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Advanced Engineering Mathematics

By Peter V. O'Neil

8th Edition © 2018
Discipline:Engineering
Course:General Engineering
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Now you can make rigorous mathematical topics accessible to your students by emphasizing visuals, numerous examples, and interesting mathematical models with O'Neil’s ADVANCED ENGINEERING MATHEMATICS, 8E. New "Math in Context" broadens the engineering connections for your students by clearly demonstrating how mathematical concepts are applied to current engineering problems. You have the flexibility to select additional topics that are best for your individual course, including many new web modules while minimizing the cost of the printed book.

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About this product

Now you can make rigorous mathematical topics accessible to your students by emphasizing visuals, numerous examples, and interesting mathematical models with O'Neil’s ADVANCED ENGINEERING MATHEMATICS, 8E. New "Math in Context" broadens the engineering connections for your students by clearly demonstrating how mathematical concepts are applied to current engineering problems. You have the flexibility to select additional topics that are best for your individual course, including many new web modules while minimizing the cost of the printed book.

THE BOOK’S SEVEN-PART ORGANIZATION BEST FITS MOST COURSE ORGANIZATIONS. Seven distinctive parts clearly focus and differentiate the mathematical ideas and methods while giving you the flexibility to select the sections best suited for your course and student needs.

DETAILED EXAMPLES ILLUSTRATE THE USE OF NOTATION AND THE THEORY. The numerous examples clarify notation, theory and the underlying computations, followed by the numerical calculations themselves.

AN INSTRUCTOR’S SOLUTIONS MANUAL OFFERS COMPLETE SOLUTIONS. You will find detailed solutions to virtually all problems in the book to save you time and effort.

ALL MATHEMATICS IS COMPLETED CORRECTLY. Although the approach is informal and proofs are included only when they offer a useful and straightforward insight into the ideas, you can trust all of the mathematics presented in this edition.

Table of contents

Chapters

Cover
Contents
Preface
Part 1: Ordinary Differential Equations
Part 2: Partial Differential Equations
Part 3: Matrices and Linear Algebra
Part 4: Systems of Differential Equations
Part 5: Vector Analysis
Part 6: Fourier Analysis
Part 7: Complex Functions
Notation
Answers to Selected Problems
Index
Show more

Part 1: Ordinary Differential Equations

Chapter 1: First-Order Differential Equations
Preview this section ↗
1.1 Terminology and Separable Equations ↗
1.1.1 Singular Solutions ↗
1.1.2 Some Applications of 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 ↗
1.4.1 The Homogeneous Differential Equation ↗
1.4.2 The Bernoulli Equation ↗
1.4.3 The Riccati Equation ↗
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
2.3.1 The Method of Variation of Parameters
2.3.2 The Method of Undetermined Coefficients
2.3 Problems
2.4 The Euler Differential Equation
2.4 Problems
2.5 Series Solutions
2.5.1 Power Series Solutions
2.5.1 Problems
2.5.2 Frobenius Solutions
2.5.2 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
3.3.1 The First Shifting Theorem
3.3.2 The Heaviside Function, Pulses, and the Second Shifting Theorem
3.3.3 Heaviside’s Formula
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
4.2.1 Properties of the Coefficients
4.2 Problems
4.3 Fourier Series
4.3.1 Fourier Series on [–L,L]
4.3.2 Fourier Cosine Series on [0,L]
4.3.3 Fourier Sine Series on [0,L]
4.3 Problems

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