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| | 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==
| + | {| class="wikitable" |
| − | {| class="wikitable sortable" | |
| | ! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes | | ! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes |
| − |
| |
| | |- | | |- |
| − | | + | | Week 1 || 1.5 || [[Integration by Substitution]] || * [[Differentiation Rules]] || |
| − | | + | * [[Linear Approximations and Differentials]] |
| − | |Week 1 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">1.5</div>
| |
| − | | |
| − | || | |
| − |
| |
| − | [[Integration by Substitution]] | |
| − | | |
| − | || | |
| − | | |
| − | * [[Differentiation Rules]] <!-- 1214-3.3 --> | |
| − | * [[Linear Approximations and Differentials|Differentials]] <!-- 1214-4.2 --> | |
| − | * [[Antiderivatives]] <!-- 1214-4.10 -->
| |
| − | * [[The Definite Integral]] <!-- 1214-5.2 -->
| |
| − | * [[The Fundamental Theorem of Calculus]] <!-- 1214-5.3 -->
| |
| − | | |
| − | ||
| |
| − | | |
| − | * Recognize when to use integration by substitution.
| |
| − | * Use substitution to evaluate indefinite integrals.
| |
| − | * Use substitution to evaluate definite integrals.
| |
| − | | |
| | |- | | |- |
| − | | + | | Week 1 & 2 || 2.1 || [[Area between Curves]] || * [[Toolkit Functions]] || [[Graphing Elementary Functions]] |
| − | | |
| − | |Week 2 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">2.1</div>
| |
| − | | |
| − | || | |
| − |
| |
| − | [[Area between Curves]] | |
| − | | |
| − | || | |
| − | | |
| − | * [[Toolkit Functions|Graphing Elementary Functions]] <!-- 1073-Mod 1.2 --> | |
| − | * [[The Definite Integral]] <!-- 1214-5.2 -->
| |
| − | * [[The Fundamental Theorem of Calculus]] <!-- 1214-5.3 -->
| |
| − | * [[Integration by Substitution]] <!-- 1224-1.5 -->
| |
| − | | |
| − | ||
| |
| − | | |
| − | * Determine the area of a region between two curves by integrating with respect to the independent variable.
| |
| − | * Find the area of a compound region.
| |
| − | * Determine the area of a region between two curves by integrating with respect to the dependent variable.
| |
| − | | |
| | |- | | |- |
| − | | + | | Week 2 || 2.2 || [[Determining Volumes by Slicing]] || * '''[[Areas of basic shapes]]''' || |
| − | | + | * '''[[Volume of a cylinder]]''' |
| − | |Week 2 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">2.2</div>
| |
| − | | |
| − | || | |
| − |
| |
| − | [[Determining Volumes by Slicing]] | |
| − | | |
| − | || | |
| − | | |
| − | * '''[[Areas of basic shapes]]''' <!-- Grades 6-12 --> | |
| − | * '''[[Volume of a cylinder]]''' <!-- Grades 6-12 --> | |
| − | * [[Toolkit Functions|Graphing elementary functions]] <!-- 1073-Mod 1.2 -->
| |
| − | * [[The Fundamental Theorem of Calculus]] <!-- 1214-5.3 -->
| |
| − | * [[Integration by Substitution]] <!-- 1224-1.5 -->
| |
| − | | |
| − | ||
| |
| − | | |
| − | * Determine the volume of a solid by integrating a cross-section (the slicing method).
| |
| − | * Find the volume of a solid of revolution using the disk method.
| |
| − | * Find the volume of a solid of revolution with a cavity using the washer method
| |
| − | | |
| − | | |
| | |- | | |- |
| − | | + | | Week 3 || 2.3 || [[Volumes of Revolution, Cylindrical Shells]] || * [[Toolkit Functions]] || [[Graphing elementary functions]] |
| − | | |
| − | |Week 3 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">2.3</div>
| |
| − | | |
| − | || | |
| − |
| |
| − | [[Volumes of Revolution, Cylindrical Shells]] | |
| − | | |
| − | || | |
| − | | |
| − | * [[Toolkit Functions|Graphing elementary functions]] <!-- 1073-Mod 1.2 --> | |
| − | * [[Determining Volumes by Slicing]] <!-- 1224-2.2 -->
| |
| − | * [[The Fundamental Theorem of Calculus]] <!-- 1214-5.3 -->
| |
| − | * [[Integration by Substitution]] <!-- 1224-1.5 -->
| |
| − | | |
| − | ||
| |
| − | | |
| − | * Calculate the volume of a solid of revolution by using the method of cylindrical shells.
| |
| − | * Compare the different methods for calculating a volume of revolution.
| |
| − | | |
| − | | |
| | |- | | |- |
| − | | + | | Week 3 || 2.4 || [[Arc Length and Surface Area]] || * [[Differentiation Rules]] || |
| − | | + | * [[The Fundamental Theorem of Calculus]] |
| − | |Week 3 | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">2.4</div>
| |
| − | | |
| − | || | |
| − |
| |
| − | [[Arc Length and Surface Area]] | |
| − | | |
| − | || | |
| − | | |
| − | * [[Differentiation Rules]] <!-- 1214-3.3 --> | |
| − | * [[The Fundamental Theorem of Calculus]] <!-- 1214-5.3 --> | |
| − | * [[Integration by Substitution]] <!-- 1224-1.5 -->
| |
| − | | |
| − | ||
| |
| − | | |
| − | * Determine the length of a plane curve between two points.
| |
| − | * Find the surface area of a solid of revolution.
| |
| − | | |
| − | | |
| | |- | | |- |
| − | | + | | Week 4 || 2.5 || [[Physical Applications]] || * '''[[Areas of basic shapes]]''' || |
| − | | + | * '''[[Volume of a cylinder]]''' |
| − | |Week 4 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">2.5</div>
| |
| − | | |
| − | || | |
| − |
| |
| − | [[Physical Applications]] | |
| − | | |
| − | || | |
| − | | |
| − | * '''[[Areas of basic shapes]]''' <!-- Grades 6-12 --> | |
| − | * '''[[Volume of a cylinder]]''' <!-- Grades 6-12 --> | |
| − | * '''[[Basic Physics (Mass, Force, Work, Newton's Second Law, Hooke's Law)]]''' <!-- Grades 6-12 -->
| |
| − | * [[The Fundamental Theorem of Calculus]] <!-- 1214-5.3 -->
| |
| − | * [[Integration by Substitution]] <!-- 1224-1.5 -->
| |
| − | | |
| − | ||
| |
| − | | |
| − | * Determine the mass of a one-dimensional object from its linear density function.
| |
| − | * Determine the mass of a two-dimensional circular object from its radial density function.
| |
| − | * Calculate the work done by a variable force acting along a line.
| |
| − | * Calculate the work done in stretching/compressing a spring.
| |
| − | * Calculate the work done in lifting a rope/cable.
| |
| − | * Calculate the work done in pumping a liquid from one height to another.
| |
| − | * Find the hydrostatic force against a submerged vertical plate.
| |
| − | | |
| − | | |
| | |- | | |- |
| − | | + | | Week 4 & 5 || 2.6 || [[Moments and Center of Mass]] || * [[Toolkit Functions]] || [[Graphing elementary functions]] |
| − | | |
| − | |Week 4 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">2.6</div>
| |
| − | | |
| − | || | |
| − | | |
| − | [[Moments and Center of Mass]] | |
| − | | |
| − | || | |
| − | | |
| − | * [[Toolkit Functions|Graphing elementary functions]] <!-- 1073-Mod 1.2 --> | |
| − | * [[The Fundamental Theorem of Calculus]] <!-- 1214-5.3 -->
| |
| − | * [[Integration by Substitution]] <!-- 1224-1.5 -->
| |
| − | | |
| − | ||
| |
| − | | |
| − | * Find the center of mass of objects distributed along a line.
| |
| − | * Find the center of mass of objects distributed in a plane.
| |
| − | * Locate the center of mass of a thin plate.
| |
| − | * Use symmetry to help locate the centroid of a thin plate.
| |
| − | | |
| | |- | | |- |
| − | | + | | Week 5 || 3.1 || [[Integration by Parts]] || * [[Differentiation Rules]] || |
| − | | + | * [[Linear Approximations and Differentials]] |
| − | |Week 5 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">3.1</div>
| |
| − | | |
| − | || | |
| − | | |
| − | [[Integration by Parts]] | |
| − | | |
| − | || | |
| − | | |
| − | * [[Differentiation Rules]] <!-- 1214-3.3 --> | |
| − | * [[Linear Approximations and Differentials|Differentials]] <!-- 1214-4.2 --> | |
| − | * [[The Fundamental Theorem of Calculus]] <!-- 1214-5.3 -->
| |
| − | * [[Integration by Substitution]] <!-- 1224-1.5 -->
| |
| − | | |
| − | ||
| |
| − | | |
| − | * Recognize when to use integration by parts.
| |
| − | * Use the integration-by-parts formula to evaluate indefinite integrals.
| |
| − | * Use the integration-by-parts formula to evaluate definite integrals.
| |
| − | * Use the tabular method to perform integration by parts.
| |
| − | * Solve problems involving applications of integration using integration by parts.
| |
| − | | |
| | |- | | |- |
| − | | + | | Week 6 || 3.2 || [[Trigonometric Integrals]] || * [[Trigonometric Functions]] || |
| − | | + | * [[Properties of the Trigonometric Functions]] |
| − | |Week 5 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">3.2</div>
| |
| − | | |
| − | || | |
| − | | |
| − | [[Trigonometric Integrals]] | |
| − | | |
| − | || | |
| − | | |
| − | * [[Trigonometric Functions]] <!-- 1093-2.2 --> | |
| − | * [[Properties of the Trigonometric Functions|Trigonometric Identities]] <!-- 1093-3.4 --> | |
| − | * [[The Fundamental Theorem of Calculus]] <!-- 1214-5.3 -->
| |
| − | * [[Integration by Substitution]] <!-- 1224-1.5 -->
| |
| − | * [[Integration by Parts]] <!-- 1224-3.1 -->
| |
| − | | |
| − | ||
| |
| − | | |
| − | * Evaluate integrals involving products and powers of sin(x) and cos(x).
| |
| − | * Evaluate integrals involving products and powers of sec(x) and tan(x).
| |
| − | * Evaluate integrals involving products of sin(ax), sin(bx), cos(ax), and cos(bx).
| |
| − | * Solve problems involving applications of integration using trigonometric integrals.
| |
| − | | |
| | |- | | |- |
| − | | + | | Week 6 & 7 || 3.3 || [[Trigonometric Substitution]] || * [[Completing the Square]] || |
| − | | + | * [[Trigonometric Functions]] |
| − | |Week 6 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">3.3</div>
| |
| − | | |
| − | || | |
| − | | |
| − | [[Trigonometric Substitution]] | |
| − | | |
| − | || | |
| − | | |
| − | * [[Completing the Square]] <!-- 1073-Mod 3.2--> | |
| − | * [[Trigonometric Functions]] <!-- 1093-2.2 --> | |
| − | * [[Properties of the Trigonometric Functions|Trigonometric Identities]] <!-- 1093-3.4 -->
| |
| − | * [[Integration by Substitution]] <!-- 1224-1.5 -->
| |
| − | * [[Integration by Parts]] <!-- 1224-3.1 -->
| |
| − | * [[Trigonometric Integrals]] <!-- 1224-3.2 -->
| |
| − | | |
| − | ||
| |
| − | | |
| − | * Evaluate integrals involving the square root of a sum or difference of two squares.
| |
| − | * Solve problems involving applications of integration using trigonometric substitution.
| |
| − | | |
| − | | |
| | |- | | |- |
| − | | + | | Week 7 || 3.4 || [[Partial Fractions]] || * [[Factoring Polynomials]] || |
| − | | + | * [[Completing the Square]] |
| − | |Week 6 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">3.4</div>
| |
| − | | |
| − | || | |
| − | | |
| − | [[Partial Fractions]] | |
| − | | |
| − | || | |
| − | | |
| − | * [[Factoring Polynomials]] <!-- 1073-Mod 0.2 --> | |
| − | * [[Completing the Square]] <!-- 1073-Mod 3.2--> | |
| − | * [[Dividing Polynomials|Long Division of Polynomials]] <!-- 1073-Mod 4.1 -->
| |
| − | * [[Systems of Linear Equations]] <!-- 1073-Mod 12.1 and 12.2 -->
| |
| − | * [[Antiderivatives]] <!-- 1214-4.10 -->
| |
| − | * [[Integration by Substitution]] <!-- 1224-1.5 -->
| |
| − | | |
| − | ||
| |
| − | | |
| − | * Integrate a rational function whose denominator is a product of linear and quadratic polynomials.
| |
| − | * Recognize distinct linear factors in a rational function.
| |
| − | * Recognize repeated linear factors in a rational function.
| |
| − | * Recognize distinct irreducible quadratic factors in a rational function.
| |
| − | * Recognize repeated irreducible quadratic factors in a rational function.
| |
| − | * Solve problems involving applications of integration using partial fractions.
| |
| − | | |
| | |- | | |- |
| − | | + | | Week 8 || 3.7 || [[Improper Integrals]] || * [[The Fundamental Theorem of Calculus]] || |
| − | | + | * [[Integration by Substitution]] |
| − | |Week 7 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">3.7</div>
| |
| − | | |
| − | || | |
| − | | |
| − | [[Improper Integrals]] | |
| − | | |
| − | || | |
| − | | |
| − | * [[The Fundamental Theorem of Calculus]] <!-- 1214-5.3 --> | |
| − | * [[Integration by Substitution]] <!-- 1224-1.5 -->
| |
| − | * [[Integration by Parts]] <!-- 1224-3.1 --> | |
| − | * [[Trigonometric Integrals]] <!-- 1224-3.2 -->
| |
| − | * [[Trigonometric Substitution]] <!-- 1224-3.3 -->
| |
| − | * [[Partial Fractions]] <!-- 1224-3.4 -->
| |
| − | * [[The Limit Laws]] <!-- 1214-2.3 -->
| |
| − | * [[Limits at Infinity and Asymptotes| Limits at Infinity]] <!-- 1224-4.6 -->
| |
| − | * [[L’Hôpital’s Rule]] <!-- 1214-4.8 -->
| |
| − | | |
| − | ||
| |
| − | | |
| − | * Recognize improper integrals and determine their convergence or divergence.
| |
| − | * Evaluate an integral over an infinite interval.
| |
| − | * Evaluate an integral over a closed interval with an infinite discontinuity within the interval.
| |
| − | * Use the comparison theorem to determine whether an improper integral is convergent or divergent.
| |
| − | | |
| | |- | | |- |
| − | | + | | Week 9 || 5.1 || [[Sequences]] || * [[The Limit Laws]] || [[The Limit Laws and Squeeze Theorem]] |
| − | | |
| − | |Week 8 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">4.3</div>
| |
| − | | |
| − | || | |
| − | | |
| − | [[Separation of Variables]] | |
| − | | |
| − | || | |
| − | | |
| − | * [[Factoring Polynomials]] <!-- 1073-Mod 0.2 --> | |
| − | * [[Exponential Properties]] <!-- 1073-Mod 9.1 -->
| |
| − | * [[Logarithmic Properties]] <!-- 1073-Mod 10.2 -->
| |
| − | * [[Linear Approximations and Differentials|Differentials]] <!-- 1214-4.2 -->
| |
| − | * [[Initial Value Problem]] <!-- 1214-4.10 -->
| |
| − | * [[Integration by Substitution]] <!-- 1224-1.5 -->
| |
| − | * [[Integration by Parts]] <!-- 1224-3.1 -->
| |
| − | * [[Trigonometric Integrals]] <!-- 1224-3.2 -->
| |
| − | * [[Trigonometric Substitution]] <!-- 1224-3.3 -->
| |
| − | * [[Partial Fractions]] <!-- 1224-3.4 -->
| |
| − | | |
| − | ||
| |
| − | | |
| − | * Recognize separable differential equations.
| |
| − | * Use separation of variables to solve a differential equation.
| |
| − | * Develop and analyze elementary mathematical models.
| |
| − | | |
| | |- | | |- |
| − | | + | | Week 10 || 5.2 || [[Infinite Series]] || * '''[[Sigma notation]]''' || |
| − | | + | * [[Sequences]] |
| − | |Week 8 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">4.5</div>
| |
| − | | |
| − | || | |
| − | | |
| − | [[First-Order Linear Equations]] | |
| − | | |
| − | || | |
| − | | |
| − | * [[Separation of Variables]] <!-- 1224-4.3 --> | |
| − | | |
| − | || | |
| − | | |
| − | * Write a first-order linear differential equation in standard form. | |
| − | * Find an integrating factor and use it to solve a first-order linear differential equation.
| |
| − | * Solve applied problems involving first-order linear differential equations.
| |
| − | | |
| | |- | | |- |
| − | | + | | Week 11 || 5.3 || [[The Divergence and Integral Tests]] || * [[The Limit Laws]] || |
| − | | + | * [[Limits at Infinity and Asymptotes]] |
| − | |Week 9 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">5.1</div>
| |
| − | | |
| − | || | |
| − | | |
| − | [[Sequences]] | |
| − | | |
| − | || | |
| − | | |
| − | * [[The Limit Laws| The Limit Laws and Squeeze Theorem]] <!-- 1214-2.3 --> | |
| − | * [[Limits at Infinity and Asymptotes| Limits at Infinity]] <!-- 1214-4.6 --> | |
| − | * [[L’Hôpital’s Rule]] <!-- 1214-4.8 -->
| |
| − | * [[Derivatives and the Shape of a Graph| Increasing and Decreasing Functions]] <!-- 1214-4.5 -->
| |
| − | | |
| − | ||
| |
| − | | |
| − | * Find a formula for the general term of a sequence.
| |
| − | * Find a recursive definition of a sequence.
| |
| − | * Determine the convergence or divergence of a given sequence.
| |
| − | * Find the limit of a convergent sequence.
| |
| − | * Determine whether a sequence is bounded and/or monotone.
| |
| − | * Apply the Monotone Convergence Theorem.
| |
| − | | |
| | |- | | |- |
| − | | + | | Week 11 || 5.4 || [[Comparison Tests]] || * [[Limits at Infinity and Asymptotes]] || [[Limits at Infinity]] |
| − | | |
| − | |Week 10 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">5.2</div>
| |
| − | | |
| − | || | |
| − | | |
| − | [[Infinite Series]] | |
| − | | |
| − | || | |
| − | | |
| − | * '''[[Sigma notation]]''' <!-- DNE (recommend 1093) --> | |
| − | * [[Sequences]] <!-- 10224-5.1-->
| |
| − | * [[Partial Fractions]] <!-- 1224-3.4-->
| |
| − | | |
| − | ||
| |
| − | | |
| − | * Write an infinite series using sigma notation.
| |
| − | * Find the nth partial sum of an infinite series.
| |
| − | * Define the convergence or divergence of an infinite series.
| |
| − | * Identify a geometric series.
| |
| − | * Apply the Geometric Series Test.
| |
| − | * Find the sum of a convergent geometric series.
| |
| − | * Identify a telescoping series.
| |
| − | * Find the sum of a telescoping series.
| |
| − | | |
| | |- | | |- |
| − | | + | | Week 12 || 5.5 || [[Alternating Series]] || * [[Limits at Infinity and Asymptotes]] || [[Limits at Infinity]] |
| − | | |
| − | |Week 10 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">5.3</div>
| |
| − | | |
| − | || | |
| − | | |
| − | [[The Divergence and Integral Tests]] | |
| − | | |
| − | || | |
| − | | |
| − | * [[The Limit Laws]] <!-- 1214-2.3 -->
| |
| − | * [[Limits at Infinity and Asymptotes| Limits at Infinity]] <!-- 1214-4.6 --> | |
| − | * [[Continuity]] <!-- 1214-3.5 -->
| |
| − | * [[Derivatives and the Shape of a Graph| Increasing and Decreasing Functions]] <!-- 1214-4.5 -->
| |
| − | * [[L’Hôpital’s Rule]] <!-- 1214-4.8 -->
| |
| − | * [[Improper Integrals]] <!-- 1224-3.7 -->
| |
| − | | |
| − | ||
| |
| − | | |
| − | * Use the Divergence Test to determine whether a series diverges.
| |
| − | * Use the Integral Test to determine whether a series converges or diverges.
| |
| − | * Use the p-Series Test to determine whether a series converges or diverges.
| |
| − | * Estimate the sum of a series by finding bounds on its remainder term.
| |
| − | | |
| | |- | | |- |
| − | | + | | Week 12 || 5.6 || [[Ratio and Root Tests]] || * '''[[Factorials]]''' || |
| − | | + | * [[Limits at Infinity and Asymptotes]] |
| − | |Week 11 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">5.4</div>
| |
| − | | |
| − | || | |
| − | | |
| − | [[Comparison Tests]] | |
| − | | |
| − | || | |
| − | | |
| − | * [[Limits at Infinity and Asymptotes|Limits at Infinity]] <!-- 1214-4.6--> | |
| − | * [[Derivatives and the Shape of a Graph|Increasing and Decreasing Functions]] <!-- 1214-4.5 -->
| |
| − | * [[L’Hôpital’s Rule]] <!-- 1214-4.8 -->
| |
| − | * [[Infinite Series|The Geometric Series Test]] <!-- 1224-5.2 -->
| |
| − | * [[The Divergence and Integral Tests|The p-Series Test]] <!-- 1224-5.3 --> | |
| − | | |
| − | ||
| |
| − | | |
| − | * Use the Direct Comparison Test to determine whether a series converges or diverges.
| |
| − | * Use the Limit Comparison Test to determine whether a series converges or diverges.
| |
| − | | |
| | |- | | |- |
| − | | + | | Week 13 || 6.1 || [[Power Series and Functions]] || * [[Infinite Series]] || [[The Geometric Series Test]] |
| − | | |
| − | |Week 11 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">5.5</div>
| |
| − | | |
| − | || | |
| − | | |
| − | [[Alternating Series]] | |
| − | | |
| − | || | |
| − | | |
| − | * [[Limits at Infinity and Asymptotes|Limits at Infinity]] <!-- 1214-4.6--> | |
| − | * [[Derivatives and the Shape of a Graph|Increasing and Decreasing Functions]] <!-- 1214-4.5 -->
| |
| − | * [[L’Hôpital’s Rule]] <!-- 1214-4.8 -->
| |
| − | * [[Infinite Series|The Geometric Series Test]] <!-- 1224-5.2 -->
| |
| − | * [[The Divergence and Integral Tests|The p-Series Test]] <!-- 1224-5.3 -->
| |
| − | * [[Comparison Tests]] <!-- 1224-5.4 -->
| |
| − | | |
| − | ||
| |
| − | | |
| − | * Use the Alternating Series Test to determine the convergence of an alternating series.
| |
| − | * Estimate the sum of an alternating series.
| |
| − | * Explain the meaning of absolute convergence and conditional convergence.
| |
| − | | |
| − | | |
| | |- | | |- |
| − | | + | | Week 14 || 6.2 || [[Properties of Power Series]] || * [[Differentiation Rules]] || |
| − | | + | * [[Antiderivatives]] |
| − | |Week 12 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">5.6</div>
| |
| − | | |
| − | || | |
| − | | |
| − | [[Ratio and Root Tests]] | |
| − | | |
| − | || | |
| − | | |
| − | * '''[[Factorials]]''' <!-- Grades 6-12 --> | |
| − | * [[Limits at Infinity and Asymptotes|Limits at Infinity]] <!-- 1214-4.6-->
| |
| − | * [[L’Hôpital’s Rule]] <!-- 1214-4.8 --> | |
| − | | |
| − | ||
| |
| − | | |
| − | * Use the Ratio Test to determine absolute convergence or divergence of a series.
| |
| − | * Use the Root Test to determine absolute convergence or divergence of a series.
| |
| − | * Describe a strategy for testing the convergence or divergence of a series.
| |
| − | | |
| | |- | | |- |
| − | | + | | Week 15 || 6.3 || [[Taylor and Maclaurin Series]] || * [[The Derivative as a Function]] || [[Higher-Order Derivatives]] |
| − | |Week 12 | |
| − | | |
| − | ||
| |
| − | | |
| − | <div style="text-align: center;">6.1</div>
| |
| − | | |
| − | ||
| |
| − |
| |
| − | [[Power Series and Functions]]
| |
| − | | |
| − | ||
| |
| − | | |
| − | * [[Infinite Series|The Geometric Series Test]] <!-- 1224-5.2 -->
| |
| − | * [[The Divergence and Integral Tests]] <!-- 1224-5.3 -->
| |
| − | * [[Comparison Tests]] <!-- 1224-5.4 -->
| |
| − | * [[Alternating Series]] <!-- 1224-5.5 -->
| |
| − | * [[Ratio and Root Tests]] <!-- 1224-5.6 -->
| |
| − | | |
| − | ||
| |
| − | | |
| − | * Identify a power series.
| |
| − | * Determine the interval of convergence and radius of convergence of a power series.
| |
| − | * Use a power series to represent certain functions.
| |
| − | | |
| − | |-
| |
| − | | |
| − | | |
| − | |Week 13
| |
| − | | |
| − | ||
| |
| − | | |
| − | <div style="text-align: center;">6.2</div>
| |
| − | | |
| − | ||
| |
| − | | |
| − | [[Properties of Power Series]]
| |
| − | | |
| − | ||
| |
| − | | |
| − | * [[Differentiation Rules]] <!-- 1214-3.3 -->
| |
| − | * [[Antiderivatives]] <!-- 1214-4.10 -->
| |
| − | * [[The Fundamental Theorem of Calculus]] <!-- 1214-5.3 -->
| |
| − | * [[Power Series and Functions]] <!-- 1224-6.1 -->
| |
| − | | |
| − | ||
| |
| − | | |
| − | * Combine power series by addition or subtraction.
| |
| − | * Multiply two power series together.
| |
| − | * Differentiate and integrate power series term-by-term.
| |
| − | * Use differentiation and integration of power series to represent certain functions as power series.
| |
| − | | |
| − | |- | |
| − | | |
| − | | |
| − | |Week 14 | |
| − | | |
| − | ||
| |
| − | | |
| − | <div style="text-align: center;">6.3</div>
| |
| − | | |
| − | || | |
| − | | |
| − | [[Taylor and Maclaurin Series]] | |
| − | | |
| − | || | |
| − | | |
| − | * [[The Derivative as a Function|Higher-Order Derivatives]] <!-- 1214-3.2 --> | |
| − | * [[Power Series and Functions]] <!-- 1224-6.1 -->
| |
| − | * [[Properties of Power Series]] <!-- 1224-6.2 -->
| |
| − | | |
| − | || | |
| − | | |
| − | * Find a Taylor or Maclaurin series representation of a function.
| |
| − | * Find the radius of convergence of a Taylor Series or Maclaurin series.
| |
| − | * Finding a Taylor polynomial of a given order for a function.
| |
| − | * Use Taylor's Theorem to estimate the remainder for a Taylor series approximation of a given function.
| |
| − | | |
| − | |-
| |
| − | | |
| − | | |
| − | |Week 15
| |
| − | | |
| − | ||
| |
| − | | |
| − | <div style="text-align: center;">7.1</div>
| |
| − | | |
| − | ||
| |
| − | | |
| − | [[Parametric Equations]]
| |
| − | | |
| − | ||
| |
| − | | |
| − | * [[Toolkit Functions|Sketching Elementary Functions]] <!-- 1073-Mod 1.2 -->
| |
| − | * '''[[Equation of a Circle]]''' <!-- Grades 6-12 -->
| |
| − | * '''[[Equation of an Ellipse]]''' <!-- Grades 6-12 -->
| |
| − | * [[Trigonometric Functions]] <!-- 1093-2.2 -->
| |
| − | * [[Properties of the Trigonometric Functions|Trigonometric Identities]] <!-- 1093-3.4 -->
| |
| − | | |
| − | ||
| |
| − | | |
| − | * Plot a curve described by parametric equations.
| |
| − | * Convert the parametric equations of a curve into the form y=f(x) by eliminating the parameter.
| |
| − | * Recognize the parametric equations of basic curves, such as a line and a circle.
| |
| − | | |
| − | |-
| |
| − | | |
| − | | |
| − | |Week 15
| |
| − | | |
| − | ||
| |
| − | | |
| − | <div style="text-align: center;">7.2</div>
| |
| − | | |
| − | ||
| |
| − | | |
| − | [[The Calculus of Parametric Equations]]
| |
| − | | |
| − | ||
| |
| − | | |
| − | * [[Parametric Equations]] <!-- 1224-7.1 -->
| |
| − | * [[Differentiation Rules]] <!-- 1214-3.3 -->
| |
| − | * [[The Derivative as a Function|Higher-Order Derivatives]] <!-- 1214-3.2 -->
| |
| − | * [[The Fundamental Theorem of Calculus]] <!-- 1214-5.3 -->
| |
| − | * [[Integration by Substitution]] <!-- 1224-1.5 -->
| |
| − | * [[Integration by Parts]] <!-- 1224-3.1 -->
| |
| − | | |
| − | ||
| |
| − | | |
| − | * Find the slope of the tangent line to a parametric curve at a point.
| |
| − | * Use the second derivative to determine the concavity of a parametric curve at a point.
| |
| − | * Determine the area bounded by a parametric curve.
| |
| − | * Determine the arc length of a parametric curve.
| |
| − | * Determine the area of a surface obtained by rotating a parametric curve about an axis.
| |
| − | | |
| | |} | | |} |
