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1. Introduction

2. Problem Solving

3. Scientific Programming

4. Elementary Mathematics

5.Vectors and Matrices

6. Calculus of a Single Variable

7.Calculus of Several Variables

8. Calculus of Vector Functions

9. Probability Theory and Statistics

10. Complex Analysis

11. Differential Equations

12. Differential Equations

13. Partial Differential Equations and Special Functions

14. Integral Equations and the Calculus of Variations

Unique among disciplines, physics condenses the limitlessly complex behavior of nature into a small set of underlying principles. Once these are clearly understoodand supplemented with often superficial domain knowledge, any scientific or engineering problem can be succinctly analyzed and solved. Accordingly, the study of physics leads to unsurpassed satisfaction and fulfillment. This book summarizes intermediate-, college-, and university-level physics and its associated mathematics, identifying basic formulas and concepts that should be under stood and memorized. It can be employed to supplement courses, as a reference text or as review material for the GRE and graduate comprehensive exams.Since physics incorporates broad areas of science and engineering, many treatments overemphasize technical details and problems that require time-consuming mathematical manipulations. The reader then often loses sight of fundamental issues, leading to gaps in comprehension that widen as more advanced material is introduced. This book accordingly focuses exclusively on core material relevant to practical problem solving. Fine details of the subject can later be assimilated rapidly, effectively placing leaves on the branches formed by the underlying concepts.Mathematics and physics constitute the language of science. Hence, as with any spoken language, they must be learned through repetition and memorization. The central results and equations indicated in this book are therefore indicated by shaded text. These should be rederived, transcribed into a notebook or review cards with a summary of their derivation and memorized. Problems from any source should be solved in conjunction with this book; however, undertaking time-consuming problems without recourse to worked solutions that indicate optimal calculational procedures is not recommended.

Finally, we wish to thank our many inspiring teachers, whose numerous insights

guided our approach, in particular Paul Bamberg, Alan Blair, and Sam Treiman, and,

above all, our father and grandfather, George Yevick, whose boundless love of phys

ics inspired generations of students.

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