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Advanced Engineering Mathematics by Michael D. Greenberg Book Details
| Book Name | Advanced Engineering Mathematics |
| Author | Michael D. Greenberg |
| Category | Mathematics Books, JEE and NEET Books, Education Books |
| Book Language | English |
| Pages | 1350 |
| ISBN | 817358560 |
| Country | India |
| Book Size | 70 MB |
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About Advanced Engineering Mathematics by Michael D. Greenberg Book
Advanced Engineering Mathematics is a specialized field of mathematics that goes beyond the fundamentals of basic calculus and linear algebra to address more complex and advanced mathematical concepts relevant to engineering applications. This subject is particularly important for engineering students and professionals who need to solve intricate mathematical problems encountered in various engineering disciplines. Here's an overview of what advanced engineering mathematics entails:
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Vector Calculus:
- Vector and scalar fields, gradient, divergence, and curl.
- Line integrals, surface integrals, and volume integrals in multiple dimensions.
- Stoke's theorem and the divergence theorem.
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Differential Equations:
- Ordinary differential equations (ODEs) and partial differential equations (PDEs).
- Solutions to first-order and second-order linear ODEs.
- Analytical and numerical methods for solving ODEs and PDEs.
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Complex Analysis:
- Complex numbers, complex functions, and analytic functions.
- Contour integration and the residue theorem.
- Applications in solving integrals and evaluating real-valued functions.
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Linear Algebra:
- Matrix operations, determinants, and inverses.
- Eigenvalues and eigenvectors, diagonalization.
- Applications in solving systems of linear equations and engineering problems.
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Transform Methods:
- Laplace transform and its applications in solving linear ODEs and systems.
- Fourier transform and its applications in signal processing and differential equations.
- Z-transform and its applications in discrete-time systems.
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Numerical Methods:
- Approximation techniques for solving mathematical problems.
- Numerical integration, differentiation, and solution of ODEs and PDEs.
- Root-finding methods, interpolation, and curve fitting.
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Probability and Statistics:
- Probability distributions, random variables, and expectations.
- Statistical analysis, hypothesis testing, and confidence intervals.
- Applications in reliability analysis, quality control, and data analysis.
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Partial Differential Equations (PDEs):
- Classification of PDEs, including heat equation, wave equation, and Laplace equation.
- Boundary value problems and initial value problems.
- Methods for solving PDEs, such as separation of variables and Fourier series.
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Numerical Linear Algebra:
- Direct and iterative methods for solving systems of linear equations.
- Eigenvalue problems and singular value decomposition.
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Complex Variable Methods:
- Cauchy-Riemann equations, conformal mappings, and complex potential.
- Applications in fluid dynamics and electrostatics.
"Advanced Engineering Mathematics" equips engineers with the mathematical tools needed to analyze, model, and solve complex problems encountered in engineering practice and research. This subject is essential for a deeper understanding of various engineering disciplines, including electrical, mechanical, civil, and aerospace engineering, among others.
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