Roadmap
Formula reference
- arithmetic ✅ 2023-07-28
- algebra
- derivatives ✅ 2023-07-28
- integrals ✅ 2023-08-08
- series and sequences
- multivariable
- first order ode ✅ 2023-08-08
- higher order ode ✅ 2023-08-09
- series and sequences ode
- systems of ode
Arithmetic
- types of numbers
- mathematical operations
- natural numbers ✅ 2023-09-11
- add/subtract
- multiply/divide
- integers
- add/subtract
- multiply/divide
- rational numbers
- multiply/divide
- add/subtract
- irrational numbers
- add/subtract/multiply/divide
- Real numbers
- order of operations
- scientific notation
- prime numbers/prime factorization
- counting systems
- imaginary numbers
- complex numbers
- light exploration of the fun and weird stuff beyond (hypercomplex numbers, hyper real numbers, \(p\)-adic numbers, etc...)
Algebra
- variables
- polynomials
- graphs
- functions
- linear equations
- systems of linear equations
- nonlinear equations
- applications and models
- quadratic equations
- factoring
- factoring techniques
- higher order polynomials
- \(e\) and exponential functions
- partial fractions
Trigonometry
- geometry
- \(\pi\)
- sine, cosine, and tangent
- rest of the trig functions
- inverse trig functions
- applications
- Identities
- vectors and polar coordinates
- hyperbolic trig
Calculus
Differential calculus
- Limits
- Derivatives
- applications
- power rule
- product and quotient rule
- chain rule
- l'hopital's rule
- implicit differentiation
Integral calculus
- integration
- definite and indefinite integrals
- applications
- Fundamental Theorem of Calculus
- basics of integration
- \(u\)-substitution
- integration by parts
- trigonometric substitution
- trig integrals
Series and sequences
- sequences
- infinite series
- evaluating for convergence and divergence
- Geometric series
- Telescoping series
- Harmonic series
- Ratio test
- Comparison and limit comparison test
- integral test
- root test
- power series
- taylor series
- binomial series
Multivariable Calculus
- Parametric equations
- Calculus with parametric curves
- conic sections
- working in 3D
- Linear algebra introduction
- partial derivatives
- gradient
- Lagrange multipliers
- multiple integrals
- cylindrical and spherical coordinate systems
- conversion between coordinate systems
- Jacobian
- applications
- vector fields
- line integrals
- curl and divergence
- flux and circulation
- The generalized fundamental theorem of calculus
Ordinary Differential Equations
(completed is the first pass, need to add visuals and animations)
- overview of first order ODEs
- Seperable ✅ 2023-08-09
- linear ✅ 2023-08-09
- bernoulli ✅ 2023-08-14
- homogeneous ✅ 2023-08-14
- G(ax+by)
- exact
- applications
- overview of 2nd+ order ODE's
- Linear homogeneous
- nonlinear homogeneous
- nonhomogeneous
- applications
- Laplace transformations
- inverse laplace transformations
- step functions
- solving initial value problems with laplace transformations
- dirac delta function
- series solutions to ODS's
- systems of ODE's
- homogenous systems
- nonhomogenous systems
other math things 'on the list' that I may add in the future
- Linear algebra (will most likely do a general overview before getting deep into the ODE section)
- Partial Differential equations
- Real analysis?While the current focus is math (as it is the core of many other sciences) I also would like to eventually expanding to physics, this would include things like...
- statics
- dynamics
- thermodynamics
- heat transfer
- fluid dynamics
- electromagnetism
- electrical circuits and devicesWith that in mind I have a lot to do before getting there, and I'm only one person who is doing this as a side project/hobby. While I'll try to be consistent in updating the website, I have a limited amount of time to work on this each week. There may be extended amounts of time without any updates, and when it is updated, it may be in no particular order or in an "as needed" kind of way. See about me for more info.