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El. knyga: Classical Mechanics with Maxima

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This book guides undergraduate students in the use of Maxima—a computer algebra system—in solving problems in classical mechanics. It functions well as a supplement to a typical classical mechanics textbook. When it comes to problems that are too difficult to solve by hand, computer algebra systems that can perform symbolic mathematical manipulations are a valuable tool.Maxima is particularly attractive in that it is open-source, multiple-platform software that students can download and install free of charge. Lessons learned and capabilities developed usingMaxima are easily transferred to other, proprietary software.
1 Basic Newtonian Physics with Maxima
1(24)
1.1 Introduction to Maxima
1(2)
1.1.1 Computer Algebra Systems
1(1)
1.1.2 Installing Maxima
2(1)
1.2 Interacting with Maxima
3(3)
1.2.1 The wxMaxima Screen
5(1)
1.3 Maxima as a Calculator
6(3)
1.3.1 Data Types
7(1)
1.3.2 Mathematical Functions
7(2)
1.4 1D Kinematics: Variables and Functions
9(2)
1.5 2D Kinematics: Vectors
11(1)
1.6 Projectile Motion: Solving Equations
12(1)
1.7 Position, Velocity, and Acceleration: Calculus
13(2)
1.8 Newton's Second Law: Solving ODEs
15(1)
1.9 Range of a Projectile: Root Finding
16(3)
1.10 Visualizing Motion in Maxima
19(2)
1.11 Exercises
21(4)
2 Newtonian Mechanics
25(32)
2.1 Statics
25(4)
2.2 Constant Forces: Block on a Wedge
29(3)
2.3 Velocity-Dependent Forces: Air Resistance
32(16)
2.3.1 Models of Air Resistance
32(2)
2.3.2 Falling with Linear Resistance
34(3)
2.3.3 Projectile Motion with Linear Resistance
37(2)
2.3.4 Falling with Quadratic Resistance
39(4)
2.3.5 Projectile Motion with Quadratic Resistance
43(5)
2.4 Charged Particles in an Electromagnetic Field
48(6)
2.5 Exercises
54(3)
3 Momentum and Energy
57(28)
3.1 Collisions: Conservation of Momentum
57(5)
3.2 Rockets
62(5)
3.3 Center of Mass
67(3)
3.4 Torque and Angular Momentum
70(2)
3.5 Products and Moments of Inertia
72(3)
3.6 Work and Potential Energy
75(3)
3.7 Fall from a Great Height: Conservation of Energy
78(5)
3.8 Exercises
83(2)
4 Oscillations
85(40)
4.1 Stable and Unstable Equilibrium Points
85(4)
4.2 Simple Harmonic Motion
89(3)
4.3 Two-Dimensional Harmonic Oscillator
92(5)
4.4 Damped Harmonic Oscillator
97(5)
4.4.1 Underdamped Oscillators
98(1)
4.4.2 Overdamped Oscillators
99(2)
4.4.3 Critical Damping
101(1)
4.5 Driven Damped Harmonic Oscillator
102(6)
4.6 Non-sinusoidal Driving Forces
108(7)
4.7 The Pendulum
115(7)
4.8 Exercises
122(3)
5 Physics and Computation
125(40)
5.1 Programming: Loops and Decision Structures
125(5)
5.1.1 Loops
126(3)
5.1.2 Decision Structures
129(1)
5.2 Random Numbers and Random Walks
130(8)
5.2.1 Approximating π
131(1)
5.2.2 Evolution of an Ensemble
132(2)
5.2.3 A Random Walk
134(3)
5.2.4 Nonuniform Distributions
137(1)
5.3 Iterated Maps and the Newton--Raphson Method
138(8)
5.3.1 Iterated Functions and Attractors
140(2)
5.3.2 The Newton--Raphson Method
142(4)
5.4 Liouville's Theorem and Ordinary Differential Equation Solvers
146(14)
5.4.1 The Euler Algorithm
147(8)
5.4.2 The Euler--Cromer Algorithm
155(4)
5.4.3 Comparing Algorithms
159(1)
5.5 Exercises
160(5)
6 Nonlinearity and Chaos
165(56)
6.1 Nonlinear Dynamics
165(1)
6.2 The van der Pol Oscillator
166(9)
6.2.1 The Undriven Case
166(4)
6.2.2 The Driven Case
170(5)
6.3 The Driven Damped Pendulum
175(17)
6.3.1 Solving the Driven Damped Pendulum
175(3)
6.3.2 Period Doubling
178(4)
6.3.3 Rolling Motion
182(4)
6.3.4 Chaos
186(6)
6.4 Maps and Chaos
192(15)
6.4.1 The Logistic Map
192(7)
6.4.2 Bifurcation Diagrams
199(2)
6.4.3 Diverging Trajectories
201(2)
6.4.4 Lyapunov Exponents
203(4)
6.5 Fixed Points, Stability, and Chaos
207(11)
6.5.1 Stability of Fixed Points
207(2)
6.5.2 Fixed Points of the Logistic Map
209(2)
6.5.3 Stability of Periodic Points
211(2)
6.5.4 Graphical Analysis of Fixed Points
213(5)
6.6 Exercises
218(3)
A Numerical Methods
221(34)
A.1 The Bisection Method
221(2)
A.2 Numerical Integration
223(12)
A.2.1 Rectangular Approximation
225(3)
A.2.2 Trapezoidal Approximation and Simpson's Rule
228(2)
A.2.3 Monte Carlo Methods
230(2)
A.2.4 Built-in Routines
232(3)
A.3 Runge--Kutta Algorithms
235(8)
A.4 Modeling Data
243(7)
A.4.1 Interpolation
244(4)
A.4.2 Curve Fitting
248(2)
A.5 Exercises
250(5)
Index 255
Todd Keene Timberlake is a Professor of Physics & Astronomy at Berry College in Mount Berry, GA. He received his Ph.D. in Physics from the University of Texas at Austin in 2001. He has published several articles on using computers to teach physics and astronomy in the American Journal of Physics and The Physics Teacher.

J. Wilson Mixon is Dana Professor of Economics Emeritus at Berry college. Over 70 of his articles have appeared in refereed economics journals. They continue to be downloaded in significant numbers. He maintains a web site that contains a large amount of Excel-based analysis of economic principles. In the past three years, over 27,000 have visited the site.
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