AP Calculus BC

Transcription

1 Limits and Their Properties Limits and their meaning. How are limits used in Calculus? Symmetry Differentiability Continuity How does symmetry effect differentiability? Symmetry and Differentiabili ty/ days 1-2 Delta- Epsilon/ days 3-4 Epsilon Delta What is the formal definition of limit? L Hopital s Rule/ days 5-6 L Hopital s How are difficult limits found?

2 Derivatives Using derivatives. What are applications of derivatives? Business and Economic Applications/ days 7-9 Revenue Break-Even Point Marginal Profit Marginal Cost Marginal Revenue How is Calculus applied to economic situations? Newton s Method/ days 10 Iterations How are root s determined? Approximatio ns/ days How are approximations made with derivatives?

3 Approximating Area Various ways to find area under a curve. How is area calculated? Definite integral Accumulation What is a definite integral? How does area accumulate? Definite integrals/ days Area Under a Curve/ days Why is area under a curve calculated? Summations/ days Sigma notation Riemann Sums Simpson s Rule What is a sum? How are area sums found?

4 Applications of Integration Using integration is various applications. How are integrals used? Disk Washer Shells How can volume be found? Volume/ days Arc length and Surface Area/ days Arc length Surface area How are arc length and surface area found for irregular shapes? Physics Applications/ days Work Fluid Force Center of Mass What needs to be found to determine various physical properties of objects?

5 Advanced Integration Techniques Using trick integration techniques in varying application. How is integration really used? Transcenden tal Integration/ days Separation of Variables Exponential Growth Integration by Parts Partial Fractions How are variables separated and why? What is exponential growth? What is integration by parts? When are partial fractions used? Improper and Impossible Integration/ days Improper Integrals What makes integrals improper of impossible? DEQ/ days Differential Equations Slope Fields Logistic Growth How are slope fields used in DEQ? Inverse Funtions/ days Inverse Functions How are inverse trig functions used in Calculus?

6 Parametric and vectors Applying Calculus to other mathematical areas. How does Calculus apply to multiple equations at one time? Parametric equations How are derivatives and integrals of parametric equations found? Parametrics/ days Polar Equations/ days Polar equations What are polar coordinates? How is calculus applied to polar equations? Vectors/ days Vectors Vector- valued functions How are vectors determined? How is calculus applied to vectors?

7 Sequences and Series Finding various types of series. Does a series converge? Series Sequence Infinite Series How is a series determined? Sequence and Series/ days Convergence / days Convergence Divergence How is convergence determined? Types of Series/ days Comparison Alternating Series Ratio and Root s Power Series Taylor Series Maclaurin Series What are the types of series? How can you tell if a series converges?

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