Advanced Engineering Mathematics 7th Edition by Peter V. O’Neil – Ebook PDF Instant Download/Delivery: 1111427410, 978-1111427412
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ISBN 10: 1111427410
ISBN 13: 978-1111427412
Author: Peter V. O’Neil
Advanced Engineering Mathematics 7th Edition: Through previous editions, Peter O’Neil has made rigorous engineering mathematics topics accessible to thousands of students by emphasizing visuals, numerous examples, and interesting mathematical models. Now, ADVANCED ENGINEERING MATHEMATICS features revised examples and problems as well as newly added content that has been fine-tuned throughout to improve the clear flow of ideas. The computer plays a more prominent role than ever in generating computer graphics used to display concepts and problem sets. In this new edition, computational assistance in the form of a self contained Maple Primer has been included to encourage students to make use of such computational tools. The content has been reorganized into six parts and covers a wide spectrum of topics including Ordinary Differential Equations, Vectors and Linear Algebra, Systems of Differential Equations and Qualitative Methods, Vector Analysis, Fourier Analysis, Orthogonal Expansions, and Wavelets, and much more.
Advanced Engineering Mathematics 7th Table of contents:
Part 1: Ordinary Differential Equations
Chapter 1: First-Order Differential Equations
1.1 Terminology and Separable Equations
1.1 Problems
1.2 The Linear First-Order Equation
1.2 Problems
1.3 Exact Equations
1.3 Problems
1.4 Homogeneous, Bernoulli, and Riccati Equations
1.4 Problems
Chapter 2: Second-Order Differential Equations
2.1 The Linear Second-Order Equation
2.1 Problems
2.2 The Constant Coefficient Homogeneous Equation
2.2 Problems
2.3 Particular Solutions of the Nonhomogeneous Equation
2.3 Problems
2.4 The Euler Differential Equation
2.4 Problems
2.5 Series Solutions
2.5 Problems
Chapter 3: The Laplace Transform
3.1 Definition and Notation
3.1 Problems
3.2 Solution of Initial Value Problems
3.2 Problems
3.3 The Heaviside Function and Shifting Theorems
3.3 Problems
3.4 Convolution
3.4 Problems
3.5 Impulses and the Dirac Delta Function
3.5 Problems
3.6 Systems of Linear Differential Equations
3.6 Problems
Chapter 4: Sturm-Liouville Problems and Eigenfunction Expansions
4.1 Eigenvalues, Eigenfunctions and Sturm-Liouville Problems
4.1 Problems
4.2 Eigenfunction Expansions
4.2 Problems
4.3 Fourier Series
4.3 Problems
Part 2: Partial Differential Equations
Chapter 5: The Heat Equation
5.1 Diffusion Problems in a Bounded Medium
5.1 Problems
5.2 The Heat Equation With a Forcing Term F(x,t)
5.2 Problems
5.3 The Heat Equation on the Real Line
5.3 Problems
5.4 The Heat Equation on a Half-Line
5.4 Problems
5.5 The Two-Dimensional Heat Equation
5.5 Problems
Chapter 6: The Wave Equation
6.1 Wave Motion on a Bounded Interval
6.1 Problems
6.2 Wave Motion in an Unbounded Medium
6.2 Problems
6.3 d’Alembert’s Solution and Characteristics
6.3 Problems
6.4 The Wave Equation With a Forcing Term K(x,t)
6.4 Problems
6.5 The Wave Equation in Higher Dimensions
6.5 Problems
Chapter 7: Laplace’s Equation
7.1 The Dirichlet Problem for a Rectangle
7.1 Problems
7.2 Dirichlet Problem for a Disk
7.2 Problems
7.3 The Poisson Integral Formula
7.3 Problems
7.4 The Dirichlet Problem for Unbounded Regions
7.4 Problems
7.5 A Dirichlet Problem in 3 Dimensions
7.5 Problems
7.6 The Neumann Problem
7.6 Problems
7.7 Poisson’s Equation
7.7 Problems
Chapter 8: Special Functions and Applications
8.1 Legendre Polynomials
8.1 Problems
8.2 Bessel Functions
8.2 Problems
8.3 Some Applications of Bessel Functions
8.3 Problems
Chapter 9: Transform Methods of Solution
9.1 Laplace Transform Methods
9.1 Problems
9.2 Fourier Transform Methods
9.2 Problems
9.3 Fourier Sine and Cosine Transform Methods
9.3 Problems
Part 3: Matrices and Linear Algebra
Chapter 10: Vectors and the Vector Space R^n
10.1 Vectors in the Plane and 3-Space
10.1 Problems
10.2 The Dot Product
10.2 Problems
10.3 The Cross Product
10.3 Problems
10.4 n-Vectors and the Algebraic Structure of R^n
10.4 Problems
10.5 Orthogonal Sets and Orthogonalization
10.5 Problems
10.6 Orthogonal Complements and Projections
10.6 Problems
Chapter 11: Matrices, Determinants, and Linear Systems
11.1 Matrices and Matrix Algebra
11.1 Problems
11.2 Row Operations and Reduced Matrices
11.2 Problems
11.3 Solution of Homogeneous Linear Systems
11.3 Problems
11.4 Solution of Nonhomogeneous Linear Systems
11.4 Problems
11.5 Matrix Inverses
11.5 Problems
11.6 Determinants
11.6 Problems
11.7 Cramer’s Rule
11.7 Problems
11.8 The Matrix Tree Theorem
11.8 Problems
Chapter 12: Eigenvalues, Diagonalization, and Special Matrices
12.1 Eigenvalues and Eigenvectors
12.1 Problems
12.2 Diagonalization
12.2 Problems
12.3 Special Matrices and Their Eigenvalues and Eigenvectors
12.3 Problems
12.4 Quadratic Forms
12.4 Problems
Part 4: Systems of Differential Equations
Chapter 13: Systems of Linear Differential Equations
13.1 Linear Systems
13.1 Problems
13.2 Solution of X’=AX When A Is Constant
13.2 Problems
13.3 Exponential Matrix Solutions
13.3 Problems
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