 ## Honors Calculus Course

PROGRESSIVE MATHEMATICS INITIATIVE® (PMI®)

## Units (select a unit)

• ###### Limits & Continuity
One- and Two-Sided Limits
Limits That DNE
Indeterminate Form of 0/0
Infinite Limits
Squeeze Th. & Trig Limits
Continuity
IVT
Problem Solving
• ###### Derivatives
Tangent Line Problem
Def. of Derivative
Derivative Rules
Higher Order Derivatives
Deriv. of Trig., Logs, e, Piecewise & Abs. Value
Tangent & Normal Lines
Deriv. of Inverse Functions
• ###### Applications of Derivatives
L’Hopital’s Rule
Implicit Differentiation
Related Rates
Differentials
Linear Approx. & Motion
• ###### Analyzing Functions Using Derivatives
Critical & Extreme Values
The 1st & 2nd Deriv. Tests
Connecting f, f’ and f”
Curve Sketching
Rolle’s & Mean Value Thms
Newton’s Method
Optimization
• ###### Integration
Riemann Sums
Trapezoidal Approximation
Sigma Notation
Definite & Indefinite Integrals
FTC - Parts I & II
Avg Values for Integrals
MVT for Integrals
u-Substitution for Integration
• ###### Applications of Integration
Integral Defined Functions
Net Change/Accumulation
Rate In/Rate Out
Particle Motion Revisited
Area Between Two Curves