Difference between revisions of "MAT1223"
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==Topics List== | ==Topics List== | ||
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− | |Week 2 | + | |Week 1/2 |
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− | |Week 2 | + | |Week 2/3 |
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− | * | + | * [[Areas of basic shapes]] <!-- Grades 6-12 --> |
− | * | + | * [[Volume of a cylinder]] <!-- Grades 6-12 --> |
* [[Toolkit Functions|Graphing elementary functions]] <!-- 1073-Mod 1.2 --> | * [[Toolkit Functions|Graphing elementary functions]] <!-- 1073-Mod 1.2 --> | ||
* [[The Fundamental Theorem of Calculus]] <!-- 1214-5.3 --> | * [[The Fundamental Theorem of Calculus]] <!-- 1214-5.3 --> | ||
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* Determine the volume of a solid by integrating a cross-section (the slicing method). | * 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 using the disk method. | ||
− | * Find the volume of a solid of revolution with a cavity using the washer method | + | * Find the volume of a solid of revolution with a cavity using the washer method. |
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− | |Week 3 | + | |Week 3 |
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* Calculate the volume of a solid of revolution by using the method of cylindrical shells. | * 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. | * Compare the different methods for calculating a volume of revolution. | ||
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− | * | + | * [[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 --> | * [[The Fundamental Theorem of Calculus]] <!-- 1214-5.3 --> | ||
* [[Integration by Substitution]] <!-- 1224-1.5 --> | * [[Integration by Substitution]] <!-- 1224-1.5 --> | ||
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* Calculate the work done by a variable force acting along a line. | * 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 stretching/compressing a spring. | ||
* Calculate the work done in lifting a rope/cable. | * Calculate the work done in lifting a rope/cable. | ||
* Calculate the work done in pumping a liquid from one height to another. | * Calculate the work done in pumping a liquid from one height to another. | ||
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* Use the tabular method to perform integration by parts. | * Use the tabular method to perform integration by parts. | ||
* Solve problems involving applications of integration using integration by parts. | * Solve problems involving applications of integration using integration by parts. | ||
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− | |Week | + | |Week 6 |
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* Evaluate integrals involving products and powers of sin(x) and cos(x). | * 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 and powers of sec(x) and tan(x). | ||
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* Solve problems involving applications of integration using trigonometric integrals. | * Solve problems involving applications of integration using trigonometric integrals. | ||
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− | |Week 6 | + | |Week 6/7 |
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+ | * Recognize when to use trigonometric substitution. | ||
* Evaluate integrals involving the square root of a sum or difference of two squares. | * Evaluate integrals involving the square root of a sum or difference of two squares. | ||
* Solve problems involving applications of integration using trigonometric substitution. | * Solve problems involving applications of integration using trigonometric substitution. | ||
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− | |Week | + | |Week 7/8 |
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+ | * Recognize when to use partial fraction decomposition. | ||
* Integrate a rational function whose denominator is a product of linear and quadratic polynomials. | * Integrate a rational function whose denominator is a product of linear and quadratic polynomials. | ||
* Recognize distinct linear factors in a rational function. | * Recognize distinct linear factors in a rational function. | ||
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− | |Week | + | |Week 8 |
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* Evaluate an integral over a closed interval with an infinite discontinuity within the 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. | * Use the comparison theorem to determine whether an improper integral is convergent or divergent. | ||
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* Find a recursive definition of a sequence. | * Find a recursive definition of a sequence. | ||
* Determine the convergence or divergence of a given sequence. | * Determine the convergence or divergence of a given sequence. | ||
− | * Find the limit of a convergent sequence. | + | * Find the limit of a convergent sequence. |
* Determine whether a sequence is bounded and/or monotone. | * Determine whether a sequence is bounded and/or monotone. | ||
* Apply the Monotone Convergence Theorem. | * Apply the Monotone Convergence Theorem. | ||
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− | * | + | * [[Sigma notation]] <!-- DNE (recommend 1093) --> |
* [[Sequences]] <!-- 10224-5.1--> | * [[Sequences]] <!-- 10224-5.1--> | ||
* [[Partial Fractions]] <!-- 1224-3.4--> | * [[Partial Fractions]] <!-- 1224-3.4--> | ||
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* Find the sum of a convergent geometric series. | * Find the sum of a convergent geometric series. | ||
* Identify a telescoping series. | * Identify a telescoping series. | ||
− | * Find the sum of a telescoping series. | + | * Find the sum of a convergent telescoping series. |
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− | |Week 10 | + | |Week 10/11 |
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* Use the Integral Test to determine whether a series converges or 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. | * Use the p-Series Test to determine whether a series converges or diverges. | ||
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− | |Week 11 | + | |Week 11 |
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* Use the Alternating Series Test to determine the convergence of an alternating series. | * Use the Alternating Series Test to determine the convergence of an alternating series. | ||
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* Explain the meaning of absolute convergence and conditional convergence. | * Explain the meaning of absolute convergence and conditional convergence. | ||
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− | * | + | * [[Factorials]] <!-- Grades 6-12 --> |
* [[Limits at Infinity and Asymptotes|Limits at Infinity]] <!-- 1214-4.6--> | * [[Limits at Infinity and Asymptotes|Limits at Infinity]] <!-- 1214-4.6--> | ||
* [[L’Hôpital’s Rule]] <!-- 1214-4.8 --> | * [[L’Hôpital’s Rule]] <!-- 1214-4.8 --> | ||
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− | |Week | + | |Week 13 |
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− | |Week | + | |Week 14 |
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* Differentiate and integrate power series term-by-term. | * Differentiate and integrate power series term-by-term. | ||
* Use differentiation and integration of power series to represent certain functions as power series. | * Use differentiation and integration of power series to represent certain functions as power series. | ||
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− | |Week 14 | + | |Week 14/15 |
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* Find a Taylor or Maclaurin series representation of a function. | * Find a Taylor or Maclaurin series representation of a function. | ||
* Find the radius of convergence of a Taylor Series or Maclaurin series. | * Find the radius of convergence of a Taylor Series or Maclaurin series. | ||
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Latest revision as of 09:34, 11 June 2024
Topics List
Date | Sections | Topics | Prerequisite Skills | Student Learning Outcomes |
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Week 1 |
1.5
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Week 1/2 |
2.1
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Week 2/3 |
2.2
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Week 3 |
2.3
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Week 4 |
2.5
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Week 5 |
3.1
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Week 6 |
3.2
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Week 6/7 |
3.3
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Week 7/8 |
3.4
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Week 8 |
3.7
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Week 9 |
5.1
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Week 10 |
5.2
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Week 10/11 |
5.3
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Week 11 |
5.4
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Week 12 |
5.5
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Week 12 |
5.6
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Week 13 |
6.1
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Week 14 |
6.2
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Week 14/15 |
6.3
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