So You Want to Take Physics: A Preparatory Course / Edition 1

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Overview

This introductory-level book covers numerous physical principles and is ideal for strengthening mathematical skills essential to the study of physics.
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Product Details

  • ISBN-13: 9780030960208
  • Publisher: Saunders College Publishing
  • Publication date: 10/28/1992
  • Edition number: 1
  • Pages: 304
  • Product dimensions: 8.08 (w) x 10.01 (h) x 0.74 (d)

Table of Contents

1 Keeping It in the Ballpark 1
1.1 Studying Physics 1
1.2 Scientific Notation and Significant Figures 3
1.3 Units 6
1.4 The Ballpark and the Back-of-the-Envelope 9
1.5 Word Problems! 14
2 A Visit to Lineland 23
2.1 Position and Velocity 23
2.2 The Velocity as the Slope of the Position-Time Graph 25
2.3 Acceleration 27
2.4 The Acceleration as the Curvature of the Position-Time Graph 32
2.5 Gravity 37
3 Those Special Functions 47
3.1 The Exponential Function and the Number e 47
3.2 Exponential Decay and Terminal Speed 53
3.3 Logarithms 57
3.4 Log, Semi-Log, and Log-Log Graphs 61
3.5 Circular Symmetry and Arc Length 68
3.6 Angular Kinematics 70
3.7 Circular Functions 73
4 Elements of Differential Calculus and Linear Approximation 83
4.1 The Instantaneous Velocity and the Derivative 83
4.2 Maxima, Minima, and Curvature 86
4.3 Definition of the Differential and the Chain Rule 91
4.4 Expansion Parameters and the Binomial Theorem 94
4.5 Approximations for Trigonometric Functions 99
4.6 Differential Approximation 101
5 Approximation, Probability, and Error 107
5.1 Probability 107
5.2 Error in Experiment: Types of Error 112
5.3 Random Error and Best Estimation 116
5.4 Standard Deviation 117
5.5 Error Propagation and Predicted Values 121
5.6 Using Graphs 125
6 Return to Lineland 131
6.1 The Integral 131
6.2 The Definite Integral 134
6.3 Kinematics: The Rules of Motion 138
6.4 A Bead on a Wire 140
6.5 Integrating and Differentiating Visually with a Bead on a Wire 142
6.6 Integrating and Differentiating Pathological Functions 149
6.7 When to Integrate, An Application to Density 150
7 Vectors, Displacement, and Velocity 159
7.1 Dimension 159
7.2 Vectors: Position and Displacement 161
7.3 Vector Algebra 166
Resolving a Vector into Cartesian Components 166
Vector Addition 169
7.4 Displacement, Velocity, and Acceleration 176
7.5 Cartesian Displacements in Three Dimensions 179
7.6 Velocity Addition and Reference Frames 181
8 Life on a Sphere 191
8.1 Traveling in Circles 191
8.2 Spherical Polar Coordinates 198
8.3 Life on a Sphere, Longitude, and Latitude 200
8.4 Area, Volume, and Solid Angle: Elements of Symmetry 205
8.5 Using Area and Volume Elements 212
9 Force 223
9.1 Newton's Laws and Dynamics 223
9.2 The First Law 224
9.3 The Second Law 226
9.4 The Third Law 234
10 Vector Multiplication 243
10.1 Multiplication of a Vector by a Scalar 243
10.2 The Scalar Product or Dot Product 244
10.3 The Vector Product or Cross Product 249
10.4 Work and Kinetic Energy 253
10.5 Directed Surface Area, Flux, and Volume 256
11 Visualizing Functions in Space and Time 265
11.1 The Superposition of Functions 265
11.2 Two-Dimensional Maps 267
11.3 Superposition and Harmonic Functions: Phase 277
11.4 Traveling Waves and Phase Velocity 282
11.5 Time Averages and RMS Values 285
11.6 The Final Word (Really) 288
Appendix A 293
Appendix B 297
Index 321
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