Difference between revisions of "MAT2214"
Jump to navigation
Jump to search
(minor edits to table prerequisites) |
m (→Topics List: Improving Consistency of Formatting) |
||
(93 intermediate revisions by 6 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" | ||
! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes | ! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes | ||
+ | |- | ||
− | |||
− | |Week | + | |Week 1 |
|| | || | ||
+ | 1.1 | ||
+ | || | ||
+ | |||
+ | [[Polar Coordinates]] | ||
− | + | || | |
+ | * [[Trigonometric Functions: Unit Circle Approach]] | ||
+ | * [[Inverse Trigonometric Functions]] | ||
+ | || | ||
+ | * Plot points using polar coordinates and find several polar coordinates of a single point | ||
+ | * Convert polar coordinates to rectangular coordinates and vice versa | ||
+ | * Transform equations from polar form to rectangular form and vice versa | ||
+ | |- | ||
+ | |||
+ | |||
+ | |Week 1 | ||
+ | |||
+ | || | ||
+ | 1.2 | ||
|| | || | ||
Line 17: | Line 37: | ||
|| | || | ||
− | * [[ | + | * [[Two-dimensional coordinate systems]] |
− | + | * [[Solving Equations and Inequalities| Algebraic Expressions]] | |
− | * [[Solving Equations| Algebraic Expressions]] | + | |
− | |||
− | |||
|| | || | ||
− | * 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. |
− | |||
− | |||
|- | |- | ||
− | | | + | |Weeks 1/2 |
|| | || | ||
− | + | 2.1 | |
− | |||
− | |||
|| | || | ||
− | [[Vectors]] | + | [[Vectors in The Plane, Space]] |
|| | || | ||
− | * [[Linear Equations|Line Segments]] | + | * [[Linear Equations|Line Segments]] |
− | * [[Distance Formula| | + | * [[Distance Formula| Distance Formula]] |
|| | || | ||
* Vector Algebra Operations | * Vector Algebra Operations | ||
− | * Magnitude of a vector | + | * The Magnitude of a vector |
* Unit Vectors | * Unit Vectors | ||
− | * Midpoint of a Line Segment | + | * The Midpoint of a Line Segment |
− | * | + | * The Vector projection |
− | + | |- | |
− | |||
− | |||
− | |||
− | |Week | + | |Week 2 |
|| | || | ||
− | + | 2.3 | |
− | |||
− | |||
|| | || | ||
Line 77: | Line 86: | ||
|| | || | ||
− | * [[ | + | * [[Trigonometric Functions|Basic Trig Functions]] |
− | + | * [[Vectors]] | |
− | * [[Vectors]] | ||
− | |||
|| | || | ||
− | + | * Definition of Dot Product | |
− | * | + | * Properties of Dot Product |
+ | * Angle between vectors | ||
+ | * Orthogonal vectors | ||
|- | |- | ||
− | |Week | + | |Week 2 |
|| | || | ||
− | + | 2.4 | |
− | |||
− | |||
|| | || | ||
Line 101: | Line 108: | ||
|| | || | ||
− | * [[ | + | * [[Trigonometric Functions|Basic Trig Functions]] |
− | * [[ | + | * [[Determinants]] |
− | * [[ | + | * [[Vectors]] |
|| | || | ||
− | * | + | * Definition of Cross Product |
* Properties of the cross product | * Properties of the cross product | ||
* Area of a parallelogram | * Area of a parallelogram | ||
* Cross product as a determinant | * Cross product as a determinant | ||
− | |||
+ | |- | ||
− | |||
− | |Week | + | |Week 3 |
|| | || | ||
− | + | 2.5 | |
− | |||
− | |||
|| | || | ||
− | [[ | + | [[Equations of Lines, Planes and Surfaces in Space]] |
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
|| | || | ||
− | * | + | * [[The Dot Product]] |
− | * | + | * [[The Cross Product]] |
− | * | + | * [[Quadratic Functions]] |
+ | * [[Parametric Equations]] | ||
|| | || | ||
+ | * Write the vector, parametric equation of a line through a given point in a given direction, and a line through two given points. | ||
+ | * Find the distance from a point to a given line. | ||
+ | * Write the equation of a plane through a given point with a given normal, and a plane through three given points. | ||
+ | * Find the distance from a point to a given plane. | ||
Line 148: | Line 151: | ||
− | |Week | + | |Week 3 |
|| | || | ||
− | + | 2.6 | |
− | |||
− | |||
|| | || | ||
− | [[ | + | [[Equations of Lines, Planes and Surfaces in Space|Cylinders and Quadratic Surfaces]] |
|| | || | ||
− | * [[ | + | * [[Quadratic Functions]] |
− | * [[ | + | * [[Parametric Equations]] |
− | + | * [[Conics]] | |
− | |||
− | |||
− | |||
− | * [[ | ||
|| | || | ||
− | * | + | * Find equations for cylinders that are generated by rotating lines that are parallel to a plane |
− | + | * Understand basic quadratic surfaces | |
− | + | * Understand general quadratic surfaces | |
− | * | ||
− | * | ||
− | |||
− | |||
− | |||
Line 184: | Line 176: | ||
− | | | + | |Weeks 3/4 |
|| | || | ||
+ | 3.1, 3.2 | ||
+ | || | ||
− | + | [[Curves in Space and Vector-Valued Functions]] | |
− | |||
− | |||
− | |||
− | [[ | ||
|| | || | ||
− | * [[ | + | * [[Parametric Equations]] |
− | * [[The | + | * [[Vectors]] |
− | * [[ | + | * [[The Derivative as a Function]] |
− | * [[ | + | * [[The Limit of a Function]] |
+ | * [[Continuity]] | ||
+ | * [[The Dot Product]] | ||
+ | * [[The Cross Product]] | ||
|| | || | ||
− | * | + | * Vector functions |
− | * | + | * Limits of vector functions |
− | * | + | * Continuity of vector functions |
− | + | * Differentiation rules for vector functions | |
− | + | * Curves and paths in space | |
Line 213: | Line 206: | ||
− | |Week | + | |
+ | |Week 4 | ||
|| | || | ||
− | + | 3.3 | |
− | |||
− | |||
|| | || | ||
− | |||
[[Arc Length]] | [[Arc Length]] | ||
|| | || | ||
− | * [[Distance Formula| Length of a Line]] | + | * [[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]] |
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
|| | || | ||
+ | * The arc Length of a vector function | ||
+ | * Arc length parameterization | ||
|- | |- | ||
− | | | + | |
+ | |Weeks 4/5 | ||
|| | || | ||
− | + | 3.4 | |
− | |||
− | |||
|| | || | ||
− | + | [[Motion in Space]] | |
− | [[ | ||
|| | || | ||
− | + | * [[Vectors]] | |
− | + | * [[Parametric Equations]] | |
− | * [[Vectors]] | + | * [[The Cross Product]] |
− | * [[Parametric Equations]] | + | * [[Derivatives of Vector Functions]] |
− | * [[ | ||
− | * | ||
− | |||
|| | || | ||
− | + | * The Unit tangent vector | |
− | * | + | * The curvature |
− | * | + | * The Principal Unit Normal Vector |
− | * | + | * The Binormal Vector |
− | * | + | * The tangential and normal components of acceleration |
− | + | * The Torsion | |
− | |||
− | |||
|- | |- | ||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |Week | + | |Week 5/6 |
|| | || | ||
− | + | 4.1 | |
− | |||
− | |||
|| | || | ||
Line 318: | 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]] |
− | |||
− | |||
|| | || | ||
− | + | * Functions of two variables | |
+ | * Functions of three variables | ||
* Domain and range of multivariable functions | * Domain and range of multivariable functions | ||
− | |||
* Bounded regions | * Bounded regions | ||
* Graphs and level curves of two variable functions | * Graphs and level curves of two variable functions | ||
− | * | + | * Level surfaces of three variable functions |
− | |||
− | |||
− | |||
− | |||
|- | |- | ||
− | |Week | + | |Week 6 |
|| | || | ||
− | + | 4.2 | |
− | |||
− | |||
|| | || | ||
− | [[ | + | [[Limit and Continuity of Function of Several Variables]] |
|| | || | ||
− | + | * [[Continuity]] | |
− | * [[Continuity]] | + | * [[The Limit Laws]] |
− | * [[The Limit Laws]] | + | * [[Composition of Functions]] |
− | * [[Composition of Functions]] | + | * [[The Dot Product]] |
− | * [[The Dot Product]] | ||
− | |||
|| | || | ||
* Limits of functions of two variables | * Limits of functions of two variables | ||
− | * Properties of limits of functions of | + | * Limits of functions of more than two variables |
− | * Continuity for functions of | + | * Properties of limits of functions of several variables |
+ | * Two path test of non-existing of a limit | ||
+ | * Continuity for functions of several variables | ||
* Continuity of composition | * Continuity of composition | ||
− | + | * Extreme values on closed and bounded domains | |
− | * Extreme values on closed and bounded | ||
− | |||
− | |||
|- | |- | ||
− | |Week | + | |Week 6 |
|| | || | ||
− | + | 4.3 | |
− | |||
− | |||
|| | || | ||
Line 384: | Line 319: | ||
|| | || | ||
− | * [[The Derivative as a Function| | + | * [[The Derivative as a Function|The first]] and [[The Second Derivative|second derivative]] of a function |
− | + | * [[Limit and Continuity of Function of Several Variables]] | |
− | * [[ | + | |
|| | || | ||
− | |||
* Partial derivatives for functions of two variables | * Partial derivatives for functions of two variables | ||
* Partial derivatives for functions of more than two variables | * Partial derivatives for functions of more than two variables | ||
Line 395: | Line 329: | ||
* Second order partial derivatives | * Second order partial derivatives | ||
* Mixed derivative theorem | * Mixed derivative theorem | ||
− | |||
− | |||
− | |||
|- | |- | ||
− | |Week | + | |Week 7 |
|| | || | ||
− | + | 4.4 | |
− | |||
− | |||
|| | || | ||
− | [[ | + | [[Directional Derivatives and Gradient Vectors]] |
|| | || | ||
− | + | * [[Trigonometric Functions]] | |
− | * [[ | + | * [[Vectors, Unit Vectors]] |
− | * [[ | + | * [[Partial Derivatives]] |
− | * [[ | + | * [[Gradients]] |
− | * [[ | + | * [[The Dot Product]] |
− | * [[ | ||
− | |||
|| | || | ||
− | + | * Directional derivatives for functions of two variables | |
− | * | + | * Gradients |
− | * | + | * Properties of directional derivatives |
− | * | + | * Tangents to level curves |
− | + | * Directional derivatives for functions of three variables | |
− | |||
− | |||
|- | |- | ||
− | |Week | + | |Week 7 |
|| | || | ||
− | + | 4.5 | |
− | |||
− | |||
|| | || | ||
+ | [[Tangent Plane]], | ||
+ | [[Differentiability]] | ||
− | |||
|| | || | ||
− | + | * [[Partial Derivatives]] | |
− | * [[ | + | * [[Parametric Equations]] of Lines |
− | * [[ | + | * [[Equations of Lines, Planes and Surfaces in Space]] |
− | * [[ | ||
− | |||
− | |||
|| | || | ||
− | + | * Determine the equation of a plane tangent to a given surface at a point | |
− | * | + | * Determine the parametric equation of a normal line to a given surface at a point |
− | * | + | * The linear approximation of a function of two variables at a point |
− | * | + | * The definition of differentiability for a function of two variables |
− | * | + | * Differentiability implies Continuity |
− | * | + | * Continuity of First Partial Derivatives implies Differentiability |
− | * | + | * The definition of total differentiability for a function of two variables |
+ | * Use the total differential to approximate the change in a function of two variables | ||
+ | |- | ||
− | + | |Week 7 | |
− | |||
− | |||
− | |Week | ||
|| | || | ||
− | + | 4.6 | |
− | |||
− | |||
|| | || | ||
− | [[ | + | [[The Chain Rule for Functions of more than One Variable]] |
|| | || | ||
− | + | * [[Differentiation Rules]] | |
− | * [[ | + | * [[The Chain Rule]] |
− | * [[ | + | * [[Partial Derivatives]] |
− | * [[Partial Derivatives]] | ||
− | |||
− | |||
|| | || | ||
− | + | * Chain rule for functions of one independent variable and several intermediate variables. | |
− | * | + | * Chain rule for functions of two independent variable and several intermediate variables. |
− | * | + | * Method for implicit differentiation. |
− | + | * The general chain rule for functions of several independent variables | |
− | * | ||
− | * | ||
− | |||
− | |||
− | |||
|- | |- | ||
− | + | |Week 8 | |
− | |||
− | |Week | ||
|| | || | ||
− | + | 4.7 | |
− | |||
− | |||
|| | || | ||
− | [[ | + | [[Maxima and Minima Problems]] |
|| | || | ||
− | + | * [[Extreme values on closed and bounded domains]] | |
− | * [[ | + | * [[Partial Derivatives]] |
− | * [[Partial Derivatives]] | + | * [[Maxima and Minima|Maxima, Minima and Critical Points of a Function]] |
− | * [[Maxima and Minima|Critical Points of a Function]] | + | * [[Limit and Continuity of Function of Several Variables]] |
− | * [[ | ||
|| | || | ||
− | |||
* The derivative test for local extreme values | * The derivative test for local extreme values | ||
+ | * Extreme values on closed and bounded domains | ||
* Critical points and saddle points for functions of two variables | * Critical points and saddle points for functions of two variables | ||
* Second derivative test for local extreme values | * Second derivative test for local extreme values | ||
* 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 532: | Line 432: | ||
|| | || | ||
− | * [[ | + | * [[Partial Derivatives]] |
− | * [[ | + | * [[Critical Points of a Function]] |
− | |||
|| | || | ||
− | + | * Lagrange Multipliers with One Constraint | |
− | * | + | * Lagrange Multipliers with Two Constraints |
− | * | ||
− | |||
|- | |- | ||
− | |Week | + | |Week 9/10 |
|| | || | ||
− | + | 5.1 | |
− | |||
− | |||
|| | || | ||
− | [[ | + | [[Multiple Integrals|Double Integrals over Rectangular Regions]] |
|| | || | ||
− | * [[ | + | * [[Approximating Areas]] |
− | + | * [[The Definite Integral|Limits of Riemann Sums]] | |
− | * [[Limits | ||
|| | || | ||
− | + | * Double Integral is the limit of Double Sums. | |
− | * | + | * Double Integrals over Rectangular Regions. |
− | * | + | * Interated Integrals. |
− | + | * Fubini's Theorem (part 1). | |
− | |||
|- | |- | ||
− | |Week | + | |Week 10 |
|| | || | ||
− | + | 5.2 | |
− | |||
− | |||
|| | || | ||
− | [[Double | + | [[Multiple Integrals|Double Integrals over General Regions]] |
|| | || | ||
− | * [[ | + | * [[Continuity]] |
− | * [[ | + | * [[Determining Volumes by Slicing]] |
+ | * [[Multiple Integrals|Double and Iterated Integrals over Rectangular regions]] | ||
|| | || | ||
+ | * Double integrals over bounded, general regions. | ||
+ | * Properties of double Integrals. | ||
+ | * Fubini's theorem (part 2) | ||
+ | * Changing the order of Integration. | ||
+ | * Calculating Volumes, Areas and Average Values | ||
+ | |- | ||
− | |||
− | |||
− | |||
− | |||
− | |Week | + | |Week 11 |
|| | || | ||
− | + | 5.3 | |
− | |||
− | |||
|| | || | ||
− | [[Double Integrals | + | [[Multiple Integrals|Double Integrals in Polar Coordinates]] |
|| | || | ||
− | * [[ | + | * [[Multiple Integrals|Double Integrals over General Regions]] |
− | * [[ | + | * [[Polar Coordinates]] |
− | |||
|| | || | ||
− | + | * Double Integrals over rectangular polar regions. | |
− | * Double | + | * Double Integrals over general polar regions. |
− | * | + | * Changing Cartesian Integrals into Polar Integrals. |
− | * | + | * Using Double Integrals in Polar Coordinates to find Volumes, Areas. |
− | * | ||
− | |||
− | |||
− | |||
− | |||
|- | |- | ||
− | |Week | + | |Week 11 |
|| | || | ||
− | + | 5.4 | |
− | |||
− | |||
|| | || | ||
− | [[ | + | [[Multiple Integrals|Triple Integrals in Rectangular Coordinates]] |
|| | || | ||
− | * [[Double Integrals | + | * [[Multiple Integrals|Double Integrals]] |
− | * [[ | + | * [[Multiple Integrals|Area by Double Integration]] |
− | * | + | * [[Change of Variables]] |
|| | || | ||
− | * | + | * Triple Integrals over general bounded regions. |
− | * Average value | + | * Finding Volumes by evaluating Triple Integrals. |
− | + | * Average value of a function in space. | |
+ | * Changing Integration Order and Coordinate systems. | ||
+ | |- | ||
− | |||
− | |Week | + | |Week 12 |
|| | || | ||
+ | 5.5 | ||
+ | || | ||
− | + | [[Multiple Integrals|Triple Integrals in Cylindrical and Spherical Coordinates]] | |
− | |||
− | |||
− | |||
− | [[ | ||
|| | || | ||
− | * [[Double Integrals | + | * [[Multiple Integrals|Double Integrals in Polar Form]] |
− | * [[ | + | * [[Multiple Integrals|Triple Integrals in Rectangular Coordinates]] |
|| | || | ||
− | * | + | * Integrations in Cylindrical Coordinates. |
− | * | + | * Equations relating rectangular and cylindrical coordinates. |
− | * Changing Cartesian | + | * 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. | ||
|- | |- | ||
− | |Week | + | |Week 13 |
|| | || | ||
− | + | 5.6 | |
− | + | || | |
− | + | ||
− | || | + | [[Multiple Integrals|Applications of Multiple Integrals]] |
− | |||
− | [[ | ||
|| | || | ||
− | * [[ | + | * [[Multiple Integrals|Double Integral]] |
− | + | * [[Multiple Integrals|Triple Integrals]] | |
− | * | ||
|| | || | ||
− | * | + | * Finding Masses, Moments, Centers of Masses, Moments of Inertia in Two Dimensions. |
− | + | * Finding Masses, Moments, Centers of Masses, Moments of Inertia in Three Dimensions. | |
− | * Finding | ||
− | |||
− | |||
− | |||
− | |||
|- | |- | ||
− | + | |Week 13/14 | |
− | |Week | ||
|| | || | ||
− | + | 5.7 | |
− | |||
− | |||
|| | || | ||
− | [[ | + | [[Multiple Integrals|Change of Variables in Multiple Integrals]] |
|| | || | ||
− | * [[ | + | * [[Multiple Integrals|Double Integral]] |
− | * [[Triple Integrals | + | * [[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 |
− | |||
|| | || | ||
− | + | [[Vector Fields]] | |
− | |||
− | |||
− | |||
− | [[ | ||
|| | || | ||
− | * [[ | + | * [[The Dot Product]] <!-- 2214-12.3 --> |
− | * [[ | + | * [[Directional Derivatives and Gradient Vectors]] |
− | |||
− | |||
|| | || | ||
− | + | * 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. | |
− | |||
− | |||
− | |||
|- | |- | ||
− | |Week | + | |Week 14 |
|| | || | ||
− | + | 6.2 | |
− | |||
− | |||
|| | || | ||
− | [[Line Integrals | + | [[Line Integrals]] |
|| | || | ||
− | * [[Parametric Equations]] | + | * [[Parametric Equations]] |
− | * [[Curves in Space and Vector Functions]] | + | * [[Curves in Space and Vector-Valued Functions]] |
− | * [[Arc Length]] | + | * [[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. |
+ | |- | ||
− | |||
− | |Week | + | |Week 14/15 |
|| | || | ||
− | + | 6.3 | |
− | |||
− | |||
|| | || | ||
− | [[Vector Fields | + | [[Conservative Vector Fields]] |
|| | || | ||
− | * [[ | + | * [[Vector Fields and Line Integrals]] |
− | * [[ | + | * [[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 14/15 | |
− | | | ||
|| | || | ||
− | + | 6.4 | |
− | |||
− | |||
|| | || | ||
− | [[ | + | [[Green's Theorem]] |
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | + | [[Stokes' Theorem]] | |
|| | || | ||
− | [[ | + | * [[Vector Fields]] |
+ | * [[Line Integrals]] | ||
+ | * [[Partial Derivatives]] | ||
+ | * [[The Dot Product]] | ||
+ | * [[Line Integrals|Path Independence]] | ||
+ | * [[Conservative Vector Fields]] | ||
|| | || | ||
− | * | + | * Circulation form of Green's Theorem. |
− | * | + | * Flux Form of Green’s Theorem. |
− | * | + | * 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 |
|