Ryangineer

Machine Learning Mathematics & Virtual Reality Aesthetics

"In mathematics, you don't understand things; you just get used to them." — John von Neumann

Precalculus Course Outline

Functions

This section introduces the concept of functions, including function notation and evaluating functions.

Functions Visualization — A diagram showing a function, such as f(x) = x^2, graphed on a Cartesian plane.
Mathematics Libre Texts

Linear Functions

Explore linear functions, including slope, intercepts, and graphing linear equations.

Linear Functions Visualization — Visuals illustrating the concept of slope and y-intercept, along with the graph of a linear equation, such as y = mx + b.
School Tube

Systems of Linear Functions

Learn about systems of linear equations and how to solve them using various methods such as substitution and elimination.

An illustration of two linear functions graphed on the same plane showing their point of intersection.
Open Textbook

Power and Polynomial Functions

Study power functions and polynomial functions, including their properties and graphing techniques.

Power and Polynomial Functions Visualization — Graphs of various polynomial functions, demonstrating different shapes depending on the degree of the polynomial.
Lumen Learning

Rational Functions

Examine rational functions and their characteristics, including asymptotes and solving rational equations.

Rational Functions Visualization — Graphs illustrating the asymptotic behavior of rational functions.
Lumen Learning

Modeling Using Variation

Understand the concept of variation and its applications in mathematical modeling.

Modeling Using Variation Visualization — Diagrams showing direct, inverse, joint, or combined variation in real-world contexts.
Slide Player

Exponential Functions

Explore exponential functions, exponential growth and decay, and logarithmic properties.

Exponential Functions Visualization — A graph of an exponential function, showing the characteristic rapid growth or decay.
Study.com

Logarithmic Functions

Learn about logarithmic functions, logarithmic properties, and solving logarithmic equations.

Logarithmic Functions Visualization — The graph of a logarithmic function, showing its characteristic shape.
Lumen Learning

Exponential and Logarithmic Equations and Models

Apply exponential and logarithmic functions to solve equations and model real-life situations.

Power and Polynomial Functions Visualization — Graphs depicting real-life situations that can be modeled with exponential or logarithmic functions, such as population growth or radioactive decay.
Lumen Learning

Evaluating Trigonometric Functions

Introduce trigonometric functions, including sine, cosine, and tangent, and learn to evaluate them.

Trigonometric Functions Visualization — The unit circle diagram showing sine, cosine, and tangent values for different angles.
Matter of Math

Graphing Trigonometric Functions

Study the graphs of trigonometric functions and their transformations.

Trigonometric Functions Visualization — Graphs of sine, cosine, and tangent functions.
Owlcation

Trigonometric Identities

Explore trigonometric identities, including Pythagorean identities and sum and difference identities.

Trigonometric Identities Visualization — Diagrams or proofs demonstrating trigonometric identities, such as those involving Pythagorean identities.
Steve Stein

Inverse Trigonometric Functions and Solving Trigonometric Equations

Understand inverse trigonometric functions and their properties, as well as solving trigonometric equations.

Inverse Trigonometric Functions Visualization — Graphs of inverse trigonometric functions and illustrations of how they can be used to solve trigonometric equations.
OnlineMathLearning.com

Further Applications of Trigonometry

Apply trigonometric functions to solve real-world problems and explore additional trigonometric concepts.

Real-world Trigonometric Visualization — Diagrams showing real-world applications of trigonometry, such as navigation and physics problems.
Trigonometric Identities

Analytic Geometry

Learn about analytic geometry, including distance and midpoint formulas, and equations of circles and conics.

Power and Polynomial Functions Visualization — Graphs and diagrams illustrating the principles of analytic geometry, such as the equation of a circle or elipse.
Cue Math

Sequences, Series, and the Binomial Theorem

Study sequences, series, and the binomial theorem, including arithmetic and geometric sequences, and binomial expansions.

Sequence Visualization — Diagrams or sequences demonstrating arithmetic and geometric sequences, as well as the expansion of binomials.
HotCore