Unit 68
Understanding limits, derivatives, and integrals
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Day 1
What is calculus? Historical context
Day 2
Average rate of change
Day 3
Instantaneous rate of change concept
Day 4
Secant lines and tangent lines
Day 5
Introduction to limits
Day 6
Evaluating limits graphically
Day 7
Evaluating limits numerically
Day 8
Evaluating limits algebraically
Day 9
Limits at infinity
Day 10
Continuity and discontinuity
Day 11
Definition of the derivative
Day 12
Derivative as instantaneous rate of change
Day 13
Derivative notation
Day 14
Basic differentiation rules: power rule
Day 15
Basic differentiation rules: constant and sum
Day 16
Derivatives of polynomials
Day 17
Interpreting derivatives in context
Day 18
Velocity and acceleration
Day 19
Higher-order derivatives
Day 20
Introduction to integration
Day 21
Antiderivatives
Day 22
Definite integrals: area under curves
Day 23
Riemann sums concept
Day 24
Fundamental Theorem of Calculus
Day 25
Basic integration rules
Day 26
Applications: total distance
Day 27
Applications: total accumulation
Day 28
Connecting derivatives and integrals
Day 29
Calculus in real-world contexts
Day 30
Unit assessment