Integrated Physics and Calculus, Volume 2

by Rex, Andrew; Jackson, Martin

• ISBN13: 9780201473971
• ISBN10: 0201473976
• Edition: 1st
• Format: Paperback
• Copyright: 2000-01-07
• Publisher: Addison-Wesley

Summary

This groundbreaking text combines the second and third semesters of calculus with the first and second semesters of calculus-based physics. Used successfully at the authors' school in a two-semester course, the text provides full integration of the math and physics. Through text and problems, the authors carefully develop the calculus so that it can be used in many physical applications. In turn, the physics provides examples for the development of the calculus concepts. As a result, students gain a full understanding of calculus and its relevance to physics.

Author Biography

Dr. Andrew Rex received his Ph.D. in Physics from the University of Virginia in 1982 after receiving an B.A. in Physics from Illinois Wesleyan University. At Virginia his research focused on experimental solid state physics. Since 1982 he has been a faculty member at the University of Puget Sound, and he currently holds the rank of Professor. His principal research interests have been in Mossbauer spectroscopy, the physics of sports, and Maxwell's demon and information theory. At the University of Puget Sound he has served as Director of the Pre-Engineering Program, Director of the university's Honors Program and Chair of the Physics Department.

Dr. Rex has published five books including Integrated Physics and Calculus, Vols. 1 and 2, Addison-Wesley 1999, and has written a number of scientific articles and papers. He is a member of the American Association of Physics Teachers, Phi Kappa Phi, Sigma Xi and Sigma Pi Sigma.

In 1994 he received a three-year grant from the U.S. Department of Education to develop a program that integrates freshman physics and calculus into a single course and to write a textbook for that course.

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Dr. Martin Jackson received his Ph.D. in Physics from the University of Oregon in 1990 after receiving a M.S. degree in Physics there in 1985 and a B.S. in Physics and Mathematics from the University of Puget Sound in 1984. He was named an Assistant Professor at the University of Puget Sound in 1990 in the Department of Mathematics and Computer Science and Associate Professor in 1996.

He has published scientific articles in the Journal of Differential Geometry, the American Journal of Physics, the Journal of Physics, the Journal of Mathematical Physics, and other publications.

In 1994 he and Dr. Andrew Rex received a three-year grant from the U.S. Department of Education to develop a program that integrates freshman physics and calculus into a single course and to write a textbook for that course.

Table of Contents

Functions and Vectors	1	(46)
Real Numbers, Scalars, and Vectors	1	(18)
Functions	19	(8)
Vector-Output Functions	27	(3)
Measurements, Dimensions, and SI Units	30	(8)
Mathematical Models in Physics	38	(1)
Problems	39	(8)
Derivatives and Their Applications in Kinematics	47	(46)
Limits and Continuity	47	(11)
Speed and Velocity in One-Dimensional Motion	58	(5)
Derivatives	63	(11)
Higher-Order Derivatives and Acceleration	74	(4)
Calculus of Vector-Output Functions	78	(7)
Problems	85	(8)
Definite Integrals and Antiderivatives	93	(42)
The Definite Integral	93	(9)
The Antiderivative	102	(7)
The Fundamental Theorems of Calculus	109	(5)
Applications to Kinematics---One Dimension	114	(5)
One-Dimensional Motion with Constant Acceleration	119	(5)
Applications to Kinematics---Two and Three Dimensions	124	(2)
Problems	126	(9)
Kinematics and Curves in Two and Three Dimensions	135	(30)
Examples of Kinematics in Two and Three Dimensions	135	(10)
Tangent and Principal Normal Vectors	145	(5)
Curvature	150	(8)
The Length of a Curve	158	(1)
Problems	159	(6)
Newton's Laws of Motion	165	(28)
Newton's Laws of Motion	165	(6)
Applications of Newton's Second Law	171	(16)
Newton's Second Law with Forces Varying in Time	187	(2)
Problems	189	(4)
Differential Equations	193	(30)
Introduction to Differential Equations	193	(5)
Analyzing First-Order Differential Equations	198	(10)
More Applications of Newton's Second Law	208	(5)
Further Applications of Differential Equations in Physics	213	(5)
Problems	218	(5)
Work and Line Integrals	223	(50)
Work in One-Dimensional Motion	223	(8)
Work and the Dot Product	231	(5)
Line Integrals and Work Done by a Variable Force in Three Dimensions	236	(6)
Power	242	(3)
Energy	245	(13)
The Relationship Between Force and Energy in One-Dimensional Motion	258	(6)
Problems	264	(9)
Evaluating Definite and Indefinite Integrals	273	(34)
Symbolic Methods of Finding Antiderivatives	274	(8)
Bounds on a Function	282	(5)
Numerical Approximation of a Definite Integral from Data	287	(3)
Numerical Approximation of Definite Integrals	290	(11)
Problems	301	(6)
Systems of Particles, Momentum, and Collisions	307	(28)
Center of Mass	307	(5)
Momentum	312	(4)
Collisions in One Dimension	316	(3)
Collisions in Two Dimensions	319	(5)
Center-of-Mass Motion in Collisions	324	(3)
The Rocket Problem	327	(3)
Problems	330	(5)
Rotational Motion and the Cross Product	335	(42)
Kinematics of Rotational Motion	335	(7)
Rotational Dynamics	342	(8)
Angular Momentum	350	(2)
Rolling Bodies	352	(5)
The Cross Product	357	(7)
Rotational Dynamics in Vector Form	364	(4)
Power, Work, and Energy	368	(2)
Problems	370	(7)
Sequences and Series	377	(32)
Introduction to Sequences	377	(6)
Sequences	383	(4)
Introduction to Series	387	(5)
Convergence Arguments for Series	392	(5)
Power Series	397	(2)
Taylor Series	399	(6)
Problems	405	(4)
Oscillations and Second-Order Differential Equations	409	(38)
The Simple Harmonic Oscillator	409	(9)
State-space and Systems of First-Order Differential Equations	418	(7)
The Simple Pendulum	425	(6)
Damped Harmonic Motion	431	(5)
Harmonic Motion, Equilibrium, and the Generalized Potential Energy	436	(1)
The Physical Pendulum	437	(3)
Problems	440	(7)
Functions of More Than One Variable	447	(30)
Describing Planes in Space	447	(4)
Functions of Two Variables	451	(7)
Examples of Surfaces	458	(6)
Functions of Three Variables	464	(2)
Limits and Continuity	466	(5)
Problems	471	(6)
Multiple Integrals	477	(44)
Double Integrals	477	(10)
Double Integrals Over Other Regions	487	(8)
Triple Integrals	495	(12)
Applications of Multiple Integrals in Physics	507	(8)
Problems	515	(6)
Gravitation	521	(30)
Background and History	521	(2)
Kepler's Laws of Planetary Motion	523	(3)
Newton's Law of Gravitation	526	(5)
Gravitational Potential Energy	531	(3)
The Gravitational Force Due to a Spherically Symmetric Body	534	(4)
More on Earth, the Planets, and Satellites	538	(6)
The Constant G and Fundamental Forces	544	(1)
Problems	545	(6)
Electric Charges and Forces	551	(20)
Introduction to Electric Charge	551	(2)
Coulomb's Law	553	(5)
Forces Due to Multiple or Extended Charges	558	(10)
Problems	568	(3)
Vector Fields and Electric Fields	571	(32)
Introduction to Vector Fields	571	(7)
Electric Fields	578	(14)
The Motion of Charged Particles in an Electric Field	592	(7)
Problems	599	(4)
Partial Derivatives, Gradients, and Electric Potential	603	(52)
Partial Derivatives	603	(7)
Tangent Planes and Linear Approximations	610	(4)
Gradient and Directional Derivative	614	(8)
Electric Potential	622	(11)
Electric Potential and Electric Fields	633	(3)
Calculating Electric Potentials	636	(7)
Higher-Order Partial Derivatives	643	(4)
Problems	647	(8)
Capacitors, Dielectrics, and Electric Current	655	(32)
Capacitors	655	(12)
Dielectrics	667	(3)
Electric Current	670	(9)
Conductors, Insulators, Semiconductors, and Superconductors	679	(2)
Problems	681	(6)
Optimization	687	(20)
Optimization for Functions of One Variable---Review	687	(4)
Local Extrema for Functions of Several Variables	691	(3)
A Second Derivative Test	694	(4)
Global Extrema	698	(2)
Constrained Optimization	700	(3)
Problems	703	(4)
dc Circuits	707	(30)
Batteries: Real and Ideal	707	(4)
Series and Parallel Combinations of Resistors	711	(8)
Multiloop Circuits	719	(3)
Measuring Instruments	722	(2)
RC Circuits	724	(8)
Problems	732	(5)
Line Integrals	737	(18)
Curves	737	(3)
Line Integrals	740	(5)
The Fundamental Theorem of Calculus for Line Integrals	745	(3)
The Normal Line Integral	748	(3)
Problems	751	(4)
Gauss's Law and Surface Integrals	755	(32)
Gauss's Law	755	(18)
Surfaces	773	(6)
Surface Integrals	779	(4)
Problems	783	(4)
Magnetic Fields I	787	(30)
Background and History	787	(2)
The Magnetic Force on an Electric Charge	789	(10)
The Force on a Current-Carrying Conductor	799	(4)
Current Loops and Magnetic Dipoles in Magnetic Fields	803	(6)
The Hall Effect	809	(3)
Problems	812	(5)
Magnetic Fields II; Divergence and Curl	817	(42)
The Biot-Savart Law	818	(5)
Ampere's Law	823	(6)
Parallel Current-Carrying Wires	829	(2)
Maxwell's Displacement Current	831	(3)
Magnetism in Matter	834	(4)
Divergence	838	(7)
Curl	845	(5)
Problems	850	(9)
Faraday's Law and Inductance	859	(38)
Faraday's Law	859	(14)
Inductance	873	(17)
Problems	890	(7)
Vector Calculus and Maxwell's Equations	897	(40)
Vector Calculus in the Plane	897	(8)
Vector Calculus in Space	905	(7)
Maxwell's Equations	912	(5)
Electromagnetic Waves	917	(10)
Electromagnetism, Relativity, and Quantum Physics	927	(4)
Problems	931	(6)
The Bohr Atom	937	(1)
Background: Early Theories and Experiments	937	(2)
The Bohr Model	939	(7)
Experimental Verification	946	(6)
The Bohr Model in Perspective	952	(2)
Problems	954	(1)
Appendices	A-1
A Mathematics	A-1
B The International System of Units (SI)	A-6
C Conversion Factors	A-8
D The Elements	A-11
E Astrophysical Data	A-14
F A Brief Table of Integrals	A-15
Answers to Selected Odd-Numbered Problems	AN-1
Index	I-1