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Advanced mathematics pdf for ssc cgl – Free Study Material for SSC CGL 2017
Book Name: Platform’s SSC Advanced Maths (Hindi) Vol-1
• Author: R. K. Singh
• Published By: Rukmini Prakashan
• Language: Hindi
• Pages : 229
• Format : PDF
• Size : 91 Mb (Prefer WiFi Downloading)
• Quality : Scanned (black and white)
List of chapters Covered Under This book Are
- GeoMetry
- trigonometry
- Algebra
- Height And Distance
- Co Ordinate Geometry
- Prism and pyramids
- And Other Chapters
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Note & Disclaimer – All Study Materials Here are shared Only For Educational Purposes .StudyDhaba Will Not Be Responsible . Whole Materials Is For Education Purpose Only .We Work hard to Provide You Quality Study Materials For All Competitive Exams .You can Also Share Study Materials,Notes Or Any Materials With Us .We Will Publish That Material On Our Website .It is a Humble Request To All Of You Please Share This Post With Your Friends And On Social Media .Chapter 1
First-Order Odes
| 1.1 | Basic Concepts. Modeling | Problem Set | p.8 |
| 1.2 | Geometric Meaning of y'=f(x,y). Direction Fields, Euler's Method | Problem Set | p.11 |
| 1.3 | Separable ODEs. Modeling | Problem Set | p.18 |
| 1.4 | Exact ODEs. Integrating Factors | Problem Set | p.26 |
| 1.5 | Linear ODEs. Bernoulli Equation. Population Dynamics | Problem Set | p.34 |
| 1.6 | Orthogonal Trajectories | Problem Set | p.38 |
| 1.7 | Existence and Uniqueness of Solutions for Initial Value Problems | Problem Set | p.42 |
| Review Questions and Problems | p.43 |
Chapter 2
Second-Order Linear Odes
| 2.1 | Homogeneous Linear ODEs of Second Order | Problem Set | p.53 |
| 2.2 | Homogeneous Linear ODEs with Constant Coefficients | Problem Set | p.59 |
| 2.3 | Differential Operators | Problem Set | p.61 |
| 2.4 | Modeling of Free Oscillations of a Mass-Spring System | Problem Set | p.69 |
| 2.5 | Euler-Cauchy Equations | Problem Set | p.73 |
| 2.6 | Existence and Uniqueness of Solutions. Wronskian | Problem Set | p.79 |
| 2.7 | Nonhomogeneous ODEs | Problem Set | p.84 |
| 2.8 | Modeling: Forced Oscillations. Resonance | Problem Set | p.91 |
| 2.9 | Modeling: Electric Circuits | Problem Set | p.98 |
| 2.10 | Solution by Variation of Parameters | Problem Set | p.102 |
| Review Questions and Problems | p.102 |
Chapter 3
Higher Order Linear Odes
| 3.1 | Homogeneous Linear ODEs | Problem Set | p.111 |
| 3.2 | Homogeneous Linear ODEs with Constant Coefficients | Problem Set | p.116 |
| Review Questions and Problems | p.122 | ||
| 3.3 | Nonhomogeneous Linear ODEs | Problem Set | p.122 |
Chapter 4
Systems Of Odes. Phase Plane. Qualitative Methods
| 4.1 | Systems of ODEs as Models in Engineering Applications | Problem Set | p.136 |
| 4.3 | Constant-Coefficient Systems. Phase Plane Method | Problem Set | p.147 |
| 4.4 | Criteria for Critical Points. Stability | Problem Set | p.151 |
| 4.5 | Qualitative Methods for Nonlinear Systems | Problem Set | p.159 |
| 4.6 | Nonhomogeneous Linear Systems of ODEs | Problem Set | p.163 |
| Review Questions and Problems | p.164 |
Chapter 5
Series Solutions Of Odes. Special Functions
| 5.1 | Power Series Method | Problem Set | p.174 |
| 5.2 | Legendre's Equation. Legendre Polynomials Pn(x) | Problem Set | p.179 |
| 5.3 | Extended Power Series Method: Frobenius Method | Problem Set | p.186 |
| 5.4 | Bessel's Equation. Bessel Functions Jv(x) | Problem Set | p.195 |
| 5.5 | Bessel Functions Yv(x). General Solution | Problem Set | p.200 |
| Review Questions and Problems | p.200 |
Chapter 6
Laplace Transforms
| 6.1 | Laplace Transform. Linearity. First Shifting Theorem (s-Shifting) | Problem Set | p.210 |
| 6.2 | Transforms of Derivatives and Integrals. ODEs | Problem Set | p.216 |
| 6.3 | Unit Step Function (Heaviside Function). Second Shifting Theorem (t-Shifting) | Problem Set | p.223 |
| 6.4 | Short Impulses. Dirac's Delta Function. Partial Fractions | Problem Set | p.230 |
| 6.5 | Convolution. Integral Equations | Problem Set | p.237 |
| 6.6 | Differentiation and Integration of Transforms. ODEs with Variable Coefficients | Problem Set | p.241 |
| 6.7 | Systems of ODEs | Problem Set | p.246 |
| Review Questions and Problems | p.251 |
Chapter 7
Linear Algebra: Matrices, Vectors, Determinants. Linear Systems
| 7.1 | Matrices, Vectors: Addition and Scalar Multiplication | Problem Set | p.261 |
| 7.2 | Matrix Multiplication | Problem Set | p.270 |
| 7.3 | Linear Systems of Equations. Gauss Elimination | Problem Set | p.280 |
| 7.4 | Linear Independence. Rank of a Matrix. Vector Space | Problem Set | p.287 |
| 7.7 | Determinants. Cramer's Rule | Problem Set | p.300 |
| 7.8 | Inverse of a Matrix. Gauss-Jordan Elimination | Problem Set | p.308 |
| 7.9 | Vector Spaces, Inner Product Spaces, Linear Transformations | Problem Set | p.318 |
| Review Questions and Problems | p.318 |
Chapter 8
Linear Algebra: Matrix Eigenvvalue Problems
| 8.1 | The Matrix Eigenvalue Problem. Determining Eigenvalues and Eigenvectors | Problem Set | p.329 |
| 8.2 | Some Applications of Eigenvalue Problems | Problem Set | p.333 |
| 8.3 | Symmetric, Skew-Symmetric, and Orthogonal Matrices | Problem Set | p.338 |
| 8.4 | Eigenbases. Diagonalization. Quadratic Forms | Problem Set | p.345 |
| 8.5 | Complex Matrices and Forms. | Problem Set | p.351 |
| Review Questions and Problems | p.352 |
Chapter 9
Vector Differential Calculus, Grad, Div, Curl
| 9.1 | Vectors in 2-Space and 3-Space | Problem Set | p.360 |
| 9.2 | Inner Product (Dot Product) | Problem Set | p.367 |
| 9.3 | Vector Product (Cross Product) | Problem Set | p.374 |
| 9.4 | Vector and Scalar Functions and Their Fields. Vector Calculus: Derivatives | Problem Set | p.380 |
| 9.5 | Curves. Arc Length. Curvature. Torsion | Problem Set | p.390 |
| 9.7 | Gradient of a Scalar Field. Directional Derivative | Problem Set | p.402 |
| 9.8 | Divergence of a Vector Field | Problem Set | p.405 |
| 9.9 | Curl of a Vector Field | Problem Set | p.408 |
| Review Questions and Problems | p.409 |
Chapter 10
Vector Integral Calculus. Integral Theorems
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| 10.1 | Line Integrals | Problem Set | p.418 |
| 10.2 | Path Independence of Line Integrals | Problem Set | p.425 |
| 10.3 | Calculus Review: Double Integrals. | Problem Set | p.432 |
| 10.4 | Green's Theorem in the Plane | Problem Set | p.438 |
| 10.5 | Surfaces for Surface Integrals | Problem Set | p.442 |
| 10.6 | Surface Integrals | Problem Set | p.450 |
| 10.7 | Triple Integrals. Divergence Theorem of Gauss | Problem Set | p.457 |
| 10.8 | Further Applications of the Divergence Theorem | Problem Set | p.462 |
| 10.9 | Stokes's Theorem | Problem Set | p.468 |
| Review Questions and Problems | p.469 |
Chapter 11
Fourier Analysis
| 11.1 | Fourier Series | Problem Set | p.482 |
| 11.2 | Arbitrary Period. Even and Odd Functions. Half-Range Expansions | Problem Set | p.490 |
| 11.3 | Forced Oscillations | Problem Set | p.494 |
| 11.4 | Approximation by Trigonometric Polynomials | Problem Set | p.498 |
| 11.5 | Sturm-Liouville Problems. Orthogonal Functions | Problem Set | p.503 |
| 11.6 | Orthogonal Series. Generalized Fourier Series | Problem Set | p.509 |
| 11.7 | Fourier Integral | Problem Set | p.517 |
| 11.8 | Fourier Cosine and Sine Transforms | Problem Set | p.522 |
| 11.9 | Fourier Transform. Discrete and Fast Fourier Transforms | Problem Set | p.533 |
| Review Questions and Problems | p.537 |
Chapter 12
Partial Differential Equations (Pdes)
| 12.1 | Basic Concepts of PDEs | Problem Set | p.542 |
| 12.3 | Solution by Separating Variables. Use of Fourier Series | Problem Set | p.551 |
| 12.4 | D'Alembert's Solution of the Wave Equation. Characteristics | Problem Set | p.556 |
| 12.6 | Heat Equation: Solution by Fourier Series. Steady Two-Dimensional Heat Problems. Dirichlet Problem | Problem Set | p.566 |
| 12.7 | Heat Equation: Modeling Very Long Bars. Solution by Fourier Integrals and Transforms | Problem Set | p.574 |
| 12.9 | Rectangular Membrane. Double Fourier Series | Problem Set | p.584 |
| 12.10 | Laplacian in Polar Coordinates. Circular Membrane. Fourier-Bessel Series | Problem Set | p.591 |
| 12.11 | Laplace's Equation in Cylindrical and Spherical Coordinates. Potential | Problem Set | p.598 |
| 12.12 | Solution of PDEs by Laplace Transforms | Problem Set | p.602 |
| Review Questions and Problems | p.603 |
Chapter 13
Complex Numbers And Functions. Complex Differentiation
| 13.1 | Complex Numbers and Their Geometric Representation | Problem Set | p.612 |
| 13.2 | Polar Form of Complex Numbers. Powers and Roots | Problem Set | p.618 |
| 13.3 | Derivative. Analytic Function | Problem Set | p.624 |
| 13.4 | Cauchy-Riemann Equations. Laplace's Equation | Problem Set | p.629 |
| 13.5 | Exponential Function | Problem Set | p.632 |
| 13.6 | Trigonometric and Hyperbolic Functions. Euler's Formula | Problem Set | p.636 |
| 13.7 | Logarithm. General Power. Principal Value | Problem Set | p.640 |
| Review Questions and Problems | p.641 |
Chapter 14
Complex Integration
| 14.1 | Line Integral in the Complex Plane | Problem Set | p.651 |
| 14.2 | Cauchy's Integral Theorem | Problem Set | p.659 |
| 14.3 | Cauchy's Integral Formula | Problem Set | p.663 |
| 14.4 | Derivatives of Analytic Functions | Problem Set | p.667 |
| Review Questions and Problems | p.668 |
Chapter 15
Power Series, Taylor Series
| 15.1 | Sequences, Series, Convergence Tests | Problem Set | p.679 |
| 15.2 | Power Series | Problem Set | p.684 |
| 15.3 | Functions Given by Power Series | Problem Set | p.689 |
| 15.4 | Taylor and Maclaurin Series | Problem Set | p.697 |
| 15.5 | Uniform Convergence. | Problem Set | p.704 |
| Review Questions and Problems | p.706 |
Chapter 16
Laurent Series. Residue Integration
| 16.1 | Laurent Series | Problem Set | p.714 |
| 16.2 | Singulariteis and Zeros. Infinity | Problem Set | p.719 |
| 16.3 | Residue Integration Method | Problem Set | p.725 |
| 16.4 | Residue Integration of Real Integrals | Problem Set | p.733 |
| Review Questions and Problems | p.733 |
Chapter 17
Confomal Mapping
| 17.1 | Geometry of Analytic Functions: Conformal Mapping | Problem Set | p.741 |
| 17.2 | Linear Fractional Transformations (Mobius Transformations) | Problem Set | p.745 |
| 17.3 | Special Linear Fractional Transformations | Problem Set | p.750 |
| 17.4 | Conformal Mapping by Other Functions | Problem Set | p.754 |
| Review Questions and Problems | p.756 | ||
| 17.5 | Riemann Surfaces | Problem Set | p.756 |
Chapter 18
Advanced Mathematics Pdf
Complex Analysis And Potential Theory
| 18.1 | Electrostactic Fields | Problem Set | p.762 |
| 18.2 | Use of Conformal Mapping. Modeling | Problem Set | p.766 |
| 18.3 | Heat Problems | Problem Set | p.769 |
| 18.4 | Fluid Flow | Problem Set | p.776 |
| 18.5 | Poisson's Integral Formula for Potentials | Problem Set | p.781 |
| 18.6 | General Properties of Harmonic Functions. Uniqueness Theorem for the Dirichlet Problem | Problem Set | p.784 |
| Review Questions and Problems | p.785 |
Chapter 19
Numerics In General
| 19.1 | Introduction | Problem Set | p.796 |
| 19.2 | Solution of Equations by Iteration | Problem Set | p.807 |
| 19.3 | Interpolation | Problem Set | p.819 |
| 19.4 | Spline Interpolation | Problem Set | p.826 |
| 19.5 | Numeric Integration and Differentiation | Problem Set | p.839 |
| Review Questions and Problems | p.841 |
Chapter 20
Numeric Linear Algebra
| 20.1 | Linear Systems: Gauss Elimation | Problem Set | p.851 |
| 20.2 | Linear Systems: LU-Factorization, Matrix Inversion | Problem Set | p.857 |
| 20.3 | Linear Systems: Solution by Iteration | Problem Set | p.863 |
| 20.4 | Linear Systems: Ill-Conditioning, Norms | Problem Set | p.871 |
| 20.5 | Least Squares Method | Problem Set | p.875 |
| 20.7 | Inclusion of Matrix Eigenvalues | Problem Set | p.884 |
| 20.8 | Power Method for Eigenvalues | Problem Set | p.887 |
| 20.9 | Tridiagonalization and QR-Factorization | Problem Set | p.896 |
| Review Questions and Problems | p.896 |
Chapter 21
Numerics For Odes And Pdes
| 21.1 | Methods for First-Order ODEs | Problem Set | p.910 |
| 21.2 | Multistep Methods | Problem Set | p.915 |
| 21.3 | Methdos for Systems and Higher Order ODEs | Problem Set | p.922 |
| 21.4 | Methods for Elliptic PDEs | Problem Set | p.930 |
| 21.5 | Neumann and Mixed Problems. Irregular Boundary | Problem Set | p.935 |
| 21.6 | Methods for Parabolic PDEs | Problem Set | p.941 |
| 21.7 | Method for Hyberbolic PDEs | Problem Set | p.944 |
| Review Questions and Problems | p.945 |
Chapter 22
Advanced Math Books Pdf
Unconstrained Optimization. Linear Programming
Advanced Mathematics Precalculus Pdf Answers
| 22.1 | Basic Concepts. Unconstrained Optimization: Method of Steepest Descent | Problem Set | p.953 |
| 22.2 | Linear Programming | Problem Set | p.957 |
| 22.3 | Simplex Method | Problem Set | p.961 |
| Review Questions and Problems | p.968 | ||
| 22.4 | Simplex Method: Difficulties | Problem Set | p.968 |
Chapter 23
Graphs. Combinatorial Optimization
| 23.1 | Graphs and Digraphs | Problem Set | p.974 |
| 23.2 | Shortest Path Problems. Complexity | Problem Set | p.979 |
| 23.3 | Bellman's Principle. Dijkstra's Algorithm | Problem Set | p.983 |
| 23.4 | Shortest Spanning Trees: Greedy Algorithm | Problem Set | p.987 |
| 23.5 | Shortest Spanning Trees: Prims's Algorithm | Problem Set | p.990 |
| 23.6 | Flows in Networks | Problem Set | p.997 |
| 23.7 | Maximum Flow: Ford-Fulkerson Algorithm | Problem Set | p.1000 |
| 23.8 | Bipartite Graphs. Assignment Problems | Problem Set | p.1005 |
| Review Questions and Problems | p.1006 |
Chapter 24
Data Analysis, Probability Theory
| 24.1 | Data Representation. Average. Spread | Problem Set | p.1015 |
| 24.2 | Experiments, Outcomes, Events | Problem Set | p.1017 |
| 24.3 | Probability | Problem Set | p.1024 |
| 24.4 | Permutations and Combinations | Problem Set | p.1028 |
| 24.5 | Random Variables. Probability Distributions | Problem Set | p.1034 |
| 24.6 | Mean and Variance of a Distribution | Problem Set | p.1038 |
| 24.7 | Binomial, Poisson, and Hypergeometric Distributions | Problem Set | p.1044 |
| 24.8 | Normal Distribution | Problem Set | p.1050 |
| 24.9 | Distributions of Several Random Variables | Problem Set | p.1059 |
| Review Questions and Problems | p.1060 |
Chapter 25
Mathematical Statistics
| 25.2 | Point Estimation of Parameters | Problem Set | p.1067 |
| 25.3 | Confidence Intervals | Problem Set | p.1077 |
| 25.4 | Testing of Hypotheses. Decisions | Problem Set | p.1086 |
| 25.5 | Quality Control | Problem Set | p.1091 |
| 25.6 | Acceptance Sampling | Problem Set | p.1095 |
| 25.7 | Goodness of Fit. X^2-Test | Problem Set | p.1099 |
| 25.8 | Nonparametric Tests | Problem Set | p.1102 |
| 25.9 | Regression. Fitting Straight Lines. Correlation | Problem Set | p.1111 |
| Review Questions and Problems | p.1111 |