LAPC 2012: Apparently there is Life After preCalculus after all! We made the entire 4th Quarter an intro to Calculus as our final project. This is a preCalculus class, right? What better way to prepare for taking Calculus next year than to actually do some Calculus now! We focused on the skills in the 3 of 5 units I review from AB Calculus in my BC class.
Unit 2 was Limits, Continuity and the Definition of the Derivative as the limit of the Difference Quotient. Unit 3 was all about the Existence of the Derivative and Differentiation Rules such as Power, Trig, Product, Quotient and Chain. We didn't have time for Unit 4 which included some Applications of the Derivative (min/max, related rates) other than rates of change, tangent lines and displacement problems.
Last, but not least, Unit 5 was about Definite and Indefinite Integrals and the First Fundamental Theorem. We didn't have time for Unit 6 on Applications of the AntiDerivative (arc length, volume, surface area, Second Fundamental Theorem) other than area and acuumulator functions.
The only difference here, compared to my BC class, is that we used a TI83 instead of a TI89 as needed. Also, in BC we get into a lot more theory for Riemann Sums including limits of series of constants and we write programs using TI-BASIC to estimate these sums when exact answers are not possible!
Unit 2-1: 1-Sided and 2-Sided Limits
Unit 2-2: Definition of Continuity
Unit 2-3: Min/Max and Intermediate Value Theorem
Intro to Calculus in preCalculus 2-3: Definition of the Derivative
Unit 2-4: Definition of the Derivative
Unit 2-6: When does the Derivative Exist?
Unit 3-1: Power and Product Rules
Unit 3-2: Quotient Rule
Unit 3-3: Trig Rules
preCalculus: Intro to Calculus 3-3 Trig Function Derivatives
Unit 3-4: Displacement, Velocity, Acceleration, Parametrics
Unit 3-5: Chain Rule
Unit 5-1: AntiDerivatives
Unit 5-2: Differential Equations
Unit 5-3: Definite Integrals
Unit 5-5: Riemann SumsUnit 5-9: Indefinite Integrals
Unit 5-10: U-Substitution
Well, that's all folks!