Chapters:

Introduction.

Introduction Lecture

• Videos: Please note that the video is refering to Chapters 12, 13, 14, 15, 16, 17 as 13, 14, 15, 16, 17, 18.

Vector review.

Vector Review Lecture

• Videos: Please note that the video refers to Chapter 12.6 but it covers the Chapter 12.6 material.

Sections 12.6: A Survey of Quadric Surfaces.

Section 12.6Lecture

Learning objectives are

• Recognize and sketch quadric surfaces.


• Videos: Please note that the video refers to Chapter 12.6 but it covers the Chapter 12.6 material.

Sections 12.7: Cylindrical and Spherical Coordinates.

Section 12.7 Lecture

Learning objectives are

• Convert points and equations between rectangular, polar, cylindrical, and spherical coordinates.


• Videos: Please note that the video refers to Chapter 12.7 but it covers the Chapter 12.7 material.

Sections 13.1: Vector-Valued Functions.

Section 13.1 Lecture

Learning objectives are

• Identify and give examples of common vector and scalar functions.
• Determine the domain and range of a vector function.
• Analyze the intersections of space curves.
• Sketch a parametrized space curve using projections onto the major planes.
• Construct a parametrization of space curves resulting from intersecting surfaces.

Sections 13.2: Calculus of Vector-Valued Functions.

Section 13.2 Lecture

Learning objectives are

• Evaluate limits, derivatives, and integrals of vector functions.
• Apply the product rule to scalar, dot, and cross products of vector functions.
• Calculate tangent lines of vector


• Videos:

Sections 13.3: Arc Length and Speed.

Section 13.3 Lecture

Learning objectives are

• Calculate the velocity and speed of a parametrized curve.
• Determine an arc length parametrization of a space curve.

Sections 14.1: Functions of Two or More Variables.

Section 14.1 Lecture

Learning objectives are

• Identify the domain and range of multivariable functions.
• Describe the level curves of a two-variable function using a contour map.


• Videos: Please note that the video refers to Chapter 15.1 but it covers the Chapter 14.1 material.

Sections 14.2: Limits and Continuity in Several variables.

Section 14.2 Lecture

Learning objectives are

• Comprehend the concept of limit for two-variable functions and understand the basic limit laws.
• Evaluate the limit of multivariable functions at continuous points.
• Demonstrate that a limit fails to exist by calculating the limit of two distinct paths along the domain.
• Utilize substitution and the Squeeze Theorem to evaluate limits.


• Videos: Please note that the video refers to Chapter 15.2 but it covers the Chapter 14.2 material.

Sections 14.3: Partial Derivatives.

Section 14.3 Lecture

Learning objectives are

• Compute partial derivatives of multivariable functions.
• Recognize partial derivatives as rates of change along the major axes of a function's domain.
• Apply Clairaut's Theorem to mixed partial derivates.


• Videos: Please note that the video refers to Chapter 15.3 but it covers the Chapter 14.3 material.

Sections 14.4: Differentiability, Tangent planes, and Linear Approximations.

Section 14.4 Lecture

Learning objectives are

• Find the equation of the tangent plane to a two-variable function at a given point.
• Apply the criterion for differentiability to two-variable functions to determine differentiability.
• Approximate values and change of a differentiable function using tangent planes.


• Videos: Please note that the video refers to Chapter 15.2 but it covers the Chapter 14.2 material.

Sections 14.5: The Gradient and Dirrectional Derivatives.

Section 14.5 Lecture

Learning objectives are

• Calculate the gradient if a function.
• Calculate the directional derivative of a function using the gradient
• Apply the chain rule to a path along a surface to determine rates of change along the path.
• Understand the basic geometric properties of the gradient and use the gradient to determine the equation of the tangent plane to a level surface.


• Videos:

Sections 14.6: Multivariable Calculus Chain Rule.

Section 14.6 Lecture

Learning objectives are

• Use a dependency tree to apply the Chain Rule to multivariable functions.
• Perform implicit differentiation using the Chain Rule.


• Videos:

Sections 14.7:Optimization in Several Variables.

Section 14.7 Lecture

Learning objectives are

• Calculate the critical points of a two-variable function and use the Second Derivative Test to identify local extrema and saddle points.
• Recognize closed and bounded domains.
• Determine the absolute extrema of a two-variable function restricted to a closed, bounded domain.


• Videos:

Sections 14.8: Lagrange Multipliers: Optimizing with a Constraint.

Section 14.8 Lecture

Learning objectives are

• Apply Lagrange Multipliers to determine the absolute extrema of a multivariable function restricted to a constraint.


• Videos:

Sections 15.1: Integration in Two Variables.

Section 15.1 Lecture

Learning objectives are

• Recognize that the double integral of a two-variable function over a region is the signed volume contained under the surface.
• Apply Fubini's Theorem to evaluate a double integral over a rectangle as an iterated integral.


• Videos:

Sections 15.2: Double Integrals Over More General Regions.

Section 15.2 Lecture

Learning objectives are

• Evaluate double integrals over vertically or horizontally simple regions as an iterated integral
• Represent the area of a region as a double integral.
• Understand the Mean Value Theorem for Integrals and connect it to the Mean Value Theorem for Derivatives.


• Videos:

Sections 15.3: Triple Integrals.

Section 15.3 Lecture

Learning objectives are

• Apply Fubini's Theorem to evaluate a triple integral over a box as an iterated integral.
• Evaluate triple integrals over x-simple, y-simple, or z-simple solids as an iterated integral.Evaluate triple integrals over x-simple, y-simple, or z-simple solids as an iterated integral.


• Videos:

Sections 15.4: Integration in Polar, Cylindrical, and Spherical Coordinates.

Section 15.4 Lecture

Learning objectives are

• Evaluate integrals in polar, cylindrical, and spherical coordinates through a transformation, including the Jacobian of the transformation as a term in the integrand.


• Videos:

Sections 15.5: Applications of Mulriple Integrals.

Section 15.5 Lecture

Learning objectives are

• Calculate the total mass and center of mass for regions and solids.


• Videos:

Sections 15.6: Change of Variables.

Section 15.6 Lecture

Learning objectives are

• Analyze transformations by calculating the Jacobian of the transformation and graphing the image of regions and solids.
• Evaluate double and triple integrals by changing variables using a transformation.


• Videos:

Sections 16.1: Vector Fields.

Section 16.1 Lecture

Learning objectives are

• Compute the divergence and curl of vector fields.
• Calculate a potential function for conservative vector fields.
• Visualize a vector field by graphing the vectors assigned to a sampling of points.


• Videos:

Sections 16.2: Line Integrals.

Section 16.2 Lecture

Learning objectives are

• Compute scalar line integrals using a parametrization of the curve and an arc length differential.
• Compute vector line integrals using a regular parametrization of the curve in a positive direction and a vector differential.
• Represent the work performed against a vector field along a curve as a vector line integral.


• Videos:

Sections 16.3: Conservative Vector Fields.

Section 16.3 Lecture

Learning objectives are

• Apply the Fundamental Theorem for Conservative Vector Fields and recognize its connection to the Fundamental Theorem of Calculus.
• Understand that vector fields are conservative if and only if they are path-independent.
• Inspect vector fields to determine if they are conservative over a simply connected domain by verifying that the cross-partials condition is satisfied.


• Videos:

Sections 16.4: Parametrized Surfaces and Surface Integrals.

Section 16.4 Lecture

Learning objectives are

• Sketch parametrized surfaces using grid lines and identify standard parametrizations for common surfaces.
• Calculate normal vectors of a regular parametrized surface using the cross product of the tangent vectors.
• Compute scalar surface integrals as a double integral of the integrand over the parametrized surface multiplied by the magnitude of the normal vector of the surface.
• Represent surface area as a scalar surface integral with an integrand of one.


• Videos:

Sections 16.5: Surface Inegrals of Vector Fields.

Section 16.5 Lecture

Learning objectives are

• Understand that surfaces are orientable if a continuously varying normal vector can be specified at each point. An example of a non-orientable surface is the Mobius strip.
• Understand that vector surface integrals compute the accumulation of the vector field normal to the surface.
• Represent the flux of a vector field through a surface as a vector surface integral.


• Videos:

Sections 17.1: Green's Theorem.

Section 17.1 Lecture

Learning objectives are

• Apply Green's Theorem to domains with a boundary consisting of a simple, closed curve, oriented counterclockwise.
• Calculate the area of a region in the plane using Green's Theorem.
• Recognize and apply Green's Theorem using multiple representations of the formula.


• Videos:

Sections 17.2: Stokes' Theorem.

Section 17.2 Lecture

Learning objectives are

• Understand how Stoke's Theorem relates the circulation around the boundary to the surface integral of the curl.


• Videos:

Sections 17.3: Divergence Theorem.

Section 17.3 Lecture

Learning objectives are

• Understand how the Divergence Theorem relates the divergence of a vector field through a solid to the flux of the field through the boundary.
• Understand the connection between the Fundamental Theorem of Calculus and the Fundamental Theorem for Line Integrals, Green's Theorem, Stoke's Theorem, and the Divergence Theorem.


• Videos: