Through previous editions, Peter O’Neil has made rigorous topics accessible to thousands of students by emphasizing visuals, numerous examples, and interesting models.

Now, ADVANCED 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 , Vectors and Linear Algebra, of Differential Equations and Qualitative , Vector Analysis, Fourier Analysis, Orthogonal Expansions, and Wavelets, and much more.

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 , 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. Statistics

Author: Peter O'Neil
Edition: 7th Edition
ISBN: 1111427410 | 9781111427412
Type: eBook | Solution Manual
Language: English