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| | ! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes | | ! Date !! Sections !! Topics !! Prerequisite Skills !! Student Learning Outcomes |
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| − | | + | |Week 1 || 1.2 || [[Three-Dimensional Coordinate Systems]] || || |
| − | | |
| − | |Week 1 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">1.1</div>
| |
| − | | |
| − | || | |
| − |
| |
| − | [[Polar Coordinates]] | |
| − | | |
| − | || | |
| − | * [[Trigonometric Functions: Unit Circle Approach]] <!-- 1093-2.2 -->
| |
| − | * [[Inverse Trigonometric Functions]] <!-- 1093-3.1 -->
| |
| − | || | |
| − | * 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
| |
| | |- | | |- |
| − | | + | |Weeks 1 || 2.1 || [[Vectors in The Plane, Space]] || || |
| − | | |
| − | | |
| − | |Week 1 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">1.2</div>
| |
| − | | |
| − | || | |
| − |
| |
| − | [[Three-Dimensional Coordinate Systems]] | |
| − | | |
| − | || | |
| − | | |
| − | * [[Two-dimensional coordinate systems]] <!-- 2233-3.3 -->
| |
| − | * [[Solving Equations and Inequalities| Algebraic Expressions]] <!-- 1073-Mod R -->
| |
| − | | |
| − | | |
| − | | |
| − | || | |
| − | | |
| − | * Three-dimensional coordinate systems.
| |
| − | * Distance Formula in Space.
| |
| − | * Standard Equation for a Sphere.
| |
| | |- | | |- |
| − | | + | |Week 1 || 2.3 || [[The Dot Product]] || || |
| − | | |
| − | |Weeks 1/2 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">2.1</div>
| |
| − | | |
| − | || | |
| − |
| |
| − | | |
| − | [[Vectors in The Plane, Space]] | |
| − | | |
| − | || | |
| − | | |
| − | * [[Linear Equations|Line Segments]] <!-- 1073-Mod R -->
| |
| − | * [[Distance Formula| Distance Formula]] <!-- DNE (recommend pairing with discussion of absolute value function) -->
| |
| − | | |
| − | ||
| |
| − | | |
| − | * Vector Algebra Operations
| |
| − | * The Magnitude of a vector
| |
| − | * Unit Vectors
| |
| − | * The Midpoint of a Line Segment
| |
| − | * The Vector projection
| |
| | |- | | |- |
| − | | + | |Week 2 || 2.4 || [[The Cross Product]] Scalar triple product || || |
| − | | |
| − | | |
| − | |Week 2 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">2.3</div>
| |
| − | | |
| − | || | |
| − |
| |
| − | [[The Dot Product]] | |
| − | | |
| − | | |
| − | || | |
| − | | |
| − | * [[Trigonometric Functions|Basic Trig Functions]] <!-- 1093-2.2 -->
| |
| − | * [[Vectors]] <!-- 2214-12.2 --> <!-- 2233-1.1 -->
| |
| − | | |
| − | || | |
| − | * Definition of Dot Product
| |
| − | * Properties of Dot Product
| |
| − | * Angle between vectors
| |
| − | * Orthogonal vectors
| |
| − | | |
| | |- | | |- |
| − | | + | |Week 2 || 2.5 || [[Equations of Lines, Planes and Surfaces in Space]] || || |
| − | | |
| − | |Week 2 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">2.4</div>
| |
| − | | |
| − | || | |
| − |
| |
| − | [[The Cross Product]] | |
| − | | |
| − | || | |
| − | | |
| − | * [[Trigonometric Functions|Basic Trig Functions]] <!-- 1093-2.2 -->
| |
| − | * [[Determinants]] <!-- 2233-6.1,6.2 -->
| |
| − | * [[Vectors]]
| |
| − | | |
| − | || | |
| − | | |
| − | * Definition of Cross Product
| |
| − | * Properties of the cross product
| |
| − | * Area of a parallelogram
| |
| − | * Cross product as a determinant
| |
| − | | |
| | |- | | |- |
| − | | + | |Week 3 || 2.6 || [[Equations of Lines, Planes and Surfaces in Space|Equaitons of Curves. Equations of Surfaces]] || || |
| − | | |
| − | | |
| − | |Week 3 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">2.5</div>
| |
| − | | |
| − | || | |
| − |
| |
| − | | |
| − | [[Equations of Lines, Planes and Surfaces in Space]] | |
| − | | |
| − | || | |
| − | | |
| − | * [[The Dot Product]] <!-- 2214-12.3 -->
| |
| − | * [[The Cross Product]]
| |
| − | * [[Quadratic Functions]] <!-- 1073-Mod R -->
| |
| − | * [[Parametric Equations]] <!-- 1224-7.1 -->
| |
| − | | |
| − | || | |
| − | | |
| − | * 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.
| |
| − | | |
| | |- | | |- |
| − | | + | |Weeks 3 || 3.1, 3.2 || [[Curves in Space and Vector-Valued Functions]] Derivatives and integrals of vector functions || || |
| − | | |
| − | |Week 3 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">2.6</div>
| |
| − | | |
| − | || | |
| − |
| |
| − | | |
| − | [[Equations of Lines, Planes and Surfaces in Space|Cylinders and Quadratic Surfaces]] | |
| − | | |
| − | || | |
| − | | |
| − | * [[Quadratic Functions]] <!-- 1073-Mod R -->
| |
| − | * [[Parametric Equations]] <!-- 1224-7.1 -->
| |
| − | * '''[[Conics]]''' <!-- DNE (recommend 1093) -->
| |
| − | | |
| − | || | |
| − | | |
| − | * Find equations for cylinders that are generated by rotating lines that are parallel to a plane
| |
| − | * Understand basic quadratic surfaces
| |
| − | * Understand general quadratic surfaces
| |
| − | | |
| | |- | | |- |
| − | | + | |Week 4 || 3.3 || [[Arc Length]] || || |
| − | | |
| − | |Weeks 3/4 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">3.1, 3.2</div>
| |
| − | | |
| − | || | |
| − | | |
| − | [[Curves in Space and Vector-Valued Functions]] | |
| − | | |
| − | || | |
| − | | |
| − | * [[Parametric Equations]] <!-- 1224-7.1 -->
| |
| − | * [[Vectors]] <!-- 2214-12.2 --> <!-- 2233-1.1 -->
| |
| − | * [[The Derivative as a Function]] <!-- 1214-3.2 -->
| |
| − | * [[The Limit of a Function]] <!-- 1214-2.2 -->
| |
| − | * [[Continuity]] <!-- 1214-2.4 -->
| |
| − | * [[The Dot Product]] <!-- 2214-12.3 -->
| |
| − | * [[The Cross Product]] <!-- 2214-12.4 -->
| |
| − | | |
| − | || | |
| − | | |
| − | * Vector functions
| |
| − | * Limits of vector functions
| |
| − | * Continuity of vector functions
| |
| − | * Differentiation rules for vector functions
| |
| − | * Curves and paths in space
| |
| − | | |
| | |- | | |- |
| − | | + | |Weeks 4/5 || 3.4 || [[Motion in Space]] || || |
| − | | |
| − | | |
| − | |Week 4 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">3.3</div>
| |
| − | | |
| − | ||
| |
| − |
| |
| − | [[Arc Length]]
| |
| − | | |
| − | || | |
| − | | |
| − | * '''[[Distance Formula| The Length of a Line Segment]]''' <!-- DNE (recommend pairing with discussion of absolute value function) -->
| |
| − | * [[Curves in Space and Vector-Valued Functions|Vector Functions]] <!-- 1224-7.1 -->
| |
| − | * [[Line Integrals|Integrals of Vector Functions]], [[Derivatives of Vector Functions]]<!-- 2214-13.2 -->
| |
| − | | |
| − | || | |
| − | | |
| − | * The arc Length of a vector function
| |
| − | * Arc length parameterization
| |
| − | | |
| | |- | | |- |
| − | | + | |Week 5/6 || 4.1 || [[Functions of Several Variables]] || || |
| − | | |
| − | |Weeks 4/5 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">3.4</div>
| |
| − | | |
| − | || | |
| − |
| |
| − | [[Motion in Space]] | |
| − | | |
| − | || | |
| − | * [[Vectors]] <!-- 1214-12.2 -->
| |
| − | * [[Parametric Equations]] <!-- 1224-7.1 -->
| |
| − | * [[The Cross Product]] <!-- 2214-12.4 -->
| |
| − | * [[Derivatives of Vector Functions]] <!-- 1224-7.1 -->
| |
| − | || | |
| − | * The Unit tangent vector
| |
| − | * The curvature
| |
| − | * The Principal Unit Normal Vector
| |
| − | * The Binormal Vector
| |
| − | * The tangential and normal components of acceleration
| |
| − | * The Torsion
| |
| − | | |
| − | | |
| | |- | | |- |
| − | | + | |Week 6 || 4.2 || [[Limit and Continuity of Function of Several Variables]] || || |
| − | | |
| − | | |
| − | |Week 5/6 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">4.1</div>
| |
| − | | |
| − | || | |
| − |
| |
| − | | |
| − | [[Functions of Several Variables]] | |
| − | | |
| − | || | |
| − | | |
| − | * [[Domain of a Function]] <!-- 1073-Mod 1.2 -->
| |
| − | * [[Range of a Function]] <!-- 1073-Mod 1.2 -->
| |
| − | * [[Solving Equations and Inequalities]] <!-- 1073-Mod R -->
| |
| − | * [[Graphs| Graphing a Function]] <!-- 1073-Mod R -->
| |
| − | | |
| − | || | |
| − | * Functions of two variables
| |
| − | * Functions of three variables
| |
| − | * Domain and range of multivariable functions
| |
| − | * Bounded regions
| |
| − | * Graphs and level curves of two variable functions
| |
| − | * Level surfaces of three variable functions
| |
| | |- | | |- |
| − | | + | |Week 6 || 4.3 || [[Partial Derivatives]] || || |
| − | | |
| − | |Week 6 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">4.2</div>
| |
| − | | |
| − | || | |
| − |
| |
| − | | |
| − | [[Limit and Continuity of Function of Several Variables]] | |
| − | | |
| − | || | |
| − | | |
| − | * [[Continuity]] <!-- 1214-2.2, 2.4 -->
| |
| − | * [[The Limit Laws]] <!-- 1214-2.3 -->
| |
| − | * [[Composition of Functions]] <!-- 1073-Mod 7.1 -->
| |
| − | * [[The Dot Product]] <!-- 2214-12.3 -->
| |
| − | | |
| − | || | |
| − | | |
| − | * Limits of functions of two variables
| |
| − | * Limits of functions of more than two variables
| |
| − | * 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
| |
| − | * Extreme values on closed and bounded domains
| |
| | |- | | |- |
| − | | + | |Week 7 || 4.4 || [[Directional Derivatives and Gradient Vectors]] || || |
| − | | |
| − | |Week 6 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">4.3</div>
| |
| − | | |
| − | || | |
| − | | |
| − | [[Partial Derivatives]] | |
| − | | |
| − | ||
| |
| − | | |
| − | * [[The Derivative as a Function|The first]] and [[The Second Derivative|second derivative]] of a function <!-- 1214-3.2 -->
| |
| − | * [[Limit and Continuity of Function of Several Variables]] <!-- 2214-14.2 -->
| |
| − | | |
| − | | |
| − | || | |
| − | * Partial derivatives for functions of two variables
| |
| − | * Partial derivatives for functions of more than two variables
| |
| − | * Partial derivatives and continuity
| |
| − | * Second order partial derivatives
| |
| − | * Mixed derivative theorem
| |
| | |- | | |- |
| − | | + | |Week 7 || 4.5 || [[Tangent Plane]], [[Differentiability]] || || |
| − | | |
| − | |Week 7 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">4.4</div>
| |
| − | | |
| − | || | |
| − | | |
| − | [[Directional Derivatives and Gradient Vectors]]
| |
| − | | |
| − | ||
| |
| − | * [[Trigonometric Functions]] <!-- 1093-2.2 -->
| |
| − | * [[Vectors, Unit Vectors]] <!-- 2214-12.2 --> <!-- 2233-1.1 -->
| |
| − | * [[Partial Derivatives]] <!-- 1214-14.3 -->
| |
| − | * [[Gradients]]
| |
| − | * [[The Dot Product]] <!-- 2214-12.3 -->
| |
| − | || | |
| − | * Directional derivatives for functions of two variables
| |
| − | * Gradients
| |
| − | * Properties of directional derivatives
| |
| − | * Tangents to level curves
| |
| − | * Directional derivatives for functions of three variables
| |
| | |- | | |- |
| − | | + | |Week 7 || 4.6 || [[The Chain Rule for Functions of more than One Variable]] || || |
| − | | |
| − | |Week 7 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">4.5</div>
| |
| − | | |
| − | || | |
| − | [[Tangent Plane]], | |
| − | [[Differentiability]]
| |
| − | | |
| − | | |
| − | || | |
| − | * [[Partial Derivatives]] <!-- 1214-14.3 -->
| |
| − | * [[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 8 || 4.7 || [[Maxima and Minima Problems]] || || |
| − | | |
| − | | |
| − | |Week 7 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">4.6</div>
| |
| − | | |
| − | || | |
| − | | |
| − | [[The Chain Rule for Functions of more than One Variable]] | |
| − | | |
| − | || | |
| − | * [[Differentiation Rules]] <!-- 1214-3.3 -->
| |
| − | * [[The Chain Rule]] <!-- 1214-3.6 -->
| |
| − | * [[Partial Derivatives]] <!-- 1214-14.3 -->
| |
| − | | |
| − | || | |
| − | * 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 8/9 || 4.8 || [[Lagrange Multipliers]] || || |
| − | |Week 8 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">4.7</div>
| |
| − | | |
| − | || | |
| − | | |
| − | [[Maxima and Minima Problems]] | |
| − | | |
| − | || | |
| − | * [[Extreme values on closed and bounded domains]] <!-- 2214-14.2 -->
| |
| − | * [[Partial Derivatives]] <!-- 1214-14.3 -->
| |
| − | * [[Maxima and Minima|Maxima, Minima and Critical Points of a Function]] <!-- 1214-4.3 -->
| |
| − | * [[Limit and Continuity of Function of Several Variables]] <!-- 2214-14.2 -->
| |
| − | | |
| − | || | |
| − | * The derivative test for local extreme values
| |
| − | * Extreme values on closed and bounded domains
| |
| − | * Critical points and saddle points for functions of two variables
| |
| − | * Second derivative test for local extreme values
| |
| − | * Absolute maxima and minima on closed and bounded regions
| |
| − | | |
| | |- | | |- |
| − | | + | |Week 9/10 || 5.1 || [[Multiple Integrals|Double Integrals over Rectangular Regions]] || || |
| − | |Week 8/9 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">4.8</div>
| |
| − | | |
| − | || | |
| − | | |
| − | [[Lagrange Multipliers]] | |
| − | | |
| − | || | |
| − | | |
| − | * [[Partial Derivatives]] <!-- 1214-14.3 -->
| |
| − | * [[Critical Points of a Function]] <!-- 1214-4.3 -->
| |
| − | | |
| − | || | |
| − | * Lagrange Multipliers with One Constraint
| |
| − | * Lagrange Multipliers with Two Constraints
| |
| − | | |
| | |- | | |- |
| − | | + | |Week 10 || 5.2 || [[Multiple Integrals|Double Integrals over General Regions]] || || |
| − | | |
| − | |Week 9/10 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">5.1</div>
| |
| − | | |
| − | || | |
| − | | |
| − | [[Multiple Integrals|Double Integrals over Rectangular Regions]] | |
| − | | |
| − | || | |
| − | | |
| − | * [[Approximating Areas]] <!-- 1214-5.1 -->
| |
| − | * [[The Definite Integral|Limits of Riemann Sums]] <!-- 1214-5.2 -->
| |
| − | | |
| − | || | |
| − | * Double Integral is the limit of Double Sums.
| |
| − | * Double Integrals over Rectangular Regions.
| |
| − | * Interated Integrals.
| |
| − | * Fubini's Theorem (part 1).
| |
| − | | |
| | |- | | |- |
| − | | + | |Week 11 || 5.3 || [[Multiple Integrals|Double Integrals in Polar Coordinates]] || || |
| − | | |
| − | |Week 10 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">5.2</div>
| |
| − | | |
| − | || | |
| − | | |
| − | [[Multiple Integrals|Double Integrals over General Regions]] | |
| − | | |
| − | || | |
| − | | |
| − | * [[Continuity]] <!-- 1214-3.5 -->
| |
| − | * [[Determining Volumes by Slicing]] <!-- 1224-2.2 -->
| |
| − | * [[Multiple Integrals|Double and Iterated Integrals over Rectangular regions]] <!-- 2214-5.1 -->
| |
| − | | |
| − | || | |
| − | * 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 11 || 5.4 || [[Multiple Integrals|Triple Integrals in Rectangular Coordinates]] || || |
| − | |Week 11 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">5.3</div>
| |
| − | | |
| − | || | |
| − | | |
| − | [[Multiple Integrals|Double Integrals in Polar Coordinates]] | |
| − | | |
| − | ||
| |
| − | | |
| − | * [[Multiple Integrals|Double Integrals over General Regions]] <!-- 2214-15.2 -->
| |
| − | * [[Polar Coordinates]] <!-- 1093-5.1 -->
| |
| − | | |
| − | || | |
| − | * Double Integrals over rectangular polar regions.
| |
| − | * Double Integrals over general polar regions.
| |
| − | * Changing Cartesian Integrals into Polar Integrals.
| |
| − | * Using Double Integrals in Polar Coordinates to find Volumes, Areas.
| |
| − | | |
| | |- | | |- |
| − | | + | |Week 12 || 5.5 || [[Multiple Integrals|Triple Integrals in Cylindrical and Spherical Coordinates]] || || |
| − | | |
| − | |Week 11 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;"> 5.4</div>
| |
| − | | |
| − | || | |
| − | | |
| − | [[Multiple Integrals|Triple Integrals in Rectangular Coordinates]] | |
| − | | |
| − | ||
| |
| − | | |
| − | * [[Multiple Integrals|Double Integrals]] <!-- 2214-5.1, 2214-5.2 -->
| |
| − | * [[Multiple Integrals|Area by Double Integration]] <!-- 2214-15.3 -->
| |
| − | * '''[[Change of Variables]]''' <!-- DNE (recommend 1073) -->
| |
| − | | |
| − | || | |
| − | | |
| − | * 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 13 || 5.6 || [[Multiple Integrals|Applications of Multiple Integrals]] || || |
| − | | |
| − | | |
| − | |Week 12 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">5.5</div>
| |
| − | | |
| − | || | |
| − | | |
| − | [[Multiple Integrals|Triple Integrals in Cylindrical and Spherical Coordinates]] | |
| − | | |
| − | ||
| |
| − | | |
| − | * [[Multiple Integrals|Double Integrals in Polar Form]] <!-- 2214-15.4 -->
| |
| − | * [[Multiple Integrals|Triple Integrals in Rectangular Coordinates]] <!-- 2214-15.5 -->
| |
| − | | |
| − | || | |
| − | | |
| − | * 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.
| |
| − | | |
| | |- | | |- |
| − | | + | |Week 13/14 || 5.7 || [[Multiple Integrals|Change of Variables in Multiple Integrals]] || || |
| − | | |
| − | |Week 13 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">5.6</div>
| |
| − | | |
| − | || | |
| − |
| |
| − | [[Multiple Integrals|Applications of Multiple Integrals]] | |
| − | | |
| − | || | |
| − | | |
| − | * [[Multiple Integrals|Double Integral]] <!-- 2214-5.2,2214-5.3 -->
| |
| − | * [[Multiple Integrals|Triple Integrals]] <!-- 2214-5.3,2214-5.4 -->
| |
| − | | |
| − | ||
| |
| − | | |
| − | * Finding Masses, Moments, Centers of Masses, Moments of Inertia in Two Dimensions.
| |
| − | * Finding Masses, Moments, Centers of Masses, Moments of Inertia in Three Dimensions.
| |
| − | | |
| | |- | | |- |
| − | | + | |Week 14 || 6.1 || [[Vector Fields]] || || |
| − | |Week 13/14 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">5.7</div>
| |
| − | | |
| − | || | |
| − |
| |
| − | [[Multiple Integrals|Change of Variables in Multiple Integrals]] | |
| − | | |
| − | || | |
| − | | |
| − | * [[Multiple Integrals|Double Integral]] <!-- 2214-5.2,2214-5.3 -->
| |
| − | * [[Multiple Integrals|Triple Integrals]] <!-- 2214-5.3,2214-5.4 -->
| |
| − | | |
| − | ||
| |
| − | | |
| − | * 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 || 6.2 || [[Line Integrals]] || || |
| − | |Week 14 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">6.1</div>
| |
| − | | |
| − | || | |
| − | | |
| − | [[Vector Fields]] | |
| − | | |
| − | || | |
| − | | |
| − | * [[The Dot Product]] <!-- 2214-12.3 -->
| |
| − | * [[Directional Derivatives and Gradient Vectors]] <!-- 2214-14.5 -->
| |
| − | || | |
| − | * 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 14/15 || 6.3 || [[Conservative Vector Fields]] || || |
| − | | |
| − | |Week 14 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">6.2</div>
| |
| − | | |
| − | || | |
| − | | |
| − | [[Line Integrals]] | |
| − | | |
| − | || | |
| − | | |
| − | * [[Parametric Equations]] <!-- 1224-7.1 -->
| |
| − | * [[Curves in Space and Vector-Valued Functions]] <!-- 2214-13.1 -->
| |
| − | * [[Arc Length]] <!-- 1224-13.3 -->
| |
| − | | |
| − | || | |
| − | * 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.
| |
| − | | |
| | |- | | |- |
| − | | + | |Weeks 14/15 || 6.4 || [[Green's Theorem]] [[Stokes' Theorem]] || || |
| − | | |
| − | |Week 14/15
| |
| − | | |
| − | ||
| |
| − | | |
| − | <div style="text-align: center;">6.3</div>
| |
| − | | |
| − | ||
| |
| − | | |
| − | [[Conservative Vector Fields]]
| |
| − | | |
| − | ||
| |
| − | | |
| − | * [[Vector Fields and Line Integrals]] <!-- 2214-16.2 -->
| |
| − | * [[Partial Derivatives]] <!-- 1214-14.3 -->
| |
| − | | |
| − | ||
| |
| − | * 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 | |
| − | | |
| − | || | |
| − | | |
| − | <div style="text-align: center;">6.4</div>
| |
| − | | |
| − | || | |
| − | | |
| − | [[Green's Theorem]] | |
| − | | |
| − | [[Stokes' Theorem]] | |
| − | | |
| − | || | |
| − | | |
| − | * [[Vector Fields]]
| |
| − | * [[Line Integrals]] <!-- 2214-16.2 -->
| |
| − | * [[Partial Derivatives]] <!-- 1214-14.3 -->
| |
| − | * [[The Dot Product]] <!-- 2214-16.3 -->
| |
| − | * [[Line Integrals|Path Independence]]
| |
| − | * [[Conservative Vector Fields]] <!-- 2214-16.3 -->
| |
| − | | |
| − | || | |
| − | | |
| − | * Circulation form of Green's Theorem.
| |
| − | * Flux Form of Green’s Theorem.
| |
| − | * Applying Green's Theorem to find Work, Flux.
| |
| | |} | | |} |
