Functions, Calculus & Analysis
See how quantities change, graphs move, derivatives respond and integration gathers information.
The mathematics behind gradients, optimization and learning from change.
- 11
- lessons
- 146
- visual explanations
- 4
- chapters
Algebra & Logarithms
See why symbolic tools were created and how they simplify hard calculations.
LESSONGeometric Series: Formal Identity vs Numerical SumWhy does correct algebra fail when r is substituted outside the convergence interval?
8 pictures · Open →
LESSONHow Logarithms Were BornWhy did mathematics need logarithms, and why does the natural logarithm appear in calculus?
19 pictures · Open →
LESSONIs e^x PolynomialWhat is the mathematical foundation of is e^x polynomial?
11 pictures · Open →
LESSONTwo Forms of the Exponential FunctionWhy do the limit and power-series definitions produce the same e^mu?
4 pictures · Open →Functions & Differentiation
Read graphs, local change and limits as one connected visual story.
LESSONDifferentiation Does Not Destroy ProbabilityWhat is the mathematical foundation of differentiation does not destroy probability?
1 pictures · Open →
LESSONFacts About Differentiation: When Limits Preserve SlopesWhat does differentiation keep, amplify, or fail to preserve when functions change with n?
20 pictures · Open →
LESSONLimit For CalculusWhat is the mathematical foundation of limit for calculus?
14 pictures · Open →
LESSONTracing Graphs: Read Shape, Motion, and ChangeHow can an equation tell us where a graph sits, moves, turns, breaks, and bends?
20 pictures · Open →Analysis & Integration
Move from geometric area to modern ways of measuring and integrating.
Vector Calculus
Use one operator to ask about direction, flow and rotation.
