Physics for scientists and engineers : an interactive approach

Description

Physics for Scientists and Engineers: An Interactive Approach by Robert Lewis Hawkes, Javed Iqbal, Firas Mansour, Marina Milner-Bolotin, Peter J. Williams Physics is all around us. From taking a walk to driving your car, from microscopic processes to the enormity of space, and in the everchanging technology of our modern world, we encounter physics daily. As physics is a subject we are constantly immersed in and is used to forge tomorrow’s most exciting discoveries, our goal is to remove the intimidation factor of physics and replace it with a sense of curiosity and wonder. Physics for Scientists and Engineers takes this approach using inspirational examples and applications to bring physics to life in the most relevant and real ways for its students. The text is written with Canadian students and instructors in mind and is informed by Physics Education Research (PER) with international context and examples. Physics for Scientists and Engineers gives students unparalleled practice opportunities and digital support to foster student comprehension and success. Cover......Page 1 Brief Table of Contents......Page 7 Table of Contents......Page 9 Preface......Page 18 About the Authors......Page 27 Text Walkthrough......Page 29 Chapter 1: Introduction to Physics......Page 35 1-1 What Is Physics?......Page 36 1-2 Experiments, Measurement, and Uncertainties......Page 41 1-3 Mean, Standard Deviation, and SDOM......Page 43 1-4 Significant Digits......Page 46 1-5 Scientific Notation......Page 48 1-6 SI Units......Page 49 1-7 Dimensional Analysis......Page 51 1-8 Unit Conversion......Page 53 1-9 Approximations in Physics......Page 54 1-10 Fermi Problems......Page 55 Key Terms......Page 58 Problems by Section......Page 59 Comprehensive Problems......Page 62 Data-Rich Problem......Page 63 Open Problems......Page 64 Chapter 2: Scalars and Vectors......Page 65 2-1 Definitions of Scalars and Vectors......Page 66 2-2 Vector Addition: Geometric and Algebraic Approaches......Page 68 2-3 Cartesian Vector Notation......Page 73 2-4 The Dot Product of Two Vectors......Page 76 2-5 The Cross Product of Vectors......Page 79 Key Concepts and Relationships......Page 82 Key Terms......Page 83 Problems by Section......Page 84 Comprehensive Problems......Page 86 Chapter 3: Motion in One Dimension......Page 89 3-1 Distance and Displacement......Page 90 3-2 Speed and Velocity......Page 93 3-3 Acceleration......Page 100 3-4 Mathematical Description of One-Dimensional Motion with Constant Acceleration......Page 106 3-5 Analyzing the Relationships between x (t), y (t), and a (t) Plots......Page 110 3-6 Free Fall......Page 116 3-7 Relative Motion in One Dimension......Page 121 3-8 Calculus of Kinematics......Page 124 Key Concepts and Relationships......Page 127 Key Terms......Page 128 Problems by Section......Page 132 Comprehensive Problems......Page 139 Open Problems......Page 142 Chapter 4: Motion in Two and Three Dimensions......Page 145 4-1 Position, Velocity, and Acceleration......Page 146 4-2 Projectile Motion......Page 149 4-3 Circular Motion......Page 158 4-4 Relative Motion in Two and Three Dimensions......Page 162 Key Concepts and Relationships......Page 166 Key Terms......Page 167 Problems by Section......Page 169 Comprehensive Problems......Page 171 Data-Rich Problem......Page 174 Chapter 5: Forces and Motion......Page 175 5-1 Dynamics and Forces......Page 176 5-2 Mass and the Force of Gravity......Page 177 5-3 Newton's Laws of Motion......Page 180 5-4 Applying Newton's Laws......Page 185 5-5 Component-Free Solutions......Page 195 5-6 Friction......Page 196 5-7 Spring Forces and Hooke's Law......Page 202 5-8 Fundamental and Non-Fundamental Forces......Page 205 5-9 Uniform Circular Motion......Page 206 5-10 Reference Frames and Fictitious Forces......Page 210 5-11 Momentum and Newton's Second Law......Page 212 Key Concepts and Relationships......Page 214 Key Terms......Page 215 Problems by Section......Page 218 Comprehensive Problems......Page 222 Open Problem......Page 224 Chapter 6: Work and Energy......Page 225 6-1 What Is Energy?......Page 226 6-2 Work Done by a Constant Force in One Dimension......Page 227 6-3 Work Done by a Constant Force in Two and Three Dimensions......Page 228 6-4 Work Done by Variable Forces......Page 232 6-5 Kinetic Energy-The Work-Energy Theorem......Page 236 6-6 Conservative Forces and Potential Energy......Page 243 6-7 Conservation of Mechanical Energy......Page 246 6-8 Force from Potential Energy......Page 251 6-9 Power......Page 254 Key Concepts and Relationships......Page 255 Key Terms......Page 256 Problems by Section......Page 258 Comprehensive Problems......Page 262 Open Problem......Page 266 Chapter 7: Linear Momentum, Collisions, and Systems of Particles......Page 267 7-1 Linear Momentum......Page 268 7-2 Rate of Change of Linear Momentum and Newton's Laws......Page 270 7-3 Impulse......Page 271 7-4 Systems of Particles and Centre of Mass......Page 275 7-5 Systems of Particles and Conservation of Momentum......Page 278 7-6 Collisions......Page 281 7-7 Variable Mass and Rocket Propulsion......Page 287 Key Concepts and Relationships......Page 290 Key Terms......Page 291 Problems by Section......Page 293 Comprehensive Problems......Page 295 Open Problem......Page 297 Chapter 8: Rotational Kinematics and Dynamics......Page 299 8-1 Angular Variables......Page 300 8-2 Kinematic Equations for Rotation......Page 302 8-3 Torque......Page 304 8-4 Moment of Inertia of a Point Mass......Page 311 8-5 Systems of Particles and Rigid Bodies......Page 313 8-6 Rotational Kinetic Energy and Work......Page 321 8-7 Angular Momentum......Page 326 Key Concepts and Relationships......Page 333 Key Terms......Page 334 Problems by Section......Page 336 Comprehensive Problems......Page 339 Data-Rich Problem......Page 343 Open Problems......Page 344 Chapter 9: Rolling Motion......Page 345 9-1 Rolling and Slipping......Page 346 9-2 Relationships between Rotation and Translation for a Rolling Object......Page 347 9-3 Rolling Motion: Two Perspectives......Page 348 9-4 Newton's Second Law and Rolling......Page 350 9-5 Mechanical Energy and Rolling......Page 354 9-6 Rolling without Friction......Page 361 9-7 Rolling Friction......Page 363 Key Concepts and Relationships......Page 364 Key Terms......Page 365 Problems by Section......Page 366 Comprehensive Problems......Page 370 Data-Rich Problems......Page 374 Open Problems......Page 375 Chapter 10: Equilibrium and Elasticity......Page 379 10-1 The Conditions for Equilibrium......Page 380 10-2 Centre of Gravity......Page 382 10-3 Applying the Conditions for Equilibrium......Page 385 10-4 Applying the Conditions for Equilibrium: Working with Unknown Forces......Page 392 10-5 Deformation and Elasticity......Page 397 10-6 Ductile and Brittle Materials......Page 400 Key Concepts and Relationships......Page 404 Key Terms......Page 405 Problems by Section......Page 406 Comprehensive Problems......Page 411 Open Problem......Page 416 Chapter 11: Gravitation......Page 417 11-1 Universal Gravitation......Page 418 11-2 Acceleration Due to Gravity......Page 421 11-3 Orbits and Weightlessness......Page 423 11-4 Gravitational Potential Energy......Page 426 11-5 Force from Potential Energy......Page 429 11-6 Escape Speed......Page 430 11-7 Kepler's Laws......Page 431 11-8 Types of Orbits......Page 437 11-9 Detection of Exoplanets......Page 441 Key Terms......Page 445 Questions......Page 446 Problems by Section......Page 447 Comprehensive Problems......Page 450 Open Problems......Page 452 Chapter 12: Fluids......Page 455 12-1 Phases of Matter......Page 456 12-2 Density and Pressure......Page 457 12-3 Pressure in Fluids......Page 460 12-4 Pascal's Principle......Page 466 12-5 Buoyancy and Archimedes' Principle......Page 468 12-6 Fluids in Motion......Page 473 12-7 The Continuity Equation: Conservation of Fluid Mass......Page 475 12-8 Conservation of Energy for Moving Fluids......Page 477 12-9 Conservation of Fluid Momentum......Page 483 12-10 Viscous Flow......Page 485 Key Concepts and Relationships......Page 490 Key Terms......Page 491 Problems by Section......Page 492 Comprehensive Problems......Page 497 Chapter 13: Oscillations......Page 499 13-1 Periodic Motion......Page 500 13-2 Simple Harmonic Motion......Page 501 13-3 Uniform Circular Motion and Simple Harmonic Motion......Page 506 13-4 Mass-Spring Systems......Page 507 13-5 Energy Conservation in Simple Harmonic Motion......Page 510 13-6 The Simple Pendulum......Page 513 13-7 The Physical Pendulum......Page 515 13-8 Time Plots for Simple Harmonic Motion......Page 518 13-9 Damped Oscillations......Page 521 13-10 Resonance and Driven Harmonic Oscillators......Page 526 13-11 Simple Harmonic Motion and Differential Equations (Optional Section)......Page 528 Key Concepts and Relationships......Page 530 Key Terms......Page 532 Problems by Section......Page 533 Comprehensive Problems......Page 539 Chapter 14: Waves......Page 541 14-1 The Nature, Properties, and Classification of Waves......Page 542 14-2 The Motion of a Disturbance in a String......Page 545 14-3 Equation for a Pulse Moving in One Dimension......Page 546 14-4 Transverse Speed and Wave Speed......Page 549 14-5 Harmonic Waves......Page 552 14-6 Position Plots and Time Plots......Page 559 14-7 Phase and Phase Difference......Page 562 14-8 Energy and Power in a Travelling Wave......Page 563 14-9 Superposition of Waves......Page 567 14-10 Interference of Waves Travelling in the Same Direction......Page 569 14-11 Reflection and Transmission of Mechanical Waves......Page 571 14-12 Standing Waves......Page 572 14-13 Standing Waves on Strings......Page 575 14-14 String Musical Instruments (Optional Section)......Page 577 14-15 The Wave Equation in One Dimension (Optional Section)......Page 581 Key Concepts and Relationships......Page 583 Key Terms......Page 584 Problems by Section......Page 585 Chapter 15: Sound and Interference......Page 595 15-1 Sound Waves......Page 596 15-2 Wave Propagation and Huygens' Principle......Page 600 15-3 Reflection and Refraction......Page 601 15-4 Standing Waves in Air Columns......Page 602 15-5 Interference......Page 606 15-6 Measuring Sound Levels......Page 611 15-7 The Doppler Effect......Page 615 Key Concepts and Relationships......Page 620 Problems by Section......Page 621 Comprehensive Problems......Page 623 Open Problem......Page 624 Chapter 16: Temperature and the Zeroth Law of Thermodynamics......Page 625 16-1 The Need for a Macroscopic Description......Page 626 16-3 State Variables......Page 627 16-4 Pressure......Page 628 16-5 Temperature and Thermal Expansion......Page 630 16-6 Thermometers and Temperature Scales......Page 632 16-8 Ideal Gases......Page 633 16-9 The Constant-Volume Gas Thermometer......Page 635 16-10 Temperature and Mechanical Energy......Page 636 16-11 Statistical Measures......Page 638 16-12 Phase Diagrams......Page 640 Key Terms......Page 641 Problems by Section......Page 642 Comprehensive Problems......Page 644 Open Problem......Page 645 Chapter 17: Heat, Work, and the First Law of Thermodynamics......Page 647 17-2 Temperature Changes Due to Heat Transfer......Page 648 17-3 The Flow of Heat between Objects......Page 650 17-4 Phase Changes and Latent Heat......Page 651 17-5 Changing the Internal Energy Via Work......Page 653 17-6 The First Law of Thermodynamics......Page 654 17-7 Different Types of Processes......Page 655 17-8 Energy Transfer Mechanisms......Page 659 Key Terms......Page 663 Problems by Section......Page 664 Comprehensive Problems......Page 665 Data-Rich Problem......Page 666 Open Problem......Page 667 Chapter 18: Heat Engines and the Second Law of Thermodynamics......Page 669 18-1 Heat Engines and Heat Pumps......Page 670 18-2 Efficiency and the Carnot Cycle......Page 672 18-3 Entropy......Page 676 18-4 Entropy and the Second Law of Thermodynamics......Page 677 18-5 The Domain of the Second Law of Thermodynamics......Page 679 18-6 Consequences of the Second Law of Thermodynamics......Page 680 18-7 A Microscopic Look at Entropy......Page 682 Key Concepts and Relationships......Page 684 Problems by Section......Page 685 Comprehensive Problems......Page 687 Open Problem......Page 689 Chapter 19: Electric Fields and Forces......Page 691 19-1 Electric Charge......Page 692 19-2 Charging by Electrical Induction......Page 694 19-3 Coulomb's Law......Page 696 19-4 Multiple Point Charges and the Superposition Principle......Page 699 19-5 Electrical Forces for Continuous Charge Distributions......Page 700 19-6 Electric Field......Page 705 19-7 Electric Fields and the Superposition Principle......Page 708 19-8 Electric Field Vectors and Lines......Page 709 19-9 Electric Fields from Continuous Charge Distributions......Page 712 19-10 Dielectrics and Dipoles......Page 714 19-11 Electric Field Essentials......Page 717 Key Concepts and Relationships......Page 718 Key Terms......Page 719 Problems by Section......Page 721 Comprehensive Problems......Page 723 Data-Rich Problems......Page 725 Open Problems......Page 726 Chapter 20: Gauss's Law......Page 727 20-1 Gauss's Law and Electric Field Lines......Page 728 20-2 Electric Flux......Page 729 20-3 Gauss's Law......Page 734 20-4 Strategy for Using Gauss's Law......Page 739 20-5 Gauss's Law for Cylindrical Symmetry......Page 742 20-6 Gauss's Law for Planar Symmetry......Page 745 20-7 Conductors and Electric Fields......Page 746 20-8 When Can Gauss’s Law Be Used to Find the Electric Field?......Page 751 20-9 Gauss's Law for Gravity......Page 755 Key Concepts and Relationships......Page 758 Key Terms......Page 759 Questions......Page 760 Problems by Section......Page 762 Comprehensive Problems......Page 765 Data-Rich Problems......Page 766 Open Problems......Page 767 Chapter 21: Electrical Potential Energy and Electric Potential......Page 769 21-1 Work and Electric Fields......Page 770 21-2 Electrical Potential Energy......Page 772 21-3 Electric Potential......Page 776 21-4 Equipotential Lines and Electric Field Lines......Page 779 21-5 Electric Potentials from Continuous Distributions of Charge......Page 780 21-6 The Electron Volt......Page 782 21-7 Calculating Electric Field from Electric Potential......Page 784 21-8 Electric Potentials and Fields for Conductors......Page 787 21-9 Electric Potential: Powerful Ideas......Page 791 Key Concepts and Relationships......Page 793 Key Terms......Page 794 Questions......Page 795 Problems by Section......Page 797 Comprehensive Problems......Page 800 Data-Rich Problems......Page 802 Open Problems......Page 804 Chapter 22: Capacitance......Page 807 22-1 Capacitors and Capacitance......Page 808 22-2 Electric Fields in Parallel-Plate Capacitors......Page 810 22-3 Calculating Capacitance......Page 815 22-4 Combining Capacitors......Page 817 22-5 Dielectrics and Capacitors......Page 819 22-6 Energy Storage in Capacitors......Page 821 22-7 Applications of Capacitors......Page 823 Key Terms......Page 827 Problems by Section......Page 829 Comprehensive Problems......Page 831 Data-Rich Problem......Page 833 Open Problems......Page 834 Chapter 23: Electric Current and Fundamentals of DC Circuits......Page 835 23-1 Electric Current: The Microscopic Model......Page 836 23-2 Electric Conductivity and Resistivity: The Microscopic Model......Page 839 23-3 Ohm's Law......Page 840 23-4 Series and Parallel Electric Circuits......Page 843 23-5 Analysis of DC Circuits and Kirchhoff's Laws......Page 848 23-6 RC Circuits......Page 859 Key Concepts and Relationships......Page 864 Key Terms......Page 865 Problems by Section......Page 867 Comprehensive Problems......Page 870 Open Problems......Page 872 Chapter 24: Magnetic Fields and Magnetic Forces......Page 873 24-1 Magnetic Field and Magnetic Force......Page 874 24-2 The Motion of a Charged Particle in a Uniform Magnetic Field......Page 879 24-3 Applications: Charged Particles Moving in a Uniform Magnetic Field......Page 882 24-4 The Magnetic Force on a Current-Carrying Wire......Page 889 24-5 The Torque on a Current-Carrying Loop in a Magnetic Field......Page 890 24-6 The Biot-Savart Law......Page 894 24-7 Ampere's Law......Page 899 24-8 The Magnetic Force between Two Parallel Current-Carrying Conductors......Page 907 24-9 The Magnetic Properties of Materials......Page 908 Key Concepts and Relationships......Page 912 Key Terms......Page 913 Problems by Section......Page 916 Comprehensive Problems......Page 920 Data-Rich Problems......Page 926 Chapter 25: Electromagnetic Induction......Page 927 25-1 In Faraday's Lab: Science in the Making......Page 928 25-2 Magnetic Flux and Its Rate of Change......Page 929 25-3 Faraday's Law of Electromagnetic Induction......Page 931 25-4 Induced emf and Induced Electric Fields......Page 939 25-5 Self-Inductance and Mutual Inductance......Page 941 25-6 Applications of Faraday's Law of Electromagnetic Induction......Page 945 25-7 RL Circuits......Page 950 25-8 Energy Stored in a Magnetic Field......Page 953 Key Concepts and Relationships......Page 956 Key Terms......Page 957 Problems by Section......Page 961 Comprehensive Problems......Page 964 Open Problem......Page 970 Chapter 26: Alternating Current Circuits......Page 971 26-1 Simple Loads in AC Circuits......Page 972 26-2 The LC Circuit......Page 976 26-3 Phasors......Page 977 26-4 Series RLC Circuits......Page 979 26-5 Resonance......Page 981 26-6 Power in AC Circuits......Page 983 Key Concepts and Relationships......Page 986 Key Terms......Page 987 Problems by Section......Page 988 Comprehensive Problems......Page 989 Open Problem......Page 990 Chapter 27: Electromagnetic Waves and Maxwell's Equations......Page 991 27-1 The Laws of Electric and Magnetic Fields......Page 992 27-2 Displacement Current and Maxwell's Equations......Page 993 27-3 Electromagnetic Waves......Page 996 27-4 The Electromagnetic Spectrum......Page 1001 27-5 The Energy and Momentum of Electromagnetic Waves......Page 1003 27-6 Radiation Pressure......Page 1006 27-7 How Are Electromagnetic Waves Generated?......Page 1008 27-8 Polarization......Page 1010 Key Concepts and Relationships......Page 1014 Problems by Section......Page 1015 Comprehensive Problems......Page 1019 Chapter 28: Geometric Optics......Page 1021 28-1 Evidence for the Geometric Optics Approach......Page 1022 28-2 Reflection of Light......Page 1025 28-3 Mirrors......Page 1027 28-4 Refraction of Light......Page 1035 28-5 Images Formed by Thin Lenses......Page 1040 28-6 The Human Eye and Vision Correction......Page 1047 28-7 Brewster's Angle......Page 1050 Key Concepts and Relationships......Page 1051 Key Terms......Page 1052 Questions......Page 1053 Problems by Section......Page 1054 Comprehensive Problems......Page 1057 Open Problem......Page 1060 Chapter 29: Physical Optics......Page 1061 29-2 Interference......Page 1062 29-3 Double-Slit Interference......Page 1066 29-4 Diffraction Gratings......Page 1068 29-5 Thin Film Interference......Page 1070 29-6 Single-Slit Diffraction......Page 1075 29-7 Actual Intensity Pattern for Double Slits......Page 1078 29-8 Resolution Limit......Page 1079 Key Concepts and Relationships......Page 1081 Key Terms......Page 1082 Problems by Section......Page 1085 Comprehensive Problems......Page 1088 Data-Rich Problem......Page 1089 Open Problem......Page 1090 Chapter 30: Relativity......Page 1091 30-2 Reference Frames and the Michelson-Morley Experiment......Page 1092 30-3 Postulates of Special Relativity and Time Dilation......Page 1094 30-4 Length Contraction......Page 1098 30-5 Lorentz Transformation......Page 1100 30-6 Spacetime......Page 1102 30-7 Relativistic Momentum and Energy......Page 1105 30-8 Relativistic Velocity Addition......Page 1109 30-9 Relativistic Doppler Shift......Page 1111 30-10 Gravitational Time Dilation in General Relativity......Page 1113 30-11 Relativity and the Global Positioning System......Page 1120 Key Concepts and Relationships......Page 1122 Key Terms......Page 1124 Problems by Section......Page 1126 Comprehensive Problems......Page 1128 Open Problem......Page 1131 Chapter 31: Fundamental Discoveries of Modern Physics......Page 1133 31-1 The Connection between Matter and Electricity......Page 1134 31-2 Temperature and the Emission of Light......Page 1135 31-3 Gas Discharge Spectra......Page 1136 31-4 Cathode Rays......Page 1138 31-5 The Millikan Oil Drop Experiment......Page 1140 31-6 Thomson's Model of the Atom......Page 1142 31-7 Rutherford Scattering......Page 1143 31-8 The Photoelectric Effect......Page 1145 31-9 The Bohr Model of the Atom......Page 1146 31-10 Compton Scattering......Page 1148 Key Concepts and Relationships......Page 1150 Key Terms......Page 1152 Comprehensive Problems......Page 1154 Open Problem......Page 1155 Chapter 32: Introduction to Quantum Mechanics......Page 1157 32-1 Matter Waves and de Broglie's Hypothesis......Page 1158 32-2 Heisenberg's Uncertainty Principle......Page 1161 32-3 The Schrodinger Equation......Page 1165 32-4 Solving the Time-Independent Schrodinger Equation......Page 1169 32-5 A Particle in a One-Dimensional Box......Page 1170 32-6 The Finite Square Well Potential......Page 1175 32-7 Quantum Tunnelling......Page 1178 32-8 The Quantization of Angular Momentum......Page 1182 32-9 The Schrodinger Equation for a Hydrogen Atom......Page 1183 32-10 Intrinsic Angular Momentum-Spin......Page 1187 Key Concepts and Relationships......Page 1192 Key Terms......Page 1193 Problems by Section......Page 1194 Chapter 33: Introduction to Solid-State Physics......Page 1197 33-1 Crystal Structures......Page 1198 33-2 Electrons in a Box......Page 1199 33-3 Periodic Potential......Page 1202 33-4 Metals and Insulators......Page 1203 33-5 Semiconductors......Page 1204 33-7 The pn Junction Diode......Page 1207 33-8 Other Semiconductor Devices......Page 1209 33-9 Nanotechnology......Page 1212 Key Concepts and Relationships......Page 1214 Key Terms......Page 1215 Problems by Section......Page 1216 Comprehensive Problems......Page 1218 Chapter 34: Introduction to Nuclear Physics......Page 1221 34-1 Nuclear Terminology and Nuclear Units......Page 1222 34-2 Nuclear Size and Nuclear Force......Page 1223 34-3 Nuclear Binding Energy......Page 1225 34-4 Nuclear Decay and Radioactivity......Page 1227 34-5 Nuclear Reactions......Page 1230 34-6 a, B and y Decays......Page 1232 34-7 Nuclear Stability......Page 1241 34-8 Nuclear Fission and Nuclear Fusion......Page 1244 34-9 Ionizing Radiation......Page 1250 34-10 Nuclear Medicine and Some Other Applications......Page 1252 Key Concepts and Relationships......Page 1255 Problems by Section......Page 1256 Comprehensive Problems......Page 1259 Chapter 35: Introduction to Particle Physics......Page 1261 35-1 Classification of Particles......Page 1262 35-2 Gauge Bosons......Page 1264 35-3 Antiparticles......Page 1266 35-4 Quarks and the Standard Model......Page 1267 35-5 Composite Particles......Page 1268 35-6 Colour Quantum Number and Quark Confinement......Page 1271 35-7 Conservation Laws......Page 1272 35-8 The Production and Decay of Particles......Page 1274 35-9 Feynman Diagrams......Page 1276 35-10 Pions and Muons......Page 1278 35-11 Particle Accelerators......Page 1279 35-12 Beyond the Standard Model......Page 1284 Key Concepts and Relationships......Page 1288 Key Terms......Page 1289 Problems by Section......Page 1290 Comprehensive Problems......Page 1292 Appendix A: Answers to Selected Questions......Page 1293 Appendix B: SI Units and Prefixes......Page 1317 Appendix C: Geometry and Trigonometry......Page 1319 Appendix D: Key Calculus Ideas......Page 1321 Appendix E: Useful Mathematical Formulas and Mathematical Symbols Used in the Text and Their Meaning......Page 1325 Appendix F: Periodic Table......Page 1329 Index......Page 1331