توابع نمایی، لگاریتمی و مثلثاتی واقعی برای فیزیکدانان

Real Exponential, Logarithmic, and Trigonometric Functions for Physicists builds on the author's previous books focused on mathematics for scientists. This new work presents a rigorous study of the underlying mathematical functions used in physics and provides its readers a deeper understanding for those studying and practicing the physical sciences. This in-depth Delivers a thorough introduction to the math behind commonly used functions in physics and other disciplines Provides readers with a strong foundation for developing analytic and problem-solving skills Applies real life examples to bring theory to life for science students Real Exponential, Logarithmic, and Trigonometric Functions for Physicists is a valuable guide for physics and math students, and is a concise text for instructors teaching in courses on number theory and other areas of the sciences where mathematics is needed. Cover Half Title Title Page Copyright Page Preface Acknowledgments Author Biography Table of Contents Chapter 1: Review of Logic, Set Theory, and Isomorphism 1.1 LOGIC 1.2 SET THEORY 1.3 ISOMORPHISM 1.4 EXAMPLES REFERENCES Chapter 2: Review of Natural Numbers and Integers 2.1 NOTATION 2.2 NATURAL NUMBERS 2.3 INTEGERS 2.4 EXAMPLES REFERENCE Chapter 3: Review of Rational Numbers 3.1 NOTATION 3.2 DEFINITION OF RATIONAL NUMBERS 3.3 PROPERTIES OF RATIONAL NUMBERS 3.4 ADDITION OF RATIONAL NUMBERS 3.5 MULTIPLICATION OF RATIONAL NUMBERS 3.6 EXPONENTIATION OF RATIONAL NUMBERS WITH INTEGER EXPONENTS 3.7 INEQUALITIES OF RATIONAL NUMBERS 3.8 ISOMORPHISM BETWEEN Q AND Z 3.9 EXAMPLES REFERENCE Chapter 4: Review of Real Numbers 4.1 NOTATION 4.2 DEFINITION OF REAL NUMBERS 4.3 PROPERTIES OF REAL NUMBERS 4.4 ADDITION OF REAL NUMBERS 4.5 MULTIPLICATION OF REAL NUMBERS 4.6 EXPONENTIATION OF REAL NUMBERS WITH INTEGER EXPONENTS 4.7 ROOT OF ORDER n 4.8 INEQUALITIES IN REAL NUMBERS 4.9 ISOMORPHISM BETWEEN R AND Q 4.10 EXAMPLES REFERENCE Chapter 5: Exponentiation of Real Numbers with Rational Number Exponents 5.1 NOTATION 5.2 INITIAL NOTES 5.3 ADDITIONAL PROPERTIES OF THE EXPONENTIATION OF NONEGATIVE REAL NUMBERS WITH INTEGER EXPONENTS 5.4 DEFINITION OF THE EXPONENTIATION OF REAL NUMBERS WITH RATIONAL NUMBER EXPONENTS 5.5 PROPERTIES OF THE EXPONENTIATION OF REAL NUMBERS WITH RATIONAL NUMBER EXPONENTS 5.6 EXAMPLES Chapter 6: Real Number Sequences and Limits 6.1 NOTATION 6.2 IRRATIONAL NUMBERS 6.3 CONVERGENT REAL NUMBER SEQUENCES 6.4 PROPERTIES OF LIMITS OF REAL SEQUENCES 6.5 EXAMPLES REFERENCE Chapter 7: Exponentiation of Real Numbers with Real Number Exponents 7.1 NOTATION 7.2 ADDITIONAL PROPERTIES OF CONVERGENT REAL SEQUENCES 7.3 DEFINITION OF THE EXPONENTIATION OF REAL NUMBERS WITH REAL NUMBER EXPONENTS 7.4 PROPERTIES OF THE EXPONENTIATION OF REAL NUMBERS WITH REAL NUMBER EXPONENTS 7.5 EXAMPLES Chapter 8: “e” and the Exponential Function 8.1 NOTATION 8.2 THE BINOMIAL THEOREM 8.3 GEOMETRIC SERIES 8.4 REAL SEQUENCES le(n) AND ge(n) 8.5 DEFINITION OF THE NUMBER “e” 8.6 DEFINITION OF THE EXPONENTIAL FUNCTION 8.7 PROPERTIES OF THE EXPONENTIAL FUNCTION 8.8 EXAMPLES Chapter 9: Logarithmic Functions and the Natural Logarithmic Function 9.1 NOTATION 9.2 DEFINITION OF LOGARITHMIC FUNCTIONS 9.3 PROPERTIES OF LOGARITHMIC FUNCTIONS 9.4 DEFINITION OF THE NATURAL LOGARITHMIC FUNCTION 9.5 PROPERTIES OF THE NATURAL LOGARITHMIC FUNCTION 9.6 EXAMPLES Chapter 10: Elements of Geometry 10.1 NOTATION 10.2 POINTS 10.3 GEOMETRIC FIGURES 10.4 PLANES 10.5 LINES 10.6 RAYS AND ANGLES 10.7 SEGMENTS 10.8 POLYGONS 10.9 EXAMPLES Chapter 11: Elements of Planar Geometry 11.1 NOTATION 11.2 TRIANGLES 11.3 PYTHAGORAS’ THEOREM 11.4 QUADRILATERALS 11.5 AREAS OF POLYGONS 11.6 CIRCLES, ˇ, AND RADIANS 11.7 AREA OF A CIRCLE 11.8 EXAMPLES Chapter 12: Elements of Analytic Planar Geometry 12.1 NOTATION 12.2 CARTESIAN COORDINATES 12.3 EQUATION OF A PLANAR GEOMETRIC FIGURE 12.4 EQUATIONS OF LINES 12.5 DISTANCE BETWEEN TWO POINTS IN CARTESIAN 12.6 EQUATION OF A CIRCLE 12.7 EXAMPLES REFERENCE Chapter 13: Trigonometric Functions 13.1 NOTATION 13.2 THE “TRIGONOMETRIC CIRCLE” 13.3 COSINE, SINE, AND TANGENT FUNCTIONS 13.4 RIGHT TRIANGLES AND TRIGONOMETRIC FUNCTIONS 13.5 SOME VALUES OF THE TRIGONOMETRIC FUNCTIONS 13.6 GENERAL PROPERTIES OF TRIGONOMETRIC FUNCTIONS 13.7 EXAMPLES Chapter 14: Trigonometric Functions of a Sum 14.1 NOTATION 14.2 COSINE AND SINE OF A SUM 14.3 TANGENT OF A SUM 14.4 EXAMPLES Appendix A.1 NOTES ON NOTATION A.2 INITIAL PROPERTIES A.3 ADDITIONAL PROPERTIES OF THE INTEGER NUMBER EXPONENTIATION (OF NON-NEGATIVE REAL NUMBERS) A.4 PROPERTIES OF REAL EXPONENTIATION WITH RATIONAL EXPONENTS A.5 PROPERTIES OF IRRATIONAL NUMBERS A.6 PROPERTIES OF REAL NUMBER SEQUENCES A.7 PROPERTIES OF LIMITS OF REAL SEQUENCES A.8 PROPERTIES OF REAL EXPONENTIATION WITH REAL EXPONENTS A.9 PROPERTIES OF “e” AND THE EXPONENTIAL FUNCTION A.10 PROPERTIES OF LOGARITHMIC FUNCTIONS A.11 PROPERTIES OF THE NATURAL LOGARITHMIC FUNCTION A.12 PROPERTIES OF POINTS AND GEOMETRIC FIGURES A.13 PROPERTIES OF PLANE GEOMETRIC FIGURES A.14 PROPERTIES OF ANALYTIC PLANAR GEOMETRY A.15 PROPERTIES OF TRIGONOMETRIC FUNCTIONS Index