D. Continuity as a property of functions. • An intuitive understanding of continuity. (Close values of the domain lead to close values of the range.) • Understanding continuity in terms of limits. • Geometric understanding of graphs of continuous functions (Intermediate Value Theorem and Extreme Value Theorem). I can… (Add newly created “I Can” statements that are the Clear Learning Targets in this column, based on the grade level indicator listed to the left.) Add your resources and strategies here E. Parametric, polar, and vector functions. The analysis of planar curves includes those given in parametric form, polar form, and vector form. I can… (Add newly created “I Can” statements that are the Clear Learning Targets in this column, based on the grade level indicator listed to the left.) Add your resources and strategies here II. Derivatives
E. Applications of derivatives. • Analysis of curves, including the notions of monotonicity and concavity. + Analysis of planar curves given in parametric form, polar and vector form, including velocity and acceleration vectors. • Optimization, both absolute (global) and relative (local) extrema. • Modeling rates of change, including related rates problems. • Use of implicit differentiation to find the derivative of an inverse function. • Interpretation of the derivative as a rate of change in varied applied contexts, including velocity, speed, and acceleration. +Geometric interpretation of differential equations via slope fields and the relationship between slope fields and solution curves for differential equations. + Numerical solution of differential equations using Euler's method. + L'Hopital's Rule, including its use in determining limits and convergence of improper integrals and series. I can… (Add newly created “I Can” statements that are the Clear Learning Targets in this column, based on the grade level indicator listed to the left.) Add your resources and strategies here F. Computation of derivatives. • Knowledge of derivatives of basic functions, including power, exponential, logarithmic, trigonometric, and inverse trigonometric functions. • Basic rules for the derivative of sums, products, and quotients of functions. • Chain rule and implicit differentiation. + Derivatives of parametric, polar, and vector functions. I can… (Add newly created “I Can” statements that are the Clear Learning Targets in this column, based on the grade level indicator listed to the left.) Add your resources and strategies here
• Solving separable differential equations and using them in modeling. In particular, studying the equation y' = ky and exponential growth. (Add newly created “I Can” statements that are the Clear Learning Targets in this column, based on the grade level indicator listed to the left.) F. Numerical approximations to definite integrals. Use of Riemann and trapezoidal sums to approximate definite integrals of functions represented algebraically, graphically, and by tables of values. I can… (Add created “I Can” statements that are the Clear Learning Targets in this column, based on the grade level indicator listed to the left.) Add your resources and strategies here IV. Polynomial Approximations and Series College level Standard and Benchmark College level Indicators Learning Targets Strategies/Resources A. Concept of series A series is defined as a sequence of partial sums, and convergence is defined in terms of the limit of the sequence of partial sums. Technology can be used to explore convergence or divergence. I can… (Add newly created “I Can” statements that are the Clear Learning Targets in this column, based on the grade level indicator listed to the left.) Add your resources and strategies here