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Part I - Ordinary Differential Equations Chapter 1 - First Order Differential Equations Chapter 2 - Linear Second Order Differential Equations Chapter 3 - The Laplace Transform Chapter 4 - Series Solutions Chapter 5 - Numerical Approximation of Solutions Part II - Vectors and Linear Algebra Chapter 6 - Vectors and Vector Spaces Chapter 7 - Matrices and Systems of Linear Equations Chapter 8 - Determinants Chapter 9 - Eigenvalues, Diagonalization and Special Matrices Part III - Systems of Differential Equations and Qualitative Methods Chapter 10 - Systems of Linear Differential Equations Chapter 11 - Qualitative Methods and Systems of Nonlinear Differential Equations Part IV - Vector Analysis Chapter 12 - Vector Differential Calculus Chapter 13 - Vector Integral Calculus Part V - Fourier Analysis, Orthogonal Expansions and Wavelets Chapter 14 - Fourier Series Chapter 15 - The Fourier Integral and Fourier Transforms Chapter 16 - Special Functions, Orthogonal Expansions and Wavelets Part VI - Partial Differential Equations Chapter 17 - The Wave Equation Chapter 18 - The Heat Equation Chapter 19 - The Potential Equation Part VII - Complex Analysis Chapter 20 - Geometry and Arithmetic of Complex Numbers Chapter 21 - Complex Functions Chapter 22 - Complex Integration Chapter 23 - Series Representations of Functions Chapter 24 - Singularities and the Residue Theorem Chapter 25 - Conformal Mappings Part VIII - Probability and Statistics Chapter 26 - Counting and Probability Chapter 27 - StatisticsSynopsis:
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. "Advanced Engineering Mathematics" features a greater number of examples and problems and is 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, incorporating the use of leading software packages. Computational assistance, exercises and projects have been included to encourage students to make use of these computational tools.The content is organized into eight 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, Partial Differential Equations, Complex Analysis, and Probability and Statistics.
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