Interactive Engineering Physics with Numerical Methods

Timo Budarz, Sierra Brown, Aug 29, 2017

This is an open-source, comprehensive engineering physics textbook for the first three semesters of a degree in engineering, physics or chemistry. An emphasis is placed on fundamental principles as well as numerical solutions to equations where no analytical solution exists.

Table of Contents

  1. Introduction
    1. Introduction
    2. Precision and Accuracy
    3. Units
    4. Estimating Error
    5. PROBLEMS
    6. Lab Exercise
  2. Kinematics
    1. When Left Alone
    2. Position
    3. Velocity
    4. Acceleration
    5. PROBLEMS
    6. Lab Exercise
  3. Dynamics
    1. Background
    2. Fundamental Interactions
    3. Contact Interactions
    4. Application of Newton's Second Law
    5. Motion on an Incline
    6. Friction on Moving Surfaces
    7. GeoGebra Exercise - Universal Gravitation
    8. PROBLEMS
    9. Lab Exercise - Slope and Friction of a Cart
  4. Dynamics with Variable Forces
    1. Motivation
    2. Differential Equations of Motion
    3. Air Drag
    4. Free Fall with Drag
    5. Propulsion and Machines
    6. Vehicle Resistive Forces
    7. Fuel Economy
    8. Solving Differential Equations of Motion
    9. PROBLEMS
    10. Lab Exercise - Drag Coefficient Measurement
  5. Harmonic Motion
    1. Elasticity
    2. Hooke's Law
    3. Simple Harmonic Motion
    4. The Simple Pendulum
    5. Phase Space
    6. PROBLEMS
    7. Lab Exercise
  6. Circular Motion
    1. Introduction to Circular Motion
    2. Circular Motion Derivation
    3. Circular Orbits
    4. Some Examples
    5. PROBLEMS
  7. Effective Gravitation
    1. We Can't Feel Gravity
    2. Further Examples
    3. Earth's Effective Gravitation
    4. Coriolis Force
    5. PROBLEMS
  8. Work and Energy
    1. Kinetic Energy
    2. Work
    3. Parametric Path Integrals
    4. Simpler Cases
    5. Power
    6. PROBLEMS
  9. Potential Energy
    1. What you Already Know
    2. Potential Energy Defined
    3. Potential Energy for Universal Gravitation
    4. Energy Conservation
    5. Elastic Potential Energy
    6. Dissipative Forces
    7. PROBLEMS
  10. Collisions
    1. Momentum
    2. Momentum Conservation
    3. Center of Mass
    4. Coefficient of Restitution and Elasticity
    5. Relative Velocity
    6. Collisions
    7. Some Potential Simplifications
    8. PROBLEMS
  11. Rigid Body Motion
    1. Angular Kinematics
  12. Geometric Optics I
    1. Introduction
    2. Ray Tracing Basics
    3. Ray Tracing with Curved Mirrors
    4. Heiligenschein and Albedo
    5. Color
    6. PROBLEMS
    7. Lab Exercise
  13. Geometric Optics II
    1. Refraction
    2. Snell's Law
    3. Critical Angle
    4. Polarization
    5. Dispersion and Rainbows
    6. Thin Lenses
    7. Human Eye
    8. Fermat's Principle
    9. PROBLEMS
    10. Lab Exercises - Thin Lenses, Brewster's Law
    11. Lab Exercise - Crossed Polarizers
  14. Waves
    1. Waves
    2. PROBLEMS
  15. Interference
    1. Wave Interference
    2. Thin Films
    3. Young's Double Slit Experiment
    4. Multiple Slits
    5. PROBLEMS
  16. Diffraction
    1. Single Slit Diffraction
    2. Circular Apertures and Resolving Power
    3. Angular Resolution
    4. PROBLEMS
  17. Music and Resonance
    1. Resonance
    2. Resonant Frequencies
    3. Resonance In Musical Instruments
    4. The Musical Scale
    5. Standing Waves and Resonance
    6. String and Pipe Modes
    7. Doppler Effect
    8. PROBLEMS
    9. Lab Exercise
    10. Lab Exercise II
  18. Quantization and Waves
    1. Background
    2. The Field
    3. Quantization
    4. Blackbody Radiation
    5. Photoelectric Effect
    6. Light Quanta
    7. Is a Photon a Particle?
    8. What are Field Quanta?
    9. PROBLEMS
  19. Quantizing Nature: A first Approach
    1. Phase, Waves and "Particles"
    2. Wave Nature of "Particles"
    3. Wilson-Sommerfeld Quantization Condition
    4. Wilson-Sommerfeld Application: 1D Electron Wave
    5. Wilson-Sommerfeld Application: Atomic Structure
    6. PROBLEMS
  20. Quantum Mechanics
    1. Classical Wave Equation
    2. Schrödinger's Equation
    3. "Particle" in a 1D Box
    4. Quantum Tunneling
    5. Quantum Harmonic Oscillator
    6. PROBLEMS
    7. Wave Function Lab
  21. Special Relativity
    1. The Postulates
    2. Some Definitions
    3. Relativistic Velocity Addition
    4. Time Dilation
    5. Length Contraction
    6. Momentum and Energy
    7. Energy Momentum Relation
    8. PROBLEMS
  22. Heat Transfer
    1. Convection
    2. Conduction
    3. Thermal Radiation
    4. Evaporative Cooling
    5. The Effect of Scale
    6. PROBLEMS
  23. Fundamental Physics
    1. Breaking it Down
    2. Nuclear Structure
    3. Binding Energy
    4. Radioactive Decay
    5. Decay Schemes
    6. PROBLEMS
  24. Astrophysics and Cosmology
    1. Where are We?
    2. The Milky Way
    3. One
    4. Origins
    5. General Relativity and Expansion
    6. Numerical Solution to Friedmann Equation
  25. Answers to Problems
    1. Answers
    2. Interference
  26. Electric Charge
    1. Charge
    2. Net Charge
    3. The Coulomb Force
  27. Math Review
    1. Miscellaneous Comments
    2. Problems

1.

Introduction

Introduction and Motivation

  • 1. Introduction
  • 2. Precision and Accuracy
  • 3. Units
  • 4. Estimating Error
  • 5. PROBLEMS
  • 6. Lab Exercise

1.1.

–

1.2.

–

1.3.

–

1.4.

–

1.5.

–

1.6.

–

2.

Kinematics

  • 1. When Left Alone
  • 2. Position
  • 3. Velocity
  • 4. Acceleration
  • 5. PROBLEMS
  • 6. Lab Exercise

2.1.

–

2.2.

–

2.3.

–

2.4.

–

2.5.

–

2.6.

–

3.

Dynamics

  • 1. Background
  • 2. Fundamental Interactions
  • 3. Contact Interactions
  • 4. Application of Newton's Second Law
  • 5. Motion on an Incline
  • 6. Friction on Moving Surfaces
  • 7. GeoGebra Exercise - Universal Gravitation
  • 8. PROBLEMS
  • 9. Lab Exercise - Slope and Friction of a Cart

3.1.

–

3.2.

–

3.3.

–

3.4.

–

3.5.

–

3.6.

–

3.7.

–

3.8.

–

3.9.

–

4.

Dynamics with Variable Forces

  • 1. Motivation
  • 2. Differential Equations of Motion
  • 3. Air Drag
  • 4. Free Fall with Drag
  • 5. Propulsion and Machines
  • 6. Vehicle Resistive Forces
  • 7. Fuel Economy
  • 8. Solving Differential Equations of Motion
  • 9. PROBLEMS
  • 10. Lab Exercise - Drag Coefficient Measurement

4.1.

–

4.2.

–

4.3.

–

4.4.

–

4.5.

–

4.6.

–

4.7.

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4.8.

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4.9.

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4.10.

–

5.

Harmonic Motion

Springs, elasticity and the resulting harmonic motion are discussed in this chapter.

  • 1. Elasticity
  • 2. Hooke's Law
  • 3. Simple Harmonic Motion
  • 4. The Simple Pendulum
  • 5. Phase Space
  • 6. PROBLEMS
  • 7. Lab Exercise

5.1.

–

5.2.

–

5.3.

–

5.4.

–

5.5.

–

5.6.

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5.7.

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6.

Circular Motion

  • 1. Introduction to Circular Motion
  • 2. Circular Motion Derivation
  • 3. Circular Orbits
  • 4. Some Examples
  • 5. PROBLEMS

6.1.

–

6.2.

–

6.3.

–

6.4.

–

6.5.

–

7.

Effective Gravitation

  • 1. We Can't Feel Gravity
  • 2. Further Examples
  • 3. Earth's Effective Gravitation
  • 4. Coriolis Force
  • 5. PROBLEMS

7.1.

–

7.2.

–

7.3.

–

7.4.

–

7.5.

–

8.

Work and Energy

  • 1. Kinetic Energy
  • 2. Work
  • 3. Parametric Path Integrals
  • 4. Simpler Cases
  • 5. Power
  • 6. PROBLEMS

8.1.

–

8.2.

–

8.3.

–

8.4.

–

8.5.

–

8.6.

–

9.

Potential Energy

  • 1. What you Already Know
  • 2. Potential Energy Defined
  • 3. Potential Energy for Universal Gravitation
  • 4. Energy Conservation
  • 5. Elastic Potential Energy
  • 6. Dissipative Forces
  • 7. PROBLEMS

9.1.

–

9.2.

–

9.3.

–

9.4.

–

9.5.

–

9.6.

–

9.7.

–

10.

Collisions

  • 1. Momentum
  • 2. Momentum Conservation
  • 3. Center of Mass
  • 4. Coefficient of Restitution and Elasticity
  • 5. Relative Velocity
  • 6. Collisions
  • 7. Some Potential Simplifications
  • 8. PROBLEMS

10.1.

–

10.2.

–

10.3.

–

10.4.

–

10.5.

–

10.6.

–

10.7.

–

10.8.

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11.

Rigid Body Motion

  • 1. Angular Kinematics

11.1.

–

12.

Geometric Optics I

  • 1. Introduction
  • 2. Ray Tracing Basics
  • 3. Ray Tracing with Curved Mirrors
  • 4. Heiligenschein and Albedo
  • 5. Color
  • 6. PROBLEMS
  • 7. Lab Exercise

12.1.

–

12.2.

–

12.3.

–

12.4.

–

12.5.

–

12.6.

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12.7.

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13.

Geometric Optics II

  • 1. Refraction
  • 2. Snell's Law
  • 3. Critical Angle
  • 4. Polarization
  • 5. Dispersion and Rainbows
  • 6. Thin Lenses
  • 7. Human Eye
  • 8. Fermat's Principle
  • 9. PROBLEMS
  • 10. Lab Exercises - Thin Lenses, Brewster's Law
  • 11. Lab Exercise - Crossed Polarizers

13.1.

–

13.2.

–

13.3.

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13.4.

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13.5.

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13.6.

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13.7.

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13.8.

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13.9.

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13.10.

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13.11.

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14.

Waves

This chapter is an introduction to traveling waves and all the fun things that can occur when multiple waves meet.

  • 1. Waves
  • 2. PROBLEMS

14.1.

–

14.2.

–

15.

Interference

  • 1. Wave Interference
  • 2. Thin Films
  • 3. Young's Double Slit Experiment
  • 4. Multiple Slits
  • 5. PROBLEMS

15.1.

–

15.2.

–

15.3.

–

15.4.

–

15.5.

–

16.

Diffraction

  • 1. Single Slit Diffraction
  • 2. Circular Apertures and Resolving Power
  • 3. Angular Resolution
  • 4. PROBLEMS

16.1.

–

16.2.

–

16.3.

–

16.4.

–

17.

Music and Resonance

  • 1. Resonance
  • 2. Resonant Frequencies
  • 3. Resonance In Musical Instruments
  • 4. The Musical Scale
  • 5. Standing Waves and Resonance
  • 6. String and Pipe Modes
  • 7. Doppler Effect
  • 8. PROBLEMS
  • 9. Lab Exercise
  • 10. Lab Exercise II

17.1.

–

17.2.

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17.3.

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17.4.

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17.5.

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17.6.

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17.7.

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17.8.

–

17.9.

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17.10.

–

18.

Quantization and Waves

  • 1. Background
  • 2. The Field
  • 3. Quantization
  • 4. Blackbody Radiation
  • 5. Photoelectric Effect
  • 6. Light Quanta
  • 7. Is a Photon a Particle?
  • 8. What are Field Quanta?
  • 9. PROBLEMS

18.1.

–

18.2.

–

18.3.

–

18.4.

–

18.5.

–

18.6.

–

18.7.

–

18.8.

–

18.9.

–

19.

Quantizing Nature: A first Approach

  • 1. Phase, Waves and "Particles"
  • 2. Wave Nature of "Particles"
  • 3. Wilson-Sommerfeld Quantization Condition
  • 4. Wilson-Sommerfeld Application: 1D Electron Wave
  • 5. Wilson-Sommerfeld Application: Atomic Structure
  • 6. PROBLEMS

19.1.

–

19.2.

–

19.3.

–

19.4.

–

19.5.

–

19.6.

–

20.

Quantum Mechanics

  • 1. Classical Wave Equation
  • 2. Schrödinger's Equation
  • 3. "Particle" in a 1D Box
  • 4. Quantum Tunneling
  • 5. Quantum Harmonic Oscillator
  • 6. PROBLEMS
  • 7. Wave Function Lab

20.1.

–

20.2.

–

20.3.

–

20.4.

–

20.5.

–

20.6.

–

20.7.

–

21.

Special Relativity

  • 1. The Postulates
  • 2. Some Definitions
  • 3. Relativistic Velocity Addition
  • 4. Time Dilation
  • 5. Length Contraction
  • 6. Momentum and Energy
  • 7. Energy Momentum Relation
  • 8. PROBLEMS

21.1.

–

21.2.

–

21.3.

–

21.4.

–

21.5.

–

21.6.

–

21.7.

–

21.8.

–

22.

Heat Transfer

  • 1. Convection
  • 2. Conduction
  • 3. Thermal Radiation
  • 4. Evaporative Cooling
  • 5. The Effect of Scale
  • 6. PROBLEMS

22.1.

–

22.2.

–

22.3.

–

22.4.

–

22.5.

–

22.6.

–

23.

Fundamental Physics

  • 1. Breaking it Down
  • 2. Nuclear Structure
  • 3. Binding Energy
  • 4. Radioactive Decay
  • 5. Decay Schemes
  • 6. PROBLEMS

23.1.

–

23.2.

–

23.3.

–

23.4.

–

23.5.

–

23.6.

–

24.

Astrophysics and Cosmology

  • 1. Where are We?
  • 2. The Milky Way
  • 3. One
  • 4. Origins
  • 5. General Relativity and Expansion
  • 6. Numerical Solution to Friedmann Equation

24.1.

–

24.2.

–

24.3.

–

24.4.

–

24.5.

–

24.6.

–

25.

Answers to Problems

  • 1. Answers
  • 2. Interference

25.1.

–

25.2.

–

26.

Electric Charge

  • 1. Charge
  • 2. Net Charge
  • 3. The Coulomb Force

26.1.

–

26.2.

–

26.3.

–

27.

Math Review

  • 1. Miscellaneous Comments
  • 2. Problems

27.1.

–

27.2.

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Information