I wrote this book for Japanese high school student for the reason of understanding mathematical background. However, this book may become one introduction to mathematical physics for other countries. So I translate this book. This book starts from set theory in section 1, because set theory is the fundamental part of mathematics. Then I explain differentiation of elementary function in section 2. Then I show Taylor expansion in section 3. The Taylor expansion is used as approximation. In section 4, I explain inverse trigonometric function simply. The inverse of the trigonometric function is used in the dynamics of springs and to understand energy conservation low. Then I explain outer product simply (in Japan we teach moment as a scorer for high school student. ) . In section 6, I explain elementary ordinary differential equation e.g. the dynamics under the homogeneous gravity and springs. In section 7, I explain the simple wave equation and elementary partial differential equation. In section 8, I explain Maxwell’s equations and vector analysis. And in section 9, I explain thermodynamics simply.
For the translation of this book from Japanese to English, I use Para
Japan Corporation. Equation are embedded as jpg format. To enlarge equations, double click equations.