volume-I is meant for undergraduate engineering students. Considering the vast coverage of the subject, usually this paper is taught in three to four semesters. The two volumes in Engineering Mathematics by Babu Ram offer a complete solution to these papers.
Table of contents
- Cover
- Title Page
- Contents
- Dedication
- Preface
- Symbols and Basic Formulae
-
1 - Sequences and Series
- 1.1 - SEQUENCES
- 1.2 - CONVERGENCE OF SEQUENCES
- 1.3 - THE UPPER AND LOWER LIMITS OF A SEQUENCE
- 1.4 - CAUCHY'S PRINCIPLE OF CONVERGENCE
- 1.5 - MONOTONIC SEQUENCE
- 1.6 - THEOREMS ON LIMITS
- 1.7 - SUBSEQUENCES
- 1.8 - SERIES
- 1.9 - COMPARISON TESTS
- 1.10 - D'ALEMBERI'S RATIO TEST
- 1.11 - CAUCHY'S ROOT TEST
- 1.12 - RAABE'S TEST
- 1.13 - LOGARITHMIC TEST
- 1.14 - DE MORGAN–BERIRAND TEST
- 1.15 - GAUSS'S TEST
- 1.16 - CAUCHY'S INTEGRAL TEST
- 1.17 - CAUCHY'S CONDENSATION TEST
- 1.18 - KUMMER'S TEST
- 1.19 - ALTERNATING SERIES
- 1.20 - ABSOLUTE CONVERGENCE OF A SERIES
- 1.21 - CONVERGENCE OF THE SERIES OF THE TYPE
- 1.22 - DERANGEMENT OF SERIES
- 1.23 - NATURE OF NON-ABSOLUTELY CONVERGENT SERIES
- 1.24 - EFFECT OF DERANGEMENT OF NON-ABSOLUTELY CONVERGENT SERIES
- 1.25 - UNIFORM CONVERGENCE
- 1.26 - UNIFORM CONVERGENCE OF A SERIES OF FUNCTIONS
- 1.27 - PROPERTIES OF UNIFORMLY CONVERGENT SERIES
- 1.28 - POWER SERIES
- EXERCISES
- 2 - Successive Differentiation, Mean Value Theorems and Expansion of Functions
-
3 - Curvature
- 3.1 - RADIUS OF CURVATURE OF INTRINSIC CURVES
- 3.2 - RADIUS OF CURVATURE FOR CARTESIAN CURVES
- 3.3 - RADIUS OF CURVATURE FOR PARAMETRIC CURVES
- 3.4 - RADIUS OF CURVATURE FOR PEDAL CURVES
- 3.5 - RADIUS OF CURVATURE FOR POLAR CURVES
- 3.6 - RADIUS OF CURVATURE AT THE ORIGIN
- 3.7 - CENTER OF CURVATURE
- 3.8 - EVOLUTES AND INVOLUTES
- 3.9 - EQUATION OF THE CIRCLE OF CURVATURE
- 3.10 - CHORDS OF CURVATURE PARALLEL TO THE COORDINATE AXES
- 3.11 - CHORD OF CURVATURE IN POLAR COORDINATES
- 3.12 - MISCELLANEOUS EXAMPLES
- EXERCISES
-
4 - Asymptotes and Curve Tracing
- 4.1 - DETERMINATION OF ASYMPTOTES WHEN THE EQUATION OF THE CURVE IN CARTESIAN FORM IS GIVENS
- 4.2 - THE ASYMPTOTES OF THE GENERAL RATIONAL ALGEBRAIC CURVE
- 4.3 - ASYMPTOTES PARALLEL TO COORDINATE AXES
- 4.4 - WORKING RULE FOR FINDING ASYMPTOTES OF RATIONAL ALGEBRAIC CURVE
- 4.5 - INTERSECTION OF A CURVE AND ITS ASYMPTOTES
- 4.6 - ASYMPTOTES BY EXPANSION
- 4.7 - ASYMPTOTES OF THE POLAR CURVES
- 4.8 - CIRCULAR ASYMPTOTES
- 4.9 - CONCAVITY, CONVEXITY AND SINGULAR POINTS
- 4.10 - CURVE TRACING (CARTESIAN EQUATIONS)
- 4.11 - CURVE TRACING (POLAR EQUATIONS)
- 4.12 - CURVE TRACING (PARAMETRIC EQUATIONS)
- EXERCISES
-
5 - Functions of Several Variables
- 5.1 - CONTINUITY OF A FUNCTION OF TWO VARIABLES
- 5.2 - DIFFERENTIABILITY OF A FUNCTION OF TWO VARIABLES
- 5.3 - THE DIFFERENTIAL COEFFICIENTS
- 5.4 - DISTINCTION BETWEEN DERIVATIVES AND DIFFERENTIAL COEFFICIENTS
- 5.5 - HIGHER-ORDER PARTIAL DERIVATIVES
- 5.6 - ENVELOPES AND EVOLUTES
- 5.7 - HOMOGENEOUS FUNCTIONS AND EULER'S THEOREM
- 5.8 - DIFFERENTIATION OF COMPOSITE FUNCTIONS
- 5.9 - TRANSFORMATION FROM CARTESIAN TO POLAR COORDINATES AND VICE VERSA
- 5.10 - TAYLOR'S THEOREM FOR FUNCTIONS OF SEVERAL VARIABLES
- 5.11 - APPROXIMATION OF ERRORS
- 5.12 - GENERAL FORMULA FOR ERRORS
- 5.13 - TANGENT PLANE AND NORMAL TO A SURFACE
- 5.14 - JACOBIANS
- 5.15 - PROPERTIES OF JACOBIAN
- 5.16 - NECESSARY AND SUFFICIENT CONDITIONS FOR JACOBIAN TO VANISH
- 5.17 - DIFFERENTIATION UNDER THE INTEGRAL SIGN
- 5.18 - MISCELLANEOUS EXAMPLES
- 5.19 - EXTREME VALUES
- 5.20 - LAGRANGE'S METHOD OF UNDETERMINED MULTIPLIERS
- EXERCISES
- 6 - Tangents and Normals
- 7 - Beta and Gamma Functions
-
8 - Reduction Formulas
- 8.1 - REDUCTION FORMULAS FOR ∫ SINN X DX AND ∫ COSN X DX
- 8.2 - REDUCTION FORMULA FOR ∫ SINM X COSN X DX
- 8.3 - REDUCTION FORMULAS FOR ∫ TANN X DX AND ∫ SECN X DX
- 8.4 - REDUCTION FORMULAS FOR ∫ XN SINMX DX AND ∫ XN COSMX DX
- 8.5 - REDUCTION FORMULAS FOR ∫ EAX AND ∫ XM (LOG X)N DX
- 8.6 - REDUCTION FORMULA FOR IMN = ∫ COSM X SIN NX DX.
- 8.7 - REDUCTION FORMULA FOR ∫
- EXERCISES
- 9 - Quadrature and Rectification
- 10 - Centre of Gravity and Moment of Inertia
-
11 - Volumes and Surfaces of Solids of Revolution
- 11.1 - VOLUME OF THE SOLID OF REVOLUTION (CARTESIAN EQUATIONS)
- 11.2 - VOLUME OF THE SOLID OF REVOLUTION (PARAMETRIC EQUATIONS)
- 11.3 - VOLUME OF THE SOLID OF REVOLUTION (POLAR CURVES)
- 11.4 - SURFACE OF THE SOLID OF REVOLUTION (CARTESIAN EQUATIONS)
- 11.5 - SURFACE OF THE SOLID OF REVOLUTION (PARAMETRIC EQUATIONS)
- 11.6 - SURFACE OF THE SOLID OF REVOLUTION (POLAR CURVES)
- EXERCISES
-
12 - Multiple Integrals
- 12.1 - DOUBLE INTEGRALS
- 12.2 - PROPERTIES OF A DOUBLE INTEGRAL
- 12.3 - EVALUATION OF DOUBLE INTEGRALS (CARTESIAN COORDINATES)
- 12.4 - EVALUATION OF DOUBLE INTEGRALS (POLAR COORDINATES)
- 12.5 - CHANGE OF VARIABLES IN A DOUBLE INTEGRAL
- 12.6 - CHANGE OF ORDER OF INTEGRATION
- 12.7 - AREA ENCLOSED BY PLANE CURVES (CARTESIAN AND POLAR COORDINATES)
- 12.8 - VOLUME AND SURFACE AREA AS DOUBLE INTEGRALS
- 12.9 - TRIPLE INTEGRALS AND THEIR EVALUATION
- 12.10 - CHANGE TO SPHERICAL POLAR COORDINATES FROM CARTESIAN COORDINATES IN A TRIPLE INTEGRAL
- 12.11 - VOLUME AS A TRIPLE INTEGRAL
- 12.12 - MISCELLANEOUS EXAMPLES
- EXERCISES
-
13 - Vector Calculus
- 13.1 - DIFFERENTIATION OF A VECTOR
- 13.2 - PARTIAL DERIVATIVES OF A VECTOR FUNCTION
- 13.3 - GRADIENT OF A SCALAR FIELD
- 13.4 - GEOMETRICAL INTERPRETATION OF A GRADIENT
- 13.5 - PROPERTIES OF A GRADIENT
- 13.6 - DIRECTIONAL DERIVATIVES
- 13.7 - DIVERGENCE OF A VECTOR-POINT FUNCTION
- 13.8 - PHYSICAL INTERPRETATION OF DIVERGENCE
- 13.9 - CURL OF A VECTOR-POINT FUNCTION
- 13.10 - PHYSICAL INTERPRETATION OF CURL
- 13.11 - THE LAPLACIAN OPERATOR
- 13.12 - PROPERTIES OF DIVERGENCE AND CURL
- 13.13 - INTEGRATION OF VECTOR FUNCTIONS
- 13.14 - LINE INTEGRAL
- 13.15 - WORK DONE BY A FORCE
- 13.16 - SURFACE INTEGRAL
- 13.17 - VOLUME INTEGRAL
- 13.18 - GAUSS'S DIVERGENCE THEOREM
- 13.19 - GREEN'S THEOREM IN A PLANE
- 13.20 - STOKE'S THEOREM
- 13.21 - MISCELLANEOUS EXAMPLES
- EXERCISES
-
14 - Three-Dimensional Geometry
- 14.1 - COORDINATE PLANES
- 14.2 - DISTANCE BETWEEN TWO POINTS
- 14.3 - DIRECTION RATIOS AND DIRECTION COSINES OF A LINE
- 14.4 - SECTION FORMULAE—INTERNAL DIVISION OF A LINE BY A POINT ON THE LINE
- 14.5 - STRAIGHT LINE IN THREE DIMENSIONS
- 14.6 - ANGLE BETWEEN TWO LINES
- 14.7 - SHORTEST DISTANCE BETWEEN TWO SKEW LINES
- 14.8 - EQUATION OF A PLANE
- 14.9 - EQUATION OF A PLANE PASSING THROUGH A GIVEN POINT AND PERPENDICULAR TO A GIVEN DIRECTION
- 14.10 - EQUATION OF A PLANE PASSING THROUGH THREE POINTS
- 14.11 - EQUATION OF A PLANE PASSING THROUGH A POINT AND PARALLEL TO TWO GIVEN VECTORS
- 14.12 - EQUATION OF A PLANE PASSING THROUGH TWO POINT AND PARALLEL TO A LINE
- 14.13 - ANGLE BETWEEN TWO PLANES
- 14.14 - ANGLE BETWEEN A LINE AND A PLANE
- 14.15 - PERPENDICULAR DISTANCE OF A POINT FROM A PLANE
- 14.16 - PLANES BISECTING THE ANGLES BETWEEN TWO PLANES
- 14.17 - INTERSECTION OF PLANES
- 14.18 - PLANES PASSING THROUGH THE INTERSECTION OF TWO GIVEN PLANES
- 14.19 - SPHERE
- 14.20 - EQUATION OF A SPHERE WHOSE DIAMETER IS THE LINE JOINING TWO GIVEN POINTS
- 14.21 - EQUATION OF A SPHERE PASSING THROUGH FOUR POINTS
- 14.22 - EQUATION OF THE TANGENT PLANE TO A SPHEREM
- 14.23 - CONDITION OF TANGENCY
- 14.24 - ANGLE OF INTERSECTION OF TWO SPHERES
- 14.25 - CONDITION OF ORTHOGONALITY OF TWO SPHERES
- 14.26 - CYLINDER
- 14.27 - EQUATION OF A CYLINDER WITH GIVEN AXIS AND GUIDING CURVES
- 14.28 - RIGHT CIRCULAR CYLINDER
- 14.29 - CONE
- 14.30 - EQUATION OF A CONE WITH ITS VERTEX AT THE ORIGIN
- 14.31 - EQUATION OF A CONE WITH GIVEN VERTEX AND GUIDING CURVE
- 14.32 - RIGHT CIRCULAR CONE
- 14.33 - RIGHT CIRCULAR CONE WITH VERTEX (α, β, γ), SEMI-VERTICAL ANGLE θ, AND THE DIRECTION COSINES OF THE AXIS.
- 14.34 - CONICOIDS
- 14.35 - SHAPE OF AN ELLIPSOID
- 14.36 - SHAPE OF THE HYPERBOLOID OF ONE SHEET
- 14.37 - SHAPE OF THE HYPERBOLOID OF TWO SHEETS
- 14.38 - SHAPE OF THE ELLIPTIC CONE
- 14.39 - INTERSECTION OF A CONICOID AND A LINE
- 14.40 - TANGENT PLANE AT A POINT OF CENTRAL CONICOID
- 14.41 - CONDITION OF TANGENCY
- 14.42 - EQUATION OF NORMAL TO THE CENTRAL CONICOID AT ANY POINT (α, β, γ) ON IT
- 14.43 - MISCELLANEOUS EXAMPLES
- EXERCISES
- 15 - Logic
- 16 - Elements of Fuzzy Logic
-
17 - Graphs
- 17.1 - DEFINITIONS AND BASIC CONCEPTS
- 17.2 - SPECIAL GRAPHS
- 17.3 - SUBGRAPHS
- 17.4 - ISOMORPHISMS OF GRAPHS
- 17.5 - WALKS, PATHS AND CIRCUITS
- 17.6 - EULERIAN PATHS AND CIRCUITS
- 17.7 - HAMILTONIAN CIRCUITS
- 17.8 - MATRIX REPRESENTATION OF GRAPHS
- 17.9 - PLANAR GRAPHS
- 17.10 - COLOURING OF GRAPH
- 17.11 - DIRECTED GRAPHS
- 17.12 - TREES
- 17.13 - ISOMORPHISM OF TREES
- 17.14 - REPRESENTATION OF ALGEBRAIC EXPRESSIONS BY BINARY TREES
- 17.15 - SPANNING TREE OF A GRAPH
- 17.16 - SHORTEST PATH PROBLEM
- 17.17 - MINIMAL SPANNING TREE
- 17.18 - CUT SETS
- 17.19 - TREE SEARCHING
- 17.20 - TRANSPORT NETWORKS
- EXERCISES
- Copyright
Product information
- Title: Engineering Mathematics, Volume I, Second Edition
- Author(s):
- Release date: March 2012
- Publisher(s): Pearson India
- ISBN: 9788131784709
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