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Self-Education Materials:

This section is meant to provide the core curriculum for an undergraduate degree in Physics and Mathematics, condensed down to an overview of the most important information. This is meant to act as a study guide for physics hobbyists as well as students interested in pursuing future careers in science. This is not meant to be a replacement for a college education or your standard college text book covering the relevant subject matter. Additional links and resources are provided on each page. If you find the subject matter interests you, it is highly recommended you buy a college text book on the subject in addition to studying the material provided on this website.

Curriculum Requirements for an Undergraduate Degree in Physics:

Semester 1:

Calculus I - Differentials, Derivatives, Limits,
Chemistry I -
General Physics I - Kinematics, Motion, Speed, Velocity, Acceleration, Mass, Forces, and Ballistic motion.
Electives

Semester 2:

Calculus II - Integration, By Parts, Chain Rule, Riemann Sums, Partial Derivatives
Chemitry II -
General Physics II - Intro to Circuits, Electricity and Magnetism, Heat and thermodynamics, waves and sound, etc.
Electives

Semester 3:

Calculus III - Series, Expansions, Functions, Double and Triple integrals
Differential Equations - First, Second, and higher order. Bernoulli Equation, Exact Equations, Homogeneous Equations, Integrating Factors, Series Solutions, Wronskians, Lagrangians, etc.
Mechanics - Simple Harmonic Oscillators, Basic Gravity, Kepler's Laws, All the problems from Physics 1 and 2 except this time WITH Air Resistance and much more Calculus.
Linear Algebra - Matrices, Vectors, Arrays, Matrix Mechanics, Determinants, Reduced Row Echelon, Lagrange Multipliers, Eigenvectors, etc.
Electives

Semester 4:

Math Physics - Vector Calculus, Coordinate systems, Jacobians, Intro to Differential Eq. linear algebra, etc.
Modern Physics - Intro to Quantum Mechanics, Relativity, and "Modern" physics. Laboratory Experiments: Michaelson-Moreley, Millikan Oil Drop,
Thermal Physics - Statistical Mechanics, Heat Engines, Calorimetry, macro and micro-states, thermal gradients, differentials

Semester 5:

Experimental Physics I - How to conduct experiments and write papers. Labs include: Simple undamped Pendulum, damped pendulum, (LC Circuits: High Pass Filter, Low Pass Filter, Band Pass Filter), Nuclear Magnetic Resonance, Hyper-Fine Splitting of Rb.
Electricity and Magnetism I - Electrostatics, Coulomb's Law, Gauss's Law, Ampere's Law, Dielectrics, conductors, insulators, Divergences, Gradients, vector field plots,

Semester 6:

Experimental Physics II -
Electricity and Magnetism II - Electrodynamics, Faraday's Law, Induction, wave equation for light, Stokes' Theorem, Curl, Pointing Vectors, Radios, magnets, magnetization, Maxwell's Equations, Conservation Laws.

Semester 7:

Special Relativity -
Quantum I -

Semester 8:

General Relativity -
Quantum II -

By the end of their third semester of study, all physicists should have obtained the following basic level math and physic skills.

Basic Math

  • Solve a quadratic equation for its roots.
  • Solve any n equations for n unknowns.
  • Specify the straight line that passes through any two points in a plane.
  • Use trigonometric functions and simple trig identities.
  • Know and use the areas, circumference, or volume of basic shapes.
  • Perform basic differentiation and integration accurately, for instance product and chain rules, basic u substitution, trigonometric substitution integrals.

Basic Physics

  • List and explain Newton?s Three Laws and Kepler?s Three Laws.
  • Give definitions (as vectors if necessary) for force, momentum, angular momentum, kinetic energy, Hooke?s Law, torque, angular variables, centripetal acceleration, and position and velocity under constant acceleration.
  • Define the potential energies associated with gravitational interactions between any two objects with mass, electrical interactions between any two charges, springs, and gravity near the surface of the Earth.
  • Identify and solve problems requiring the use of Newton?s 2nd Law.
  • Identify and solve problems requiring the use of energy, momentum, or angular momentum conservation.
  • Define and use the force on a charged particle due to the electric or magnetic field.
  • Determine the electric field, magnetic field, and electric potential in simple situations.
  • Understand basic circuit theory.
  • Know and be able to explain the basic right hand rules as they apply to electricity and magnetism.

By the end of their sixth semester of study, all physicists should have obtained the following intermediate level math and physics skills.

Intermediate Math

  • Integrate using u and basic trigonometric substitutions.
  • Integrate by parts.
  • Perform surface and volume integrals on basic geometric shapes.
  • Sketch the graph of any function f(x) ? identifying features such as singularities, local extrema, and asymptotic behavior.
  • Take the dot or cross product of any two vectors.
  • Take the gradient of a function, the divergence of a vector, and the curl of a vector. Draw pictures defining what the gradient, divergence and curl mean physically.
  • Solve linear, 1st order ODEs by separation of variables.
  • Solve linear, 2nd order homogeneous ODEs.
  • Perform simple matrix algebra ? multiplication, determinants, etc.
  • Perform Taylor series expansions and use the binomial theorem.
  • Explain the basic principle behind the Fourier transform and Fourier series.

Intermediate Physics

  • Know key physics constants such as c, G, Boltzman?s constant, Avogadro?s number, the masses of the proton and electron, the fundamental electric charge, and Planck?s constant.
  • Apply solutions to differential equations to physics by evaluating initial conditions, in particular to problems involving the simple harmonic oscillator or air resistance.
  • Understand basic experimental design ? for example, know how to design experiments that would test Physics I or II concepts (conservation laws, Newton?s Laws, SHM, Ohm?s Law, Snell?s Law, etc.)
  • Understand error propagation as it applies to basic experiments.
  • List and explain Maxwell?s equations in both integral and differential forms and draw pictures associated with them.
  • Understand the basic underlying principles of special relativity.
  • Derive the time delay equation in special relativity.
  • Understand the basic relevance of quantum mechanics and where it applies in nature.
  • Possess a beginning understanding of the calculus of variations and the Euler-Lagrange equations.