Introduction to Applied Mathematics

1. Front Matter

   Pages i-xii

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2. Complex Numbers

   • Lawrence Sirovich

   Pages 1-10

3. Convergence and Limit

   • Lawrence Sirovich

   Pages 11-26

4. Differentiation and Integration

   • Lawrence Sirovich

   Pages 27-76

5. Discrete Linear Systems

   • Lawrence Sirovich

   Pages 77-133

6. Fourier Series and Applications

   • Lawrence Sirovich

   Pages 134-167

7. Spaces of Functions

   • Lawrence Sirovich

   Pages 168-222

8. Partial Differential Equations

   • Lawrence Sirovich

   Pages 223-260

9. The Fourier and Laplace Transforms

   • Lawrence Sirovich

   Pages 261-293

10. Partial Differential Equations (Continued)

    • Lawrence Sirovich

    Pages 294-362

11. Back Matter

    Pages 363-370

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From the Preface: "The material in this book is based on notes for a course which I gave several times at Brown University. The target of the course was juniors and seniors majoring in applied mathematics, engineering and other sciences. My basic goal in the course was to teach standard methods, or what I regard as a basic "bag of tricks". In my opinion the material contained here, for the most part, does not depart widely from traditional subject matter. One such departure is the discussion of discrete linear systems. Besides being interesting in its own right, this topic is included because the treatment of such systems leads naturally to the use of discrete Fourier series, discrete Fourier transforms, and their extension, the Z-transform. On making the transition to continuous systems we derive their continuous analogues, viz., Fourier series, Fourier transforms, Fourier integrals and Laplace transforms. A main advantage to the approach taken is that a wide variety of techniques are seen to result from one or two very simple but central ideas. Above all, this course is intended as being one which gives the student a "can-do" frame of mind about mathematics. Students should be given confidence in using mathematics and not be made fearful of it. I have, therefore, forgone the theorem-proof format for a more informal style. Finally, a concerted effort was made to present an assortment of examples from diverse applications with the hope of attracting the interest of the student, and an equally dedicated effort was made to be kind to the reader."

• Extension
• Fourier series
• Fourier transform
• differential equation
• mathematics
• partial differential equation

• Division of Applied Mathematics, Brown University, Providence, USA

  Lawrence Sirovich

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