Exercise Notes

• Introduction
• Mathematical notation
• Differentiation and Integration
• Numerical differentiation and integration
• Dimensional analysis
• Graphical solutions
• Working with data
• Vectors
• Scripts
• Vector functions in scripts
• Exam questions
• Motion
• Parametric equations in 2D
• Parametric equations in 3D
• Position → Velocity → Acceleration → Force
• Force → Acceleration → Velocity → Position
• Examples
  • Zero Total Force = Straight Line Motion
  • Constant Force = Parabolic Motion
  • Terminal Velocity - Falling with a Linear Drag Force
  • Harmonic motion
  • Circular motion
• Numerical differentiation: $r_x$ → $v_x$ → $a_x$
• Numerical integration: $a_x$ → $v_x$ → $r_x$
• Forces
• Differential equations
• Numerical solutions of second order differential equations
• A ball is throw vertically upwards neglecting drag
• A ball is throw vertically upwards
• Mass-spring system
• Numerical solutions of differential equations of motion in three dimensions
• Satellite orbits
• A block slides down an inclined plane
• Air friction
• A bouncing ball
• A ball is thrown in the wind
• Curveball: the magnus effect
• Rocket launch
• Exam questions
• Work and Energy
• Work performed by moving along a trajectory
• Power
• Potential energy
• Gradient
• Scalar fields and vector fields
• Conservation of energy
• Exam questions
• Electricity
• Coulomb force between two point charges
• Electric field
• Line charge
• Sheet charge
• Numerical integration: $\rho$ → $E$ → $\varphi$
• Numerical differentiation: $\varphi$ → $E$ → $\rho$
• Divergence
• Motion of a charged particle in a constant electric field
• Electric deflection of an electron beam
• Oil drop experiment
• Current
• Exam questions
• Magnetism
• Magnetostatics
• The magnetic field around an infinitely-long straight wire
• The magnetic field along the axis of a current loop
• Magnetic field
• Motion of a charged particle in a constant magnetic field
• Magnetic deflection of an electron beam
• Motion of a charged particle in constant electric and magnetic fields
• J. J. Thomson's experiment to determine the charge-to-mass ratio of electrons
• A charged particle in arbitrary electric and magnetic fields
• The force on a current carrying wire
• Exam questions
• Oscillations
• Undamped oscillations of a mass-spring system
• Damped mass-spring system
• Nonlinear oscillators
• Mass-nonlinear spring system
• Relaxation oscillations: Van der Pol oscillator
• Parametric oscillator: swing
• Resonance: A damped driven mass-spring system
• Using complex numbers to describe oscillations
• Analytic solutions to differential equations
• Resonance of a damped driven oscillator
• Four cases of a driven oscillator
• Quality factor
• Normal modes: a mass on a frictionless table connected to two springs
• Normal modes: coupled oscillators
• Beats
• Beats with three frequencies
• Chaotic solutions to the driven pendulum
• Exam questions
• Waves
• Harmonic waves
• Wave pulse
• Plane waves
• Superposition of wave pulses
• Interference of plane waves
• Interference of plane waves moving at 90° to each other
• Reflecting plane waves
• Reflections of a wave pulse
• Reflections of a harmonic wave
• Circular waves
• Circular waves simulation
• Interference of circular surface waves
• Intensity of two interfering circular waves
• Interference from a single narrow slit
• Double slit experiment
• Double slit experiment, far field
• Intensity in a double slit experiment
• Optical double slit interference experiment
• N slit interference
• Intensity in an N slit experiment
• Single slit diffraction
• Diffraction by two slits of width $a$
• Doppler effect
• Doppler effect in 3D
• Shock waves
• Refraction of waves
• Snell's law
• Exam questions
• Optics
• Reflection from a spherical mirror
• Reflection from a parabolic mirror
• Refraction at a spherical interface
• Thick lens
• Optical systems
• Thin lenses
• Thin lens formula
• Thin lenses
• Real and virtual images
• Exam questions