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+ | The textbook for this course is | ||
+ | [https://openstax.org/details/books/calculus-volume-3 Calculus (Volume 3) by Gilbert Strang, Edwin Herman, et al.] | ||
+ | |||
==Topics List== | ==Topics List== | ||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes | ! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes | ||
− | |||
|- | |- | ||
− | |Week | + | |Week 1 |
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− | + | 1.1 | |
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Line 17: | Line 17: | ||
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− | + | * [[Trigonometric Functions: Unit Circle Approach]] | |
− | * [[Trigonometric Functions: Unit Circle Approach]] | + | * [[Inverse Trigonometric Functions]] |
− | * [[ | ||
− | |||
|| | || | ||
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* Plot points using polar coordinates and find several polar coordinates of a single point | * Plot points using polar coordinates and find several polar coordinates of a single point | ||
* Convert polar coordinates to rectangular coordinates and vice versa | * Convert polar coordinates to rectangular coordinates and vice versa | ||
* Transform equations from polar form to rectangular form and vice versa | * Transform equations from polar form to rectangular form and vice versa | ||
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− | |||
|- | |- | ||
− | |Week | + | |Week 1 |
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− | + | 1.2 | |
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Line 44: | Line 37: | ||
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− | * [[ | + | * [[Two-dimensional coordinate systems]] |
− | * [[Solving Equations| Algebraic Expressions]] | + | * [[Solving Equations and Inequalities| Algebraic Expressions]] |
Line 51: | Line 44: | ||
|| | || | ||
− | * Three-dimensional coordinate systems | + | * Three-dimensional coordinate systems. |
− | * Distance Formula in | + | * Distance Formula in Space. |
− | * Standard Equation for a Sphere | + | * Standard Equation for a Sphere. |
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|- | |- | ||
− | |Weeks | + | |Weeks 1/2 |
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− | + | 2.1 | |
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− | [[Vectors in The Plane]] | + | [[Vectors in The Plane, Space]] |
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− | * [[Linear Equations|Line Segments]] | + | * [[Linear Equations|Line Segments]] |
− | * [[Distance Formula| Distance Formula]] | + | * [[Distance Formula| Distance Formula]] |
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Line 82: | Line 71: | ||
* The Midpoint of a Line Segment | * The Midpoint of a Line Segment | ||
* The Vector projection | * The Vector projection | ||
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|- | |- | ||
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− | | | + | |Week 2 |
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− | + | 2.3 | |
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Line 127: | Line 86: | ||
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− | * [[ | + | * [[Trigonometric Functions|Basic Trig Functions]] |
− | * [[Vectors]] | + | * [[Vectors]] |
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Line 139: | Line 98: | ||
− | |Week | + | |Week 2 |
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− | + | 2.4 | |
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Line 151: | Line 108: | ||
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− | * [[ | + | * [[Trigonometric Functions|Basic Trig Functions]] |
− | * [[Determinants]] | + | * [[Determinants]] |
* [[Vectors]] | * [[Vectors]] | ||
Line 161: | Line 118: | ||
* Area of a parallelogram | * Area of a parallelogram | ||
* Cross product as a determinant | * Cross product as a determinant | ||
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Line 170: | Line 124: | ||
− | |Week | + | |Week 3 |
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− | + | 2.5 | |
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Line 183: | Line 135: | ||
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− | * [[The Dot Product]] | + | * [[The Dot Product]] |
* [[The Cross Product]] | * [[The Cross Product]] | ||
− | * [[Quadratic Functions]] | + | * [[Quadratic Functions]] |
− | * [[Parametric Equations]] | + | * [[Parametric Equations]] |
|| | || | ||
Line 195: | Line 147: | ||
* Find the distance from a point to a given plane. | * Find the distance from a point to a given plane. | ||
− | |||
|- | |- | ||
− | |Week | + | |Week 3 |
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− | + | 2.6 | |
− | |||
− | |||
|| | || | ||
− | [[Cylinders and Quadratic Surfaces]] | + | [[Equations of Lines, Planes and Surfaces in Space|Cylinders and Quadratic Surfaces]] |
|| | || | ||
− | * [[Quadratic Functions]] | + | * [[Quadratic Functions]] |
− | * [[Parametric Equations]] | + | * [[Parametric Equations]] |
− | * | + | * [[Conics]] |
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Line 222: | Line 171: | ||
* Understand basic quadratic surfaces | * Understand basic quadratic surfaces | ||
* Understand general quadratic surfaces | * Understand general quadratic surfaces | ||
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Line 231: | Line 176: | ||
− | |Weeks | + | |Weeks 3/4 |
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− | + | 3.1, 3.2 | |
− | |||
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Line 243: | Line 186: | ||
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− | * [[Parametric Equations]] | + | * [[Parametric Equations]] |
− | * [[Vectors]] | + | * [[Vectors]] |
− | * [[The Derivative as a Function]] | + | * [[The Derivative as a Function]] |
− | * [[The Limit of a Function]] | + | * [[The Limit of a Function]] |
− | * [[Continuity | + | * [[Continuity]] |
− | * [[The Dot Product]] | + | * [[The Dot Product]] |
− | * [[The Cross Product]] | + | * [[The Cross Product]] |
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Line 258: | Line 201: | ||
* Differentiation rules for vector functions | * Differentiation rules for vector functions | ||
* Curves and paths in space | * Curves and paths in space | ||
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Line 266: | Line 207: | ||
− | |Week | + | |Week 4 |
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− | + | 3.3 | |
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Line 278: | Line 217: | ||
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− | * | + | * [[Distance Formula| The Length of a Line Segment]] |
− | * [[Curves in Space and Vector Functions|Vector Functions]] | + | * [[Curves in Space and Vector-Valued Functions|Vector Functions]] |
− | * [[Integrals of Vector Functions]] | + | * [[Line Integrals|Integrals of Vector Functions]], [[Derivatives of Vector Functions]] |
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Line 286: | Line 225: | ||
* The arc Length of a vector function | * The arc Length of a vector function | ||
* Arc length parameterization | * Arc length parameterization | ||
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|- | |- | ||
Line 294: | Line 230: | ||
− | |Weeks | + | |Weeks 4/5 |
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− | + | 3.4 | |
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Line 305: | Line 239: | ||
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− | * [[Vectors]] | + | * [[Vectors]] |
− | * [[Parametric Equations]] | + | * [[Parametric Equations]] |
− | * [[The Cross Product]] | + | * [[The Cross Product]] |
− | * [[Derivatives of Vector Functions]] | + | * [[Derivatives of Vector Functions]] |
|| | || | ||
* The Unit tangent vector | * The Unit tangent vector | ||
Line 316: | Line 250: | ||
* The tangential and normal components of acceleration | * The tangential and normal components of acceleration | ||
* The Torsion | * The Torsion | ||
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− | |||
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|- | |- | ||
Line 324: | Line 255: | ||
− | |Week | + | |Week 5/6 |
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− | + | 4.1 | |
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Line 337: | Line 266: | ||
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− | * [[Domain of a Function]] | + | * [[Domain of a Function]] |
− | * [[Range of a Function]] | + | * [[Range of a Function]] |
− | * [[Solving Inequalities]] | + | * [[Solving Equations and Inequalities]] |
− | * [[Graphs| Graphing a Function]] | + | * [[Graphs| Graphing a Function]] |
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Line 352: | Line 281: | ||
− | |Week | + | |Week 6 |
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− | + | 4.2 | |
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Line 365: | Line 292: | ||
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− | * [[ | + | * [[Continuity]] |
− | * [[The Limit Laws | + | * [[The Limit Laws]] |
− | * [[Composition of Functions]] | + | * [[Composition of Functions]] |
− | * [[The Dot Product]] | + | * [[The Dot Product]] |
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Line 382: | Line 309: | ||
− | |Week | + | |Week 6 |
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− | + | 4.3 | |
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Line 394: | Line 319: | ||
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− | * [[The | + | * [[The Derivative as a Function|The first]] and [[The Second Derivative|second derivative]] of a function |
− | * [[ | + | * [[Limit and Continuity of Function of Several Variables]] |
Line 407: | Line 332: | ||
− | |Week | + | |Week 7 |
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− | + | 4.4 | |
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Line 418: | Line 341: | ||
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− | * [[Trigonometric Functions]] | + | * [[Trigonometric Functions]] |
− | * [[Vectors, Unit Vectors]] | + | * [[Vectors, Unit Vectors]] |
− | * [[Partial Derivatives]] | + | * [[Partial Derivatives]] |
− | * Gradients | + | * [[Gradients]] |
− | * [[The Dot Product]] | + | * [[The Dot Product]] |
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* Directional derivatives for functions of two variables | * Directional derivatives for functions of two variables | ||
Line 432: | Line 355: | ||
− | |Week | + | |Week 7 |
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− | + | 4.5 | |
− | |||
− | |||
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− | [[Tangent Plane]] | + | [[Tangent Plane]], |
[[Differentiability]] | [[Differentiability]] | ||
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− | * [[Partial Derivatives]] | + | * [[Partial Derivatives]] |
− | * [[Parametric Equations of Lines | + | * [[Parametric Equations]] of Lines |
− | * [[Equations of Planes]] | + | * [[Equations of Lines, Planes and Surfaces in Space]] |
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Line 461: | Line 382: | ||
− | |Week | + | |Week 7 |
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− | + | 4.6 | |
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Line 472: | Line 391: | ||
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− | * [[Differentiation Rules | + | * [[Differentiation Rules]] |
− | * [[The Chain Rule | + | * [[The Chain Rule]] |
− | * [[Partial Derivatives]] | + | * [[Partial Derivatives]] |
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Line 482: | Line 401: | ||
* The general chain rule for functions of several independent variables | * The general chain rule for functions of several independent variables | ||
|- | |- | ||
− | |Week | + | |Week 8 |
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− | + | 4.7 | |
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Line 493: | Line 410: | ||
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− | * [[ | + | * [[Extreme values on closed and bounded domains]] |
− | * [[Partial Derivatives]] | + | * [[Partial Derivatives]] |
− | * [[Maxima, Minima and Critical Points of a Function]] | + | * [[Maxima and Minima|Maxima, Minima and Critical Points of a Function]] |
− | * [[Continuity of | + | * [[Limit and Continuity of Function of Several Variables]] |
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Line 505: | Line 422: | ||
* Absolute maxima and minima on closed and bounded regions | * Absolute maxima and minima on closed and bounded regions | ||
|- | |- | ||
− | |Week | + | |Week 8/9 |
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− | + | 4.8 | |
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Line 517: | Line 432: | ||
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− | * [[Partial Derivatives]] | + | * [[Partial Derivatives]] |
− | * [[Critical Points of a Function]] | + | * [[Critical Points of a Function]] |
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Line 527: | Line 442: | ||
− | |Week | + | |Week 9/10 |
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− | + | 5.1 | |
− | |||
− | |||
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− | [[Double | + | [[Multiple Integrals|Double Integrals over Rectangular Regions]] |
|| | || | ||
− | * [[Approximating Areas]] | + | * [[Approximating Areas]] |
− | * [[The Definite Integral|Limits of Riemann Sums]] | + | * [[The Definite Integral|Limits of Riemann Sums]] |
|| | || | ||
− | + | * Double Integral is the limit of Double Sums. | |
− | * Double Integrals | + | * Double Integrals over Rectangular Regions. |
− | * Fubini's Theorem (part 1) | + | * Interated Integrals. |
− | + | * Fubini's Theorem (part 1). | |
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|- | |- | ||
− | |Week | + | |Week 10 |
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− | + | 5.2 | |
− | |||
− | |||
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− | [[Double Integrals over General Regions]] | + | [[Multiple Integrals|Double Integrals over General Regions]] |
|| | || | ||
− | * [[Continuity]] | + | * [[Continuity]] |
− | * [[Determining Volumes by Slicing]] | + | * [[Determining Volumes by Slicing]] |
− | * [[Double and Iterated Integrals over | + | * [[Multiple Integrals|Double and Iterated Integrals over Rectangular regions]] |
|| | || | ||
− | + | * Double integrals over bounded, general regions. | |
− | * Double integrals over bounded, | + | * Properties of double Integrals. |
− | * | ||
* Fubini's theorem (part 2) | * Fubini's theorem (part 2) | ||
− | * | + | * Changing the order of Integration. |
− | * | + | * Calculating Volumes, Areas and Average Values |
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|- | |- | ||
− | |Week | + | |Week 11 |
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− | + | 5.3 | |
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− | [[Double Integrals in Polar Coordinates]] | + | [[Multiple Integrals|Double Integrals in Polar Coordinates]] |
|| | || | ||
− | * [[Double Integrals over General Regions]] | + | * [[Multiple Integrals|Double Integrals over General Regions]] |
− | * [[ | + | * [[Polar Coordinates]] |
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− | + | * Double Integrals over rectangular polar regions. | |
− | * Integrals | + | * Double Integrals over general polar regions. |
− | * | + | * Changing Cartesian Integrals into Polar Integrals. |
− | * Changing Cartesian Integrals into Polar Integrals | + | * Using Double Integrals in Polar Coordinates to find Volumes, Areas. |
− | |||
− | |||
|- | |- | ||
− | + | |Week 11 | |
− | |Week | ||
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+ | 5.4 | ||
+ | || | ||
− | + | [[Multiple Integrals|Triple Integrals in Rectangular Coordinates]] | |
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− | |||
− | |||
− | + | * [[Multiple Integrals|Double Integrals]] | |
− | + | * [[Multiple Integrals|Area by Double Integration]] | |
− | * [[ | + | * [[Change of Variables]] |
− | * [[ | ||
− | * [[ | ||
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− | * | + | * Triple Integrals over general bounded regions. |
− | * | + | * Finding Volumes by evaluating Triple Integrals. |
− | + | * Average value of a function in space. | |
− | + | * Changing Integration Order and Coordinate systems. | |
− | |||
|- | |- | ||
− | |Week | + | |Week 12 |
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− | + | 5.5 | |
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− | [[Triple Integrals in | + | [[Multiple Integrals|Triple Integrals in Cylindrical and Spherical Coordinates]] |
|| | || | ||
− | * [[Double | + | * [[Multiple Integrals|Double Integrals in Polar Form]] |
− | * [[ | + | * [[Multiple Integrals|Triple Integrals in Rectangular Coordinates]] |
− | |||
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− | * | + | * Integrations in Cylindrical Coordinates. |
− | * | + | * Equations relating rectangular and cylindrical coordinates. |
− | * | + | * Changing Cartesian integrations into Cylindrical integrations. |
− | * | + | * Integrations in Spherical coordinates. |
− | + | * Equations relating spherical coordinates to Cartesian and cylindrical coordinates. | |
− | + | * Changing Cartesian integrations into Cylindrical integrations. | |
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|- | |- | ||
+ | |Week 13 | ||
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− | + | 5.6 | |
− | + | || | |
− | + | ||
− | || | + | [[Multiple Integrals|Applications of Multiple Integrals]] |
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− | [[ | ||
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− | * [[Double | + | * [[Multiple Integrals|Double Integral]] |
− | * [[ | + | * [[Multiple Integrals|Triple Integrals]] |
− | |||
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− | * | + | * Finding Masses, Moments, Centers of Masses, Moments of Inertia in Two Dimensions. |
− | * | + | * Finding Masses, Moments, Centers of Masses, Moments of Inertia in Three Dimensions. |
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|- | |- | ||
− | + | |Week 13/14 | |
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− | |Week | ||
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− | + | 5.7 | |
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− | [[ | + | [[Multiple Integrals|Change of Variables in Multiple Integrals]] |
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− | * [[ | + | * [[Multiple Integrals|Double Integral]] |
− | * [[Triple Integrals | + | * [[Multiple Integrals|Triple Integrals]] |
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− | * | + | * Determine the image of a region under a given transformation of variables. |
− | * | + | * Compute the Jacobian of a given transformation. |
− | + | * Evaluate a double integral using a change of variables. | |
− | + | * Evaluate a triple integral using a change of variables. | |
− | |||
|- | |- | ||
+ | |Week 14 | ||
− | + | || | |
− | | | + | 6.1 |
− | |||
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− | + | [[Vector Fields]] | |
− | |||
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− | [[ | ||
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− | * [[ | + | * [[The Dot Product]] <!-- 2214-12.3 --> |
− | * [[ | + | * [[Directional Derivatives and Gradient Vectors]] |
− | |||
− | |||
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− | + | * Vector Fields in a plane. | |
− | * | + | * Vector Fields in Space. |
− | * | + | * Potential Functions. |
− | * | + | * Gradient Fields, Conservative Vector Fields. |
− | * | + | * The Cross-Partial Test for Conservative Vector Fields. |
− | + | * Determining Whether a Vector Field is conservative. | |
− | |||
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|- | |- | ||
− | + | |Week 14 | |
− | |Week | ||
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+ | 6.2 | ||
+ | || | ||
− | + | [[Line Integrals]] | |
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− | [[Vector | + | * [[Parametric Equations]] |
+ | * [[Curves in Space and Vector-Valued Functions]] | ||
+ | * [[Arc Length]] | ||
|| | || | ||
+ | * Line Integrals of functions a long a smooth curves in a planer or in space | ||
+ | * Line Integrals of of vector fields along an oriented curves in a plane or space.. | ||
+ | * Properties of Vector Line Integrals. | ||
+ | * Evaluating Line Integrals. | ||
+ | * Applications of line integrals: Calculating Arc Length, the Mass of a wire, Work done by a force, Flux across a curve, Circulation of a force. | ||
+ | |- | ||
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− | + | |Week 14/15 | |
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− | |Week | ||
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− | + | 6.3 | |
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− | [[ | + | [[Conservative Vector Fields]] |
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− | * [[Vector Fields and Line Integrals]] | + | * [[Vector Fields and Line Integrals]] |
− | * [[Partial Derivatives]] | + | * [[Partial Derivatives]] |
− | |||
− | |||
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− | + | * Describe simple and closed curves | |
− | * | + | * Define connected and simply connected regions. |
− | * | + | * Explain how to test a vector field to determine whether it is conservative. |
− | * | + | * Find a potential function for a conservative vector field. |
− | * | + | * Use the Fundamental Theorem for Line Integrals to evaluate a line integral of a vector field. |
− | * | ||
− | |||
− | |||
|- | |- | ||
− | |Weeks | + | |Weeks 14/15 |
|| | || | ||
− | + | 6.4 | |
− | |||
− | |||
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[[Green's Theorem]] | [[Green's Theorem]] | ||
+ | |||
+ | [[Stokes' Theorem]] | ||
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− | * [[Vector Fields | + | * [[Vector Fields]] |
− | * [[Partial Derivatives]] | + | * [[Line Integrals]] |
− | * [[Dot Product]] | + | * [[Partial Derivatives]] |
− | * [[Path Independence | + | * [[The Dot Product]] |
+ | * [[Line Integrals|Path Independence]] | ||
+ | * [[Conservative Vector Fields]] | ||
|| | || | ||
− | * Circulation | + | * Circulation form of Green's Theorem. |
− | + | * Flux Form of Green’s Theorem. | |
− | * | + | * Applying Green's Theorem to find Work, Flux. |
− | * Green's | ||
− | + | |} | |
− | | |
Latest revision as of 10:10, 21 June 2023
The textbook for this course is Calculus (Volume 3) by Gilbert Strang, Edwin Herman, et al.
Topics List
Date | Sections | Topics | Prerequisite Skills | Student Learning Outcomes |
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Week 1 |
1.1 |
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Week 1 |
1.2 |
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Weeks 1/2 |
2.1 |
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Week 2 |
2.3 |
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Week 2 |
2.4 |
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Week 3 |
2.5 |
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Week 3 |
2.6 |
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Weeks 3/4 |
3.1, 3.2 |
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Week 4 |
3.3 |
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Weeks 4/5 |
3.4 |
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Week 5/6 |
4.1 |
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Week 6 |
4.2 |
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Week 6 |
4.3 |
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Week 7 |
4.4 |
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Week 7 |
4.5 |
Tangent Plane, Differentiability
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Week 7 |
4.6 |
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Week 8 |
4.7 |
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Week 8/9 |
4.8 |
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Week 9/10 |
5.1 |
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Week 10 |
5.2 |
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Week 11 |
5.3 |
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Week 11 |
5.4 |
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Week 12 |
5.5 |
| ||
Week 13 |
5.6 |
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Week 13/14 |
5.7 |
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Week 14 |
6.1 |
| ||
Week 14 |
6.2 |
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Week 14/15 |
6.3 |
| ||
Weeks 14/15 |
6.4 |
|