Difference between revisions of "MAT2214"
Jump to navigation
Jump to search
m (→Topics List: Improving Consistency of Formatting) |
|||
(40 intermediate revisions by 5 users not shown) | |||
Line 1: | Line 1: | ||
+ | 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" | ||
Line 5: | Line 8: | ||
− | |Week | + | |Week 1 |
|| | || | ||
− | + | 1.1 | |
− | |||
− | |||
|| | || | ||
Line 16: | Line 17: | ||
|| | || | ||
− | * [[Trigonometric Functions: Unit Circle Approach]] | + | * [[Trigonometric Functions: Unit Circle Approach]] |
− | * [[ | + | * [[Inverse Trigonometric Functions]] |
|| | || | ||
* 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 | ||
Line 26: | Line 27: | ||
− | |Week | + | |Week 1 |
|| | || | ||
− | + | 1.2 | |
− | |||
− | |||
|| | || | ||
Line 38: | Line 37: | ||
|| | || | ||
− | * [[ | + | * [[Two-dimensional coordinate systems]] |
− | * [[Solving Equations| Algebraic Expressions]] | + | * [[Solving Equations and Inequalities| Algebraic Expressions]] |
Line 46: | Line 45: | ||
* Three-dimensional coordinate systems. | * Three-dimensional coordinate systems. | ||
− | * Distance Formula in Space . | + | * Distance Formula in Space. |
* Standard Equation for a Sphere. | * Standard Equation for a Sphere. | ||
|- | |- | ||
− | |Weeks | + | |Weeks 1/2 |
|| | || | ||
− | + | 2.1 | |
− | |||
− | |||
|| | || | ||
Line 64: | Line 61: | ||
|| | || | ||
− | * [[Linear Equations|Line Segments]] | + | * [[Linear Equations|Line Segments]] |
− | * [[Distance Formula| Distance Formula]] | + | * [[Distance Formula| Distance Formula]] |
|| | || | ||
Line 78: | Line 75: | ||
− | |Week | + | |Week 2 |
|| | || | ||
− | + | 2.3 | |
− | |||
− | |||
|| | || | ||
Line 91: | Line 86: | ||
|| | || | ||
− | * [[ | + | * [[Trigonometric Functions|Basic Trig Functions]] |
− | * [[Vectors]] | + | * [[Vectors]] |
|| | || | ||
Line 103: | Line 98: | ||
− | |Week | + | |Week 2 |
|| | || | ||
− | + | 2.4 | |
− | |||
− | |||
|| | || | ||
Line 115: | Line 108: | ||
|| | || | ||
− | * [[ | + | * [[Trigonometric Functions|Basic Trig Functions]] |
− | * [[Determinants]] | + | * [[Determinants]] |
* [[Vectors]] | * [[Vectors]] | ||
Line 125: | Line 118: | ||
* Area of a parallelogram | * Area of a parallelogram | ||
* Cross product as a determinant | * Cross product as a determinant | ||
− | |||
− | |||
− | |||
Line 134: | Line 124: | ||
− | |Week | + | |Week 3 |
|| | || | ||
− | + | 2.5 | |
− | |||
− | |||
|| | || | ||
Line 147: | Line 135: | ||
|| | || | ||
− | * [[The Dot Product]] | + | * [[The Dot Product]] |
* [[The Cross Product]] | * [[The Cross Product]] | ||
− | * [[Quadratic Functions]] | + | * [[Quadratic Functions]] |
− | * [[Parametric Equations]] | + | * [[Parametric Equations]] |
|| | || | ||
Line 159: | 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 |
|| | || | ||
− | + | 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]] |
|| | || | ||
Line 186: | Line 171: | ||
* Understand basic quadratic surfaces | * Understand basic quadratic surfaces | ||
* Understand general quadratic surfaces | * Understand general quadratic surfaces | ||
− | |||
− | |||
− | |||
− | |||
Line 195: | Line 176: | ||
− | |Weeks | + | |Weeks 3/4 |
|| | || | ||
− | + | 3.1, 3.2 | |
− | |||
− | |||
|| | || | ||
Line 207: | Line 186: | ||
|| | || | ||
− | * [[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]] |
|| | || | ||
Line 222: | Line 201: | ||
* Differentiation rules for vector functions | * Differentiation rules for vector functions | ||
* Curves and paths in space | * Curves and paths in space | ||
− | |||
− | |||
Line 230: | Line 207: | ||
− | |Week | + | |Week 4 |
|| | || | ||
− | + | 3.3 | |
− | |||
− | |||
|| | || | ||
Line 242: | Line 217: | ||
|| | || | ||
− | * | + | * [[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]] |
|| | || | ||
Line 250: | Line 225: | ||
* The arc Length of a vector function | * The arc Length of a vector function | ||
* Arc length parameterization | * Arc length parameterization | ||
− | |||
− | |||
− | |||
|- | |- | ||
Line 258: | Line 230: | ||
− | |Weeks | + | |Weeks 4/5 |
|| | || | ||
− | + | 3.4 | |
− | |||
− | |||
|| | || | ||
Line 269: | Line 239: | ||
|| | || | ||
− | * [[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 280: | Line 250: | ||
* The tangential and normal components of acceleration | * The tangential and normal components of acceleration | ||
* The Torsion | * The Torsion | ||
− | |||
− | |||
− | |||
|- | |- | ||
Line 288: | Line 255: | ||
− | |Week | + | |Week 5/6 |
|| | || | ||
− | + | 4.1 | |
− | |||
− | |||
|| | || | ||
Line 301: | Line 266: | ||
|| | || | ||
− | * [[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]] |
|| | || | ||
Line 316: | Line 281: | ||
− | |Week | + | |Week 6 |
|| | || | ||
− | + | 4.2 | |
− | |||
− | |||
|| | || | ||
Line 329: | Line 292: | ||
|| | || | ||
− | * [[ | + | * [[Continuity]] |
− | * [[The Limit Laws | + | * [[The Limit Laws]] |
− | * [[Composition of Functions]] | + | * [[Composition of Functions]] |
− | * [[The Dot Product]] | + | * [[The Dot Product]] |
|| | || | ||
Line 346: | Line 309: | ||
− | |Week | + | |Week 6 |
|| | || | ||
− | + | 4.3 | |
− | |||
− | |||
|| | || | ||
Line 358: | Line 319: | ||
|| | || | ||
− | * [[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 371: | Line 332: | ||
− | |Week | + | |Week 7 |
|| | || | ||
− | + | 4.4 | |
− | |||
− | |||
|| | || | ||
Line 382: | Line 341: | ||
|| | || | ||
− | * [[Trigonometric Functions]] | + | * [[Trigonometric Functions]] |
− | * [[Vectors, Unit Vectors]] | + | * [[Vectors, Unit Vectors]] |
− | * [[Partial Derivatives]] | + | * [[Partial Derivatives]] |
− | * Gradients | + | * [[Gradients]] |
− | * [[The Dot Product]] | + | * [[The Dot Product]] |
|| | || | ||
* Directional derivatives for functions of two variables | * Directional derivatives for functions of two variables | ||
Line 396: | Line 355: | ||
− | |Week | + | |Week 7 |
|| | || | ||
− | + | 4.5 | |
− | |||
− | |||
|| | || | ||
− | [[Tangent Plane]] | + | [[Tangent Plane]], |
[[Differentiability]] | [[Differentiability]] | ||
|| | || | ||
− | * [[Partial Derivatives]] | + | * [[Partial Derivatives]] |
− | * [[Parametric Equations of Lines | + | * [[Parametric Equations]] of Lines |
− | * [[Equations of Planes]] | + | * [[Equations of Lines, Planes and Surfaces in Space]] |
|| | || | ||
Line 425: | Line 382: | ||
− | |Week | + | |Week 7 |
|| | || | ||
− | + | 4.6 | |
− | |||
− | |||
|| | || | ||
Line 436: | Line 391: | ||
|| | || | ||
− | * [[Differentiation Rules | + | * [[Differentiation Rules]] |
− | * [[The Chain Rule | + | * [[The Chain Rule]] |
− | * [[Partial Derivatives]] | + | * [[Partial Derivatives]] |
|| | || | ||
Line 446: | 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 |
|| | || | ||
− | + | 4.7 | |
− | |||
− | |||
|| | || | ||
Line 457: | Line 410: | ||
|| | || | ||
− | * [[ | + | * [[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]] |
|| | || | ||
Line 469: | Line 422: | ||
* Absolute maxima and minima on closed and bounded regions | * Absolute maxima and minima on closed and bounded regions | ||
|- | |- | ||
− | |Week | + | |Week 8/9 |
|| | || | ||
− | + | 4.8 | |
− | |||
− | |||
|| | || | ||
Line 481: | Line 432: | ||
|| | || | ||
− | * [[Partial Derivatives]] | + | * [[Partial Derivatives]] |
− | * [[Critical Points of a Function]] | + | * [[Critical Points of a Function]] |
|| | || | ||
Line 491: | Line 442: | ||
− | |Week | + | |Week 9/10 |
|| | || | ||
− | + | 5.1 | |
− | |||
− | |||
|| | || | ||
− | [[Double Integrals over Rectangular Regions]] | + | [[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]] |
|| | || | ||
Line 514: | Line 463: | ||
− | |Week | + | |Week 10 |
|| | || | ||
− | + | 5.2 | |
− | |||
− | |||
|| | || | ||
− | [[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 Rectangular regions]] | + | * [[Multiple Integrals|Double and Iterated Integrals over Rectangular regions]] |
|| | || | ||
Line 540: | Line 487: | ||
− | |Week | + | |Week 11 |
|| | || | ||
− | + | 5.3 | |
− | |||
− | |||
|| | || | ||
− | [[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]] |
|| | || | ||
Line 563: | Line 508: | ||
− | |Week | + | |Week 11 |
|| | || | ||
− | + | 5.4 | |
− | |||
− | |||
|| | || | ||
− | [[Triple Integrals in Rectangular Coordinates]] | + | [[Multiple Integrals|Triple Integrals in Rectangular Coordinates]] |
|| | || | ||
− | * [[Double Integrals]] | + | * [[Multiple Integrals|Double Integrals]] |
− | * [[Area by Double Integration]] | + | * [[Multiple Integrals|Area by Double Integration]] |
− | * | + | * [[Change of Variables]] |
|| | || | ||
Line 589: | Line 532: | ||
− | |Week | + | |Week 12 |
|| | || | ||
− | + | 5.5 | |
− | |||
− | |||
|| | || | ||
− | [[Triple Integrals in Cylindrical and Spherical Coordinates]] | + | [[Multiple Integrals|Triple Integrals in Cylindrical and Spherical Coordinates]] |
|| | || | ||
− | * [[Double Integrals in Polar Form]] | + | * [[Multiple Integrals|Double Integrals in Polar Form]] |
− | * [[Triple Integrals in Rectangular Coordinates]] | + | * [[Multiple Integrals|Triple Integrals in Rectangular Coordinates]] |
|| | || | ||
Line 615: | Line 556: | ||
− | |Week | + | |Week 13 |
|| | || | ||
− | + | 5.6 | |
− | |||
− | |||
|| | || | ||
− | [[Applications of Multiple Integrals]] | + | [[Multiple Integrals|Applications of Multiple Integrals]] |
|| | || | ||
− | * [[Double Integral]] | + | * [[Multiple Integrals|Double Integral]] |
− | * [[Triple Integrals]] | + | * [[Multiple Integrals|Triple Integrals]] |
|| | || | ||
Line 635: | Line 574: | ||
* Finding Masses, Moments, Centers of Masses, Moments of Inertia in Three Dimensions. | * Finding Masses, Moments, Centers of Masses, Moments of Inertia in Three Dimensions. | ||
|- | |- | ||
− | |Week | + | |Week 13/14 |
|| | || | ||
+ | 5.7 | ||
+ | || | ||
+ | |||
+ | [[Multiple Integrals|Change of Variables in Multiple Integrals]] | ||
− | + | || | |
+ | |||
+ | * [[Multiple Integrals|Double Integral]] | ||
+ | * [[Multiple Integrals|Triple Integrals]] | ||
+ | |||
+ | || | ||
+ | |||
+ | * 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 | ||
|| | || | ||
Line 648: | Line 605: | ||
* [[The Dot Product]] <!-- 2214-12.3 --> | * [[The Dot Product]] <!-- 2214-12.3 --> | ||
− | * [[Directional Derivatives and Gradient Vectors]] | + | * [[Directional Derivatives and Gradient Vectors]] |
− | |||
− | |||
− | |||
|| | || | ||
* Vector Fields in a plane. | * Vector Fields in a plane. | ||
Line 662: | Line 616: | ||
− | |Week | + | |Week 14 |
|| | || | ||
− | + | 6.2 | |
− | |||
− | |||
|| | || | ||
Line 674: | Line 626: | ||
|| | || | ||
− | * [[Parametric Equations]] | + | * [[Parametric Equations]] |
− | * [[Curves in Space and Vector Functions]] | + | * [[Curves in Space and Vector-Valued Functions]] |
− | * [[Arc | + | * [[Arc Length]] |
|| | || | ||
Line 683: | Line 635: | ||
* Properties of Vector Line Integrals. | * Properties of Vector Line Integrals. | ||
* Evaluating Line Integrals. | * Evaluating Line Integrals. | ||
− | * Applications of line integrals: Calculating the Mass of a wire, Work done by a force, Flux across a curve, Circulation of a force. | + | * 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. |
|- | |- | ||
Line 690: | Line 642: | ||
− | |Week | + | |Week 14/15 |
|| | || | ||
− | + | 6.3 | |
− | |||
− | |||
|| | || | ||
− | [[ | + | [[Conservative Vector Fields]] |
|| | || | ||
− | * [[Vector Fields and Line Integrals]] | + | * [[Vector Fields and Line Integrals]] |
− | * [[Partial Derivatives]] | + | * [[Partial Derivatives]] |
|| | || | ||
− | * | + | * 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 | |
− | |||
− | |||
|| | || | ||
[[Green's Theorem]] | [[Green's Theorem]] | ||
+ | |||
+ | [[Stokes' Theorem]] | ||
|| | || | ||
− | * [[Vector Fields | + | * [[Vector Fields]] |
− | * [[Partial Derivatives]] | + | * [[Line Integrals]] |
− | * [[Dot Product]] | + | * [[Partial Derivatives]] |
− | * [[Path Independence | + | * [[The Dot Product]] |
+ | * [[Line Integrals|Path Independence]] | ||
+ | * [[Conservative Vector Fields]] | ||
|| | || | ||
Line 736: | Line 688: | ||
* Flux Form of Green’s Theorem. | * Flux Form of Green’s Theorem. | ||
* Applying Green's Theorem to find Work, Flux. | * Applying Green's Theorem to find Work, Flux. | ||
− | | | + | |
+ | |} |
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 |
---|---|---|---|---|
Week 1 |
1.1 |
| ||
Week 1 |
1.2 |
|
| |
Weeks 1/2 |
2.1 |
| ||
Week 2 |
2.3 |
|
| |
Week 2 |
2.4 |
| ||
Week 3 |
2.5 |
| ||
Week 3 |
2.6 |
| ||
Weeks 3/4 |
3.1, 3.2 |
| ||
Week 4 |
3.3 |
| ||
Weeks 4/5 |
3.4 |
| ||
Week 5/6 |
4.1 |
| ||
Week 6 |
4.2 |
| ||
Week 6 |
4.3 |
|
| |
Week 7 |
4.4 |
| ||
Week 7 |
4.5 |
Tangent Plane, Differentiability
|
| |
Week 7 |
4.6 |
| ||
Week 8 |
4.7 |
| ||
Week 8/9 |
4.8 |
| ||
Week 9/10 |
5.1 |
| ||
Week 10 |
5.2 |
| ||
Week 11 |
5.3 |
| ||
Week 11 |
5.4 |
| ||
Week 12 |
5.5 |
| ||
Week 13 |
5.6 |
| ||
Week 13/14 |
5.7 |
| ||
Week 14 |
6.1 |
| ||
Week 14 |
6.2 |
| ||
Week 14/15 |
6.3 |
| ||
Weeks 14/15 |
6.4 |
|