ARFKEN 수리물리학, Mathematical methods for physicists 7ed, PDF

ARFKEN 수리물리학, Mathematical methods for physicists 7ed, PDF

mathematicalmethodsf.pdf

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PREFACE ........................................................................................................................................... XI 1. MATHEMATICAL PRELIMINARIES ...................................................................................................... 1 1.1. Infinite Series .................................................................................................................. 1 1.2. Series of Functions ....................................................................................................... 21 1.3. Binomial Theorem ........................................................................................................ 33 1.4. Mathematical Induction ............................................................................................... 40 1.5. Operations of Series Expansions of Functions .............................................................. 41 1.6. Some Important Series ................................................................................................. 45 1.7. Vectors ......................................................................................................................... 46 1.8. Complex Numbers and Functions ................................................................................. 53 1.9. Derivatives and Extrema .............................................................................................. 62 1.10. Evaluation of Integrals ................................................................................................. 65 1.11. Dirac Delta Functions ................................................................................................... 75 Additional Readings .................................................................................................... 82 2. DETERMINANTS AND MATRICES .................................................................................................... 83 2.1 Determinants ............................................................................................................... 83 2.2 Matrices ....................................................................................................................... 95 Additional Readings .................................................................................................. 121 3. VECTOR ANALYSIS .................................................................................................................... 123 3.1 Review of Basics Properties ........................................................................................ 124 3.2 Vector in 3 ‐ D Spaces ................................................................................................. 126 3.3 Coordinate Transformations ...................................................................................... 133 vi 3.4 Rotations in 3 ........................................................................................................ 139 3.5 Differential Vector Operators ..................................................................................... 143 3.6 Differential Vector Operators: Further Properties ...................................................... 153 3.7 Vector Integrations .................................................................................................... 159 3.8 Integral Theorems ...................................................................................................... 164

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