|
|
| (One intermediate revision by the same user not shown) |
| Line 5: |
Line 5: |
| | | | |
| | The Wikipedia summary of [https://en.wikipedia.org/wiki/Calculus calculus and its history]. | | The Wikipedia summary of [https://en.wikipedia.org/wiki/Calculus calculus and its history]. |
| | + | |
| | | | |
| | ==Topics List== | | ==Topics List== |
| − | {| class="wikitable sortable" | + | {| class="wikitable" |
| | ! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes | | ! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes |
| − |
| |
| − | |-
| |
| − |
| |
| − | |Week 1
| |
| − |
| |
| − | ||
| |
| − |
| |
| − | <div style="text-align: center;">2.2</div>
| |
| − |
| |
| − | ||
| |
| − |
| |
| − | [[The Limit of a Function]]
| |
| − |
| |
| − | ||
| |
| − |
| |
| − | * [[Functions|Evaluation of a function]] <!-- 1073-1 --> including the [[Absolute Value Functions| Absolute Value]] <!-- DNE (recommend 1073-1) -->, [[Rational Functions|Rational]] <!-- 1073-4 -->, and [[Piecewise Functions|Piecewise]] functions <!-- 1073-1 -->
| |
| − | * [[Functions|Domain and Range of a Function]] <!-- 1073-1 -->
| |
| − |
| |
| − |
| |
| − | ||
| |
| − |
| |
| − | *Describe the limit of a function using correct notation.
| |
| − | *Use a table of values to estimate the limit of a function or to identify when the limit does not exist.
| |
| − | *Use a graph to estimate the limit of a function or to identify when the limit does not exist.
| |
| − | *Define one-sided limits and provide examples.
| |
| − | *Explain the relationship between one-sided and two-sided limits.
| |
| − | *Describe an infinite limit using correct notation.
| |
| − | *Define a vertical asymptote.
| |
| − |
| |
| − |
| |
| | |- | | |- |
| − | | + | | Week 1 || 2.2 || [[The Limit of a Function]] || || |
| − | | |
| − | |Week 1/2 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">2.3</div>
| |
| − | | |
| − | || | |
| − |
| |
| − | | |
| − | [[The Limit Laws]] | |
| − | | |
| − | ||
| |
| − | | |
| − | | |
| − | | |
| − | *[[Factoring Polynomials]] <!-- 1023-P5 -->
| |
| − | *[[Simplifying Radicals|Identifying conjugate radical expressions]] <!-- 1073-R -->
| |
| − | *[[Rational Expression|Simplifying rational expressions]] <!-- 1073-4 -->
| |
| − | *[[Domain of a Function|Evaluating piecewise functions]] <!-- 1073-1.2 -->
| |
| − | *[[Trigonometric Functions|The trigonometric functions]] <!-- 1093-2.2 -->
| |
| − | | |
| − | | |
| − | || | |
| − | | |
| − | *Recognize the basic limit laws.
| |
| − | *Use the limit laws to evaluate the limit of a function.
| |
| − | *Evaluate the limit of a function by factoring.
| |
| − | *Use the limit laws to evaluate the limit of a polynomial or rational function.
| |
| − | *Evaluate the limit of a function by factoring or by using conjugates.
| |
| − | *Evaluate the limit of a function by using the squeeze theorem.
| |
| − | *Evaluate left, right, and two sided limits of piecewise defined functions.
| |
| − | *Evaluate limits of the form K/0, K≠0.
| |
| − | *Establish and use this to evaluate other limits involving trigonometric functions.
| |
| − | | |
| | |- | | |- |
| − | | + | | Week 1 & 2 || 2.3 || [[The Limit Laws]] || || |
| − | | |
| − | |Week 2/3 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">2.4</div>
| |
| − | | |
| − | ||
| |
| − |
| |
| − | [[Continuity]]
| |
| − | | |
| − | | |
| − | ||
| |
| − | | |
| − | * [[Functions|Domain and Range of a Function]] <!-- 1073-1 -->
| |
| − | * [[Interval Notation|Interval Notation]] <!-- 1023-1.7 -->
| |
| − | * [[Limits of Functions|Evaluate limits]] <!-- 1214-1 -->
| |
| − | * [[The Limit Laws]] <!-- 1214-2.3 -->
| |
| − | * [[Polynomial Functions|Finding roots of a function]]
| |
| − | | |
| − | || | |
| − | | |
| − | * Continuity at a point.
| |
| − | * Describe three kinds of discontinuities.
| |
| − | * Define continuity on an interval.
| |
| − | * State the theorem for limits of composite functions and use the theorem to evaluate limits.
| |
| − | * Provide an example of the intermediate value theorem.
| |
| − | | |
| − | | |
| | |- | | |- |
| − | | + | | Week 2 || 2.4 || [[Continuity]] || || |
| − | | |
| − | |Week 3 | |
| − | | |
| − | ||
| |
| − | | |
| − | <div style="text-align: center;">4.6</div>
| |
| − | | |
| − | ||
| |
| − |
| |
| − | [[Limits at Infinity and Asymptotes]]
| |
| − | | |
| − | ||
| |
| − | | |
| − | * [[The Limit Laws]] <!-- 1214-2.3 -->
| |
| − | * [[Continuity]] <!-- 1214-2.4 -->
| |
| − | | |
| − | || | |
| − | | |
| − | * Calculate the limit of a function that is unbounded.
| |
| − | * Identify a horizontal asymptote for the graph of a function.
| |
| − | | |
| − | | |
| − | |-
| |
| − | | |
| − | | |
| − | |Week 3/4
| |
| − | | |
| − | ||
| |
| − | | |
| − | <div style="text-align: center;">3.1</div>
| |
| − | | |
| − | ||
| |
| − |
| |
| − | | |
| − | [[Defining the Derivative]]
| |
| − | | |
| − | ||
| |
| − | | |
| − | * [[Functions|Evaluation of a function at a value]] <!-- 1073-1 -->
| |
| − | * [[Linear Functions and Slope|The equation of a line and its slope]] <!-- 1023-2.3 -->
| |
| − | * [[Limits of Functions|Evaluating limits]] <!-- 1214-1 -->
| |
| − | * [[Continuity]] <!-- 1214-2.4 -->
| |
| − | | |
| − | ||
| |
| − | | |
| − | * Recognize the meaning of the tangent to a curve at a point.
| |
| − | * Calculate the slope of a secant line (average rate of change of a function over an interval).
| |
| − | * Calculate the slope of a tangent line.
| |
| − | * Find the equation of the line tangent to a curve at a point.
| |
| − | * Identify the derivative as the limit of a difference quotient.
| |
| − | * Calculate the derivative of a given function at a point.
| |
| − | | |
| − | | |
| − | |-
| |
| − | | |
| − | | |
| − | |Week 4
| |
| − | | |
| − | ||
| |
| − | | |
| − | <div style="text-align: center;">3.2</div>
| |
| − | | |
| − | ||
| |
| − |
| |
| − | | |
| − | [[The Derivative as a Function]]
| |
| − | | |
| − | || | |
| − | | |
| − | * [[Functions and their graphs|Graphing Functions]] <!-- 1023-1.1 -->
| |
| − | * [[Continuity|Continuity of a function at a point]] <!-- 1214-2.4 -->
| |
| − | * [[Defining the Derivative|The derivative represents the slope of the curve at a point]] <!-- 1214-1 -->
| |
| − | * [[Limits of Functions|When a limit fails to exist]] <!-- 1214-2.2 -->
| |
| − | * [[The Limit Laws]] <!-- 1214-2.3 -->
| |
| − | | |
| − | ||
| |
| − | | |
| − | * Define the derivative function of a given function.
| |
| − | * Graph a derivative function from the graph of a given function.
| |
| − | * State the connection between derivatives and continuity.
| |
| − | * Describe three conditions for when a function does not have a derivative.
| |
| − | * Explain the meaning of and compute a higher-order derivative.
| |
| − | | |
| − | | |
| − | | |
| − | |-
| |
| − | | |
| − | | |
| − | |Week 4/5
| |
| − | | |
| − | ||
| |
| − | | |
| − | <div style="text-align: center;">3.3</div>
| |
| − | | |
| − | ||
| |
| − | | |
| − | | |
| − | [[Differentiation Rules]]
| |
| − | | |
| − | ||
| |
| − | | |
| − | * [[Simplifying Radicals|Radical & Rational Exponents]] <!-- 1073-Mod.R -->
| |
| − | * [[Simplifying Exponents|Re-write negative exponents]] <!-- 1073-Mod.R -->
| |
| − | * [[The Limit Laws]] <!-- 1214-2.3 -->
| |
| − | * [[The Derivative as a Function]] <!-- 1214-3.2 -->
| |
| − | | |
| − | || | |
| − | | |
| − | * State the constant, constant multiple, and power rules.
| |
| − | * Apply the sum and difference rules to combine derivatives.
| |
| − | * Use the product rule for finding the derivative of a product of functions.
| |
| − | * Use the quotient rule for finding the derivative of a quotient of functions.
| |
| − | * Extend the power rule to functions with negative exponents.
| |
| − | * Combine the differentiation rules to find the derivative of a polynomial or rational function.
| |
| − | | |
| − | | |
| − | | |
| | |- | | |- |
| − | | + | | Week 3 || 4.6 || [[Limits at Infinity and Asymptotes]] || || |
| − | | |
| − | |Week 5 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">3.4</div>
| |
| − | | |
| − | || | |
| − |
| |
| − | | |
| − | [[Derivatives_Rates_of_Change|Derivatives as Rates of Change]] | |
| − | | |
| − | || | |
| − | | |
| − | * [[Functions|Function evaluation at a value]] <!-- 1073-Mod 1.1 -->
| |
| − | * [[Solving Equations and Inequalities|Solving an algebraic equation]] <!-- 1073-Mod.R -->
| |
| − | * '''[[Understanding of Velocity and Acceleration]]''' <!-- Grades 6-12 -->
| |
| − | * [[Differentiation Rules]] <!-- 1214-3.3 -->
| |
| − | | |
| − | ||
| |
| − | | |
| − | * Determine a new value of a quantity from the old value and the amount of change.
| |
| − | * Calculate the average rate of change and explain how it differs from the instantaneous rate of change.
| |
| − | * Apply rates of change to displacement, velocity, and acceleration of an object moving along a straight line.
| |
| − | * Predict the future population from the present value and the population growth rate.
| |
| − | * Use derivatives to calculate marginal cost and revenue in a business situation.
| |
| − | | |
| − | | |
| − | | |
| | |- | | |- |
| − | | + | | Week 3 & 4 || 3.1 || [[Defining the Derivative]] || || |
| − | | |
| − | |Week 5 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">3.5</div>
| |
| − | | |
| − | || | |
| − |
| |
| − | | |
| − | [[Derivatives of the Trigonometric Functions]] | |
| − | | |
| − | ||
| |
| − | | |
| − | * [[Properties of the Trigonometric Functions|Trigonometric identities]] <!-- 1093-3.4 -->
| |
| − | * [[Graphs of the Sine and Cosine Functions]]
| |
| − | * [[Graphs of the Tangent, Cotangent, Cosecant and Secant Functions]]
| |
| − | * [[Differentiation Rules|Rules for finding Derivatives]] <!-- 1214-3.3 -->
| |
| − | | |
| − | || | |
| − | | |
| − | * Find the derivatives of the sine and cosine function.
| |
| − | * Find the derivatives of the standard trigonometric functions.
| |
| − | * Calculate the higher-order derivatives of the sine and cosine.
| |
| − | | |
| − | | |
| | |- | | |- |
| − | | + | | Week 4 || 3.2 || [[The Derivative as a Function]] || || |
| − | | |
| − | |Week 6 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">3.6</div>
| |
| − | || | |
| − |
| |
| − | | |
| − | [[Chain_Rule|The Chain Rule]] | |
| − | | |
| − | ||
| |
| − | | |
| − | * [[Composition of Functions]] <!-- 1073-7 -->
| |
| − | * [[Trigonometric Equations|Solve Trigonometric Equations]] <!-- 1093-3.3 -->
| |
| − | * [[Differentiation Rules|Rules for finding Derivatives]] <!-- 1214-3.3 -->
| |
| − | * [[Derivatives of the Trigonometric Functions]] <!-- 1214-3.5 -->
| |
| − | | |
| − | || | |
| − | | |
| − | * State the chain rule for the composition of two functions.
| |
| − | * Apply the chain rule together with the power rule.
| |
| − | * Apply the chain rule and the product/quotient rules correctly in combination when both are necessary.
| |
| − | * Recognize and apply the chain rule for a composition of three or more functions.
| |
| − | * Use interchangeably the Newton and Leibniz Notation for the Chain Rule.
| |
| − | | |
| − | | |
| | |- | | |- |
| − | | + | | Week 5 || 3.3 || [[Differentiation Rules]] || || |
| − | | |
| − | |Week 6 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">3.7</div>
| |
| − | | |
| − | || | |
| − |
| |
| − | [[Derivatives of Inverse Functions]] | |
| − | | |
| − | ||
| |
| − | | |
| − | * [[One-to-one functions|Injective Functions]] <!-- 1073-7 and 1093-1.7-->
| |
| − | * [[Inverse Functions]] <!-- 1073-7 -->
| |
| − | * [[Inverse Trigonometric Functions|Customary domain restrictions for Trigonometric Functions]] <!-- 1093-3.1 -->
| |
| − | * [[Differentiation Rules]] <!-- 1214-3.3 -->
| |
| − | * [[The Chain Rule]] <!-- 1214-3.6 -->
| |
| − | | |
| − | || | |
| − | | |
| − | * State the Inverse Function Theorem for Derivatives.
| |
| − | * Apply the Inverse Function Theorem to find the derivative of a function at a point given its inverse and a point on its graph.
| |
| − | * Derivatives of the inverse trigonometric functions.
| |
| − | | |
| − | | |
| − | | |
| | |- | | |- |
| − | | + | | Week 5 || 3.4 || [[Derivatives_Rates_of_Change | Derivative as a rate of change]] || || |
| − | | |
| − | |Week 6/7 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">3.8</div>
| |
| − | | |
| − | || | |
| − |
| |
| − | | |
| − | [[Implicit Differentiation]] | |
| − | | |
| − | || | |
| − | | |
| − | * '''[[Implicit and explicit equations]]''' <!-- DNE (recommend 1073-7) -->
| |
| − | * [[Linear Equations|Linear Functions and Slope]] <!-- 1073-Mod.R -->
| |
| − | * [[Functions|Function evaluation]] <!-- 1073-Mod 1.1 -->
| |
| − | * [[Differentiation Rules]] <!-- 1214-3.3 -->
| |
| − | * [[The Chain Rule]] <!-- 1214-3.6 -->
| |
| − | | |
| − | || | |
| − | | |
| − | * Assuming, for example, y is implicitly a function of x, find the derivative of y with respect to x.
| |
| − | * Assuming, for example, y is implicitly a function of x, and given an equation relating y to x, find the derivative of y with respect to x.
| |
| − | * Find the equation of a line tangent to an implicitly defined curve at a point.
| |
| − | | |
| − | | |
| | |- | | |- |
| − | | + | | Week 5 || 3.5 || [[Derivatives of the Trigonometric Functions]] || || |
| − | | |
| − | |Week 7 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">3.9</div>
| |
| − | | |
| − | || | |
| − | | |
| − | [[Derivatives of Exponential and Logarithmic Functions]] | |
| − | | |
| − | || | |
| − | | |
| − | * [[Logarithmic Functions|Properties of logarithms]] <!-- 1073-8 -->
| |
| − | * [[The Limit of a Function]] <!-- 1214-2.2 -->
| |
| − | * [[Differentiation Rules]] <!-- 1214-3.3 -->
| |
| − | * [[The Chain Rule]] <!-- 1214-3.6 -->
| |
| − | * [[Implicit Differentiation]] <!-- 1214-3.8 -->
| |
| − | | |
| − | || | |
| − | | |
| − | * Find the derivative of functions that involve exponential functions.
| |
| − | * Find the derivative of functions that involve logarithmic functions.
| |
| − | * Use logarithmic differentiation to find the derivative of functions containing combinations of powers, products, and quotients.
| |
| − | | |
| − | | |
| − | | |
| | |- | | |- |
| − | | + | | Week 6 || 3.6 || [[Chain_Rule | The Chain Rule]] || || |
| − | | |
| − | |Week 7/8 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">4.1</div>
| |
| − | | |
| − | || | |
| − |
| |
| − | | |
| − | [[Related Rates]] | |
| − | | |
| − | || | |
| − | | |
| − | * '''Formulas for area, volume, etc''' <!-- Geometry -->
| |
| − | * '''Similar triangles to form proportions''' <!-- Geometry -->
| |
| − | * [[Trigonometric Functions]] <!-- 1093-2.2 -->
| |
| − | * [[Properties of the Trigonometric Functions|Trigonometric Identities]] <!-- 1093-3.4 -->
| |
| − | * [[Differentiation Rules]] <!-- 1214-3.3 -->
| |
| − | * [[Implicit Differentiation]] <!-- 1214-3.8 -->
| |
| − | | |
| − | || | |
| − | | |
| − | * Express changing quantities in terms of derivatives.
| |
| − | * Find relationships among the derivatives in a given problem.
| |
| − | * Use the chain rule to find the rate of change of one quantity that depends on the rate of change of other quantities.
| |
| − | | |
| − | | |
| − | | |
| | |- | | |- |
| − | | + | | Week 6 || 3.7 || [[Derivatives of Inverse Functions]] || || |
| − | | |
| − | |Week 8 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">4.2</div>
| |
| − | | |
| − | || | |
| − |
| |
| − | | |
| − | [[Linear Approximations and Differentials]] | |
| − | | |
| − | ||
| |
| − | | |
| − | * [[Mathematical Error| Definition of Error in mathematics]] <!-- DNE (recommend Mod 1.2) -->
| |
| − | * [[Linear Equations|Slope of a Line]] <!-- 1073-Mod.R -->
| |
| − | * [[Defining the Derivative|Equation of the tangent line]] <!-- 1214-3.1 -->
| |
| − | * [[Derivatives Rates of Change|Leibnitz notation of the derivative]] <!-- 1214-3.4 -->
| |
| − | | |
| − | || | |
| − | | |
| − | * Approximate the function value close to the center of the linear approximation using the linearization.
| |
| − | * Given an expression to be evaluated/approximated, come up with the function and its linearization
| |
| − | * Understand the formula for the differential; how it can be used to estimate the change in the dependent variable quantity, given the small change in the independent variable quantity.
| |
| − | * Use the information above to estimate potential relative (and percentage) error
| |
| − | | |
| − | | |
| − | | |
| | |- | | |- |
| − | | + | | Week 6/7 || 3.8 || [[Implicit Differentiation]] || || |
| − | | |
| − | |Week 8/9 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">4.3</div>
| |
| − | | |
| − | || | |
| − |
| |
| − | | |
| − | [[Maxima and Minima]] | |
| − | | |
| − | ||
| |
| − | | |
| − | * [[The First Derivative Test|Increasing and decreasing functions]] <!-- DNE (recommend 1023-2.2) -->
| |
| − | * [[Solving Equations and Inequalities|Solve an algebraic equation]] <!-- 1073-Mod.R-->
| |
| − | * [[Interval Notation|Interval notation]] <!-- 1073-Mod.R -->
| |
| − | * [[Trigonometric Equations]] <!-- 1093-3.3 -->
| |
| − | * [[Differentiation Rules]] <!-- 1214-3.3 -->
| |
| − | * [[Derivatives of the Trigonometric Functions]] <!-- 1214-3.5 -->
| |
| − | * [[Derivatives of Exponential and Logarithmic Functions]] <!-- 1214-3.9 -->
| |
| − | * [[Continuity]] <!-- 1214-2.4 -->
| |
| − | | |
| − | || | |
| − | *
| |
| − | * Know the definitions of absolute and local extrema.
| |
| − | * Know what a critical point is and locate it (them).
| |
| − | * Use the Extreme Value Theorem to find the absolute extrema of a continuous function on a closed interval.
| |
| − | | |
| − | | |
| − | | |
| | |- | | |- |
| − | | + | | Week 8 || 3.9 || [[Derivatives of Exponential and Logarithmic Functions]] || || |
| − | | |
| − | |Week 9 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">4.4</div>
| |
| − | | |
| − | || | |
| − |
| |
| − | | |
| − | [[Mean Value Theorem]] | |
| − | | |
| − | ||
| |
| − | | |
| − | * [[Functions|Evaluating Functions]] <!-- 1073-Mod 1.1-->
| |
| − | * [[Continuity]] <!-- 1214-2.4 -->
| |
| − | * [[Defining the Derivative|Slope of a Line]] <!-- 1214-3.1 -->
| |
| − | | |
| − | || | |
| − | | |
| − | * Determine if the MVT applies given a function on an interval.
| |
| − | * Find c in the conclusion of the MVT (if algebraically feasible)
| |
| − | * Know the first 3 Corollaries of MVT (especially the 3rd)
| |
| − | | |
| − | | |
| − | | |
| | |- | | |- |
| − | | + | | Week 9 || 4.1 || [[Related Rates]] || || |
| − | | |
| − | |Week 9 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">4.5</div>
| |
| − | | |
| − | || | |
| − |
| |
| − | | |
| − | [[Derivatives and the Shape of a Graph]] | |
| − | | |
| − | ||
| |
| − | | |
| − | * [[Functions|Evaluating Functions]] <!-- 1073-Mod 1.1-->
| |
| − | * [[Maxima and Minima|Critical Points of a Function]] <!-- 1214-4.3 -->
| |
| − | * [[Derivatives and the Shape of a Graph|Second Derivatives]] <!-- 1214-4.5 -->
| |
| − | | |
| − | || | |
| − | | |
| − | * Use the First Derivative Test to find intervals on which the function is increasing and decreasing and the local extrema and their type
| |
| − | * Use the Concavity Test (aka the Second Derivative Test for Concavity) to find the intervals on which the function is concave up and down, and point(s) of inflection
| |
| − | * Understand the shape of the graph, given the signs of the first and second derivatives.
| |
| − | | |
| − | | |
| − | | |
| | |- | | |- |
| − | | + | | Week 9 || 4.3 || [[Maxima and Minima]] || || |
| − | | |
| − | |Week 10 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">4.7</div>
| |
| − | | |
| − | ||
| |
| − |
| |
| − | | |
| − | [[Applied Optimization Problems]]
| |
| − | | |
| − | ||
| |
| − | | |
| − | * '''Formulas pertaining to area and volume''' <!-- Geometry -->
| |
| − | * [[Functions|Evaluating Functions]] <!-- 1073-Mod 1.1-->
| |
| − | * [[Trigonometric Equations]] <!-- 1093-3.3 -->
| |
| − | * [[Maxima and Minima|Critical Points of a Function]] <!-- 1214-4.3 -->
| |
| − | | |
| − | || | |
| − | | |
| − | | |
| − | * Set up a function to be optimized and find the value(s) of the independent variable which provide the optimal solution.
| |
| − | | |
| − | | |
| | |- | | |- |
| − | | + | | Week 10 || 4.4 || [[Mean Value Theorem]] || || |
| − | | |
| − | |Week 10 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">4.8</div>
| |
| − | | |
| − | || | |
| − |
| |
| − | | |
| − | [[L’Hôpital’s Rule]] | |
| − | | |
| − | ||
| |
| − | | |
| − | * [[Rational Functions| Re-expressing Rational Functions ]] <!-- 1073-4 -->
| |
| − | * [[The Limit of a Function|When a Limit is Undefined]] <!-- 1214-2.2 -->
| |
| − | * [[The Derivative as a Function]] <!-- 1214-3.2 -->
| |
| − | | |
| − | || | |
| − | | |
| − | * Identify indeterminate forms produced by quotients, products, subtractions, and powers, and apply L’Hôpital’s rule in each case.
| |
| − | * Recognize when to apply L’Hôpital’s rule.
| |
| − | | |
| − | | |
| − | | |
| | |- | | |- |
| − | | + | | Week 10 || 4.5 || [[Derivatives and the Shape of a Graph]] || || |
| − | | |
| − | |Week 11 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">4.10</div>
| |
| − | | |
| − | || | |
| − |
| |
| − | | |
| − | [[Antiderivatives]] | |
| − | | |
| − | || | |
| − | | |
| − | * [[Inverse Functions]] <!-- 1073-7 -->
| |
| − | * [[The Derivative as a Function]] <!-- 1214-3.2 -->
| |
| − | * [[Differentiation Rule]] <!-- 1214-3.3 -->
| |
| − | * [[Derivatives of the Trigonometric Functions]] <!-- 1214-3.5 -->
| |
| − | | |
| − | || | |
| − | | |
| − | * Find the general antiderivative of a given function.
| |
| − | * Explain the terms and notation used for an indefinite integral.
| |
| − | * State the power rule for integrals.
| |
| − | * Use anti-differentiation to solve simple initial-value problems.
| |
| − | | |
| | |- | | |- |
| − | | + | | Week 11 || 4.7 || [[Applied Optimization Problems]] || || |
| − | | |
| − | |Week 11/12 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">5.1</div>
| |
| − | | |
| − | || | |
| − | | |
| − | [[Approximating Areas]] | |
| − | | |
| − | || | |
| − | | |
| − | * '''[[Sigma notation]]''' <!-- DNE (recommend 1093) -->
| |
| − | * '''[[Area of a rectangle]]''' <!-- Grades 6-12 -->
| |
| − | * [[Continuity]] <!-- 1214-3.5 -->
| |
| − | * [[Toolkit Functions]] <!-- 1073-Mod 1.2 -->
| |
| − | | |
| − | || | |
| − | | |
| − | * Calculate sums and powers of integers.
| |
| − | * Use the sum of rectangular areas to approximate the area under a curve.
| |
| − | * Use Riemann sums to approximate area.
| |
| − | | |
| | |- | | |- |
| − | | + | | Week 12 || 4.8 || [[L’Hôpital’s Rule]] || || |
| − | | |
| − | |Week 12 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">5.2</div>
| |
| − | | |
| − | || | |
| − | | |
| − | [[The Definite Integral]] | |
| − | | |
| − | || | |
| − | | |
| − | * [[Interval Notation|Interval notation]] <!-- 1073-Mod.R -->
| |
| − | * [[Antiderivatives]] <!-- 1214-4.10 -->
| |
| − | * [[The Limit of a Function|Limits of Riemann Sums]] <!-- 1214-2.2 -->
| |
| − | * [[Continuity]] <!-- 1214-3.5 -->
| |
| − | | |
| − | ||
| |
| − | | |
| − | * State the definition of the definite integral.
| |
| − | * Explain the terms integrand, limits of integration, and variable of integration.
| |
| − | * Explain when a function is integrable.
| |
| − | * Rules for the Definite Integral.
| |
| − | * Describe the relationship between the definite integral and net area.
| |
| − | * Use geometry and the properties of definite integrals to evaluate them.
| |
| − | * Calculate the average value of a function.
| |
| − | | |
| | |- | | |- |
| − | | + | | Week 13 || 4.10 || [[Antiderivatives]] || || |
| − | |Week 12/13 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">5.3</div>
| |
| − | | |
| − | || | |
| − |
| |
| − | [[The Fundamental Theorem of Calculus]] | |
| − | | |
| − | || | |
| − | | |
| − | * [[The Derivative as a Function|The Derivative of a Function]] <!-- 1214-2.1 -->
| |
| − | * [[Antiderivatives]] <!-- 1214-4.10 -->
| |
| − | * [[Mean Value Theorem]] <!-- 1214-4.4 -->
| |
| − | * [[Inverse Functions]] <!-- 1073-7 -->
| |
| − | | |
| − | || | |
| − | | |
| − | * Describe the meaning of the Mean Value Theorem for Integrals.
| |
| − | * State the meaning of the Fundamental Theorem of Calculus, Part 1.
| |
| − | * Use the Fundamental Theorem of Calculus, Part 1, to evaluate derivatives of integrals.
| |
| − | * State the meaning of the Fundamental Theorem of Calculus, Part 2.
| |
| − | * Use the Fundamental Theorem of Calculus, Part 2, to evaluate definite integrals.
| |
| − | * Explain the relationship between differentiation and integration.
| |
| − | | |
| | |- | | |- |
| − | | + | | Week 13 || 5.1 || [[Approximating Areas]] || || |
| − | | |
| − | |Week 13 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">5.4</div>
| |
| − | | |
| − | || | |
| − | | |
| − | [[Integration Formulas and the Net Change Theorem]] | |
| − | | |
| − | || | |
| − | | |
| − | * [[Antiderivatives|Indefinite integrals]] <!-- 1214-4.10 -->
| |
| − | * [[The Fundamental Theorem of Calculus|The Fundamental Theorem (part 2)]] <!-- 1214-5.3 -->
| |
| − | | |
| − | ||
| |
| − | | |
| − | * Apply the basic integration formulas.
| |
| − | * Explain the significance of the net change theorem.
| |
| − | * Use the net change theorem to solve applied problems.
| |
| − | * Apply the integrals of odd and even functions.
| |
| − | | |
| − | | |
| | |- | | |- |
| − | | + | | Week 14 || 5.2 || [[The Definite Integral]] || || |
| − | | |
| − | |Week 14 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">5.5</div>
| |
| − | | |
| − | ||
| |
| − | | |
| − | [[Integration by Substitution]]
| |
| − | | |
| − | || | |
| − | | |
| − | * [[The Definite Integral|Solving Basic Integrals]] <!-- 1214-5.2 -->
| |
| − | * [[The Derivative as a Function|The Derivative of a Function]] <!-- 1214-2.1 -->
| |
| − | * '''[[Change of Variables]]''' <!-- DNE (recommend 1073-R) -->
| |
| − | | |
| − | || | |
| − | | |
| − | * Use substitution to evaluate indefinite integrals.
| |
| − | * Use substitution to evaluate definite integrals.
| |
| − | | |
| − | | |
| | |- | | |- |
| − | | + | | Week 15 || 5.3 || [[The Fundamental Theorem of Calculus]] || || |
| − | | |
| − | |Week 14/15 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">5.6</div>
| |
| − | | |
| − | || | |
| − | | |
| − | [[Integrals Involving Exponential and Logarithmic Functions]] | |
| − | | |
| − | || | |
| − | | |
| − | * [[Exponential Functions]] <!-- 1073-8 -->
| |
| − | * [[Logarithmic Functions]] <!-- 1073-8 -->
| |
| − | * [[Differentiation Rules]] <!-- 1214-5.2 -->
| |
| − | * [[Antiderivatives]] <!-- 1214-4.10 -->
| |
| − | | |
| − | || | |
| − | | |
| − | * Integrate functions involving exponential functions.
| |
| − | * Integrate functions involving logarithmic functions.
| |
| − | | |
| | |- | | |- |
| − | | + | | Week 15 || 5.4 || [[Integration Formulas and the Net Change Theorem]] || || |
| − | | |
| − | |Week 15 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">5.7</div>
| |
| − | | |
| − | || | |
| − |
| |
| − | [[Integrals Resulting in Inverse Trigonometric Functions]] | |
| − | | |
| − | ||
| |
| − | | |
| − | * [[The inverse sine, cosine and tangent functions|Trigonometric functions and their inverses]] <!-- 1093-3.1 and 3.2 -->
| |
| − | * [[One-to-one functions|Injective Functions]] <!-- 1073-7 and 1093-1.7-->
| |
| − | * [[The Definite Integral|Rules for Integration]] <!-- 1214-5.2 -->
| |
| − | | |
| − | || | |
| − | | |
| − | * Integrate functions resulting in inverse trigonometric functions.
| |
| − |
| |
| | |} | | |} |
