Learning Outcomes#
These are the learning outcomes we will be studying in MTH 241, organized by topic. Also included are the relevant sections from the textbook as well as any applicable assessments.
Vector Geometry#
Number |
Learning Outcome |
Textbook Sections |
Assessments |
|---|---|---|---|
V1 |
Vector Geometry: Draw a vector in two and three dimensional space. |
12.1 |
HW V1, Checkpoint Exam, Midterm Exam 1, Final Exam |
V2 |
Vector Algebra: Compute vector algebra (addition, subtraction, and scalar multiplication) and length. |
12.2 |
HW V2, Checkpoint Exam, Midterm Exam 1, Final Exam |
V3 |
Dot Product: Compute the dot product of two vectors and use this to determine if two vectors are orthogonal. |
12.3 |
HW V3, Checkpoint Exam, Midterm Exam 1, Final Exam |
V4 |
Cross Product: Compute the cross product of two vectors and use this to find a third vector orthogonal to both. |
12.4 |
HW V4, Checkpoint Exam, Midterm Exam 1, Final Exam |
V5 |
Lines: Find the equation of a line in two and three dimensional space. |
12.5 |
HW V5, Checkpoint Exam, Midterm Exam 1, Final Exam |
V6 |
Planes: Find the equation of a plane in three dimensional space. |
12.5 |
HW V6, Checkpoint Exam, Midterm Exam 1, Final Exam |
Introduction to Vector-Valued Functions or Space Curves#
Number |
Learning Outcome |
Textbook Sections |
Assessments |
|---|---|---|---|
VVF1 |
Graphing VV Functions: Sketch the graph of a vector-valued function. Parameterize the curve formed from the intersection of two surfaces. |
13.1 |
HW VVF1, Checkpoint Exam, Midterm Exam 1, Final Exam |
VVF2 |
Calculus of VV Functions: Compute derivatives and integrals of vector-valued functions. |
13.2 |
HW VVF2, Checkpoint Exam, Midterm Exam 1, Final Exam |
VVF3 |
Arc Length: Compute the arc length of a space curve. |
13.3 |
HW VVF3, Checkpoint Exam, Midterm Exam 1, Final Exam |
VVF4 |
Curvature: Compute the curvature of a space curve. |
13.3 |
HW VVF4, Checkpoint Exam, Midterm Exam 1, Final Exam |
VVF5 |
TNB Frame: Calculate the tangent, normal, and binormal vectors for a given space curve. |
13.4 |
HW VVF5, Checkpoint Exam, Midterm Exam 1, Final Exam |
VVF6 |
Velocity and Acceleration: Compute the velocity and acceleration of a particle moving along a space curve. Find the decomposition of acceleration on the Tangent-Normal Plane. |
13.4 |
HW VVF6, Checkpoint Exam, Midterm Exam 1, Final Exam |
Scalar-Valued Functions#
Number |
Learning Outcome |
Textbook Sections |
Assessments |
|---|---|---|---|
SVF1 |
Graphing Scalar Functions: Plot the graph of a scalar function in three dimensions and in two dimensions using level curves. |
14.1 & 14.2 |
HW SVF1, Checkpoint Exam, Midterm Exam 2, Final Exam |
SVF2 |
Partial Derivatives: Compute the partial derivatives of a scalar function. |
14.3 |
HW SVF2, Checkpoint Exam, Midterm Exam 2, Final Exam |
SVF3 |
Tangent Plane: Find the equation of the plane tangent to a surface. |
14.4 |
HW SVF3, Checkpoint Exam, Midterm Exam 2, Final Exam |
SVF4 |
Chain Rule: Compute the partial derivatives of a scalar function using chain rule. |
14.5 |
HW SVF4, Checkpoint Exam, Midterm Exam 2, Final Exam |
SVF5 |
Directional Derivative: Compute the directional derivative of a scalar function. |
14.6 |
HW SVF5, Checkpoint Exam, Midterm Exam 2, Final Exam |
SVF6 |
Gradient: Compute the gradient of a scalar function and use this to maximize the directional derivative. |
14.6 |
HW SVF6, Checkpoint Exam, Midterm Exam 2, Final Exam |
Optimization of Scalar Functions#
Number |
Learning Outcome |
Textbook Sections |
Assessments |
|---|---|---|---|
O1 |
Critical Points: Find all critical points of a function of two variables. |
14.7 |
HW O1, Checkpoint Exam, Midterm Exam 2, Final Exam |
O2 |
Classifying Critical Points: Use the second derivative test to classify the critical points as a local minima, local maxima, and saddle points. |
14.7 |
HW O2, Checkpoint Exam, Midterm Exam 2, Final Exam |
O3 |
Constrained Optimization: Use the method of Lagrange Multipliers to solve constrained optimization problems involving one constraint equation. |
14.8 |
HW O3, Checkpoint Exam, Midterm Exam 2, Final Exam |
O4 |
Closed and Bounded Optimization: Find the absolute extrema for a function defined on a closed and bounded set. |
14.8 |
HW O4, Checkpoint Exam, Midterm Exam 2, Final Exam |
Double Integrals of Scalar Functions#
Number |
Learning Outcome |
Textbook Sections |
Assessments |
|---|---|---|---|
DI1 |
Double Integral (Rectangular) Compute the double integral of a two variable scalar function on a rectangular region. |
15.1 |
HW DI1, Checkpoint Exam, Midterm Exam 2, Final Exam |
DI2 |
Double Integral (General Region): Compute the double integral of a two variable function of a general region. |
15.2 |
HW DI2, Checkpoint Exam, Midterm Exam 2, Final Exam |
DI3 |
Double Integral (Polar): Compute the double integral of a two variable function over a polar region. |
15.3 |
HW DI3, Checkpoint Exam, Midterm Exam 3, Final Exam |
DI4 |
Surface Area: Use a double integral to calculate the surface area of the graph of a two variable scalar function. |
15.5 |
HW DI4, Checkpoint Exam, Midterm Exam 3, Final Exam |
DI5 |
Center of Mass: Use a double integral to calculate the center of mass for a two dimensional object given its density function. |
15.4 |
HW DI5, Checkpoint Exam, Midterm Exam 3, Final Exam |
Triple Integrals of Scalar Functions#
Number |
Learning Outcome |
Textbook Sections |
Assessments |
|---|---|---|---|
TI1 |
Rectangular Region: Compute the triple integral of a three variable function on a rectangular region. |
15.6 |
HW TI1, Checkpoint Exam, Midterm Exam 3, Final Exam |
TI2 |
General Region: Compute the triple integral of a three variable function over a general region in rectangular coordinates. |
15.6 |
HW TI2, Checkpoint Exam, Midterm Exam 3, Final Exam |
TI3 |
Cylindrical Region: Compute the triple integral or a three variable function using cylindrical coordinates. |
15.7 |
HW TI3, Checkpoint Exam, Midterm Exam 3, Final Exam |
TI4 |
Spherical Region: Compute the triple integral of a three variable function using spherical coordinates. |
15.8 |
HW TI4, Checkpoint Exam, Midterm Exam 3, Final Exam |
Vector Fields#
Number |
Learning Outcome |
Textbook Sections |
Assessments |
|---|---|---|---|
VF1 |
Graphing Vector Fields: Sketch a vector field in two and three dimensions. |
16.1 |
HW VF1, Checkpoint Exam, Midterm Exam 3, Final Exam |
VF2 |
Gradient Field: Calculate gradient field for a scalar-valued function. |
16.3 |
HW VF2, Checkpoint Exam, Midterm Exam 3, Final Exam |
VF3 |
Curl: Calculate the curl of a vector field. |
16.5 |
HW VF3, Checkpoint Exam, Midterm Exam 3, Final Exam |
VF4 |
Divergence: Calculate the divergence of a vector field. |
16.5 |
HW VF4, Checkpoint Exam, Midterm Exam 3, Final Exam |
VF5 |
Conservative Vector Fields: Test whether a vector field is conservative. |
16.3 |
HW VF5, Checkpoint Exam, Midterm Exam 3, Final Exam |
VF6 |
Potential Functions: Find the potential function for a conservative vector field. |
16.3 |
HW VF6, Checkpoint Exam, Midterm Exam 3, Final Exam |
Line Integrals#
Number |
Learning Outcome |
Textbook Sections |
Assessments |
|---|---|---|---|
LI1 |
Scalar Function Line Integrals: Calculate the line integral of a scalar function in two and three dimensions. |
16.2 |
HW LI1, Checkpoint Exam, Midterm Exam 3, Final Exam |
LI2 |
Center of Mass: Calculate the center of mass of a curve using line integrals. |
16.2 |
HW LI2, Checkpoint Exam, Midterm Exam 3, Final Exam |
LI3 |
Vector Field Line Integrals: Calculate the line integral of a vector field. |
16.2 |
HW LI3, Checkpoint Exam, Midterm Exam 3, Final Exam |
LI4 |
Fundamental Theorem of Line Integrals: Calculate the value of a line integral using the Fundamental Theorem of Line Integrals. |
16.3 |
HW LI4, Checkpoint Exam, Midterm Exam 3, Final Exam |
LI5 |
Green’s Theorem: Use Green’s Theorem to calculate line integrals and double integrals. |
16.4 |
HW LI5, Checkpoint Exam, Midterm Exam 3, Final Exam |
Surface Integrals#
Number |
Learning Outcome |
Textbook Sections |
Assessments |
|---|---|---|---|
SI1 |
Parametric Surfaces: Find a parametric representation for a surface in three dimensions. |
16.6 |
HW SI1, Checkpoint Exam, Final Exam |
SI2 |
Surface Area: Calculate the surface area of a surface using a parametric representation. |
16.6 |
HW SI2, Checkpoint Exam, Final Exam |
SI3 |
Scalar Functions Surface Integrals: Calculate the surface integral of a scalar function. |
16.7 |
HW SI3, Checkpoint Exam, Final Exam |
SI4 |
Vector Field Surface Integrals: Calculate the surface integral of a vector field. |
16.7 |
HW SI4, Checkpoint Exam, Final Exam |
SI5 |
Stokes’ Theorem: Use Stokes’ Theorem to calculate line integrals and surface integrals. |
16.8 |
HW SI5, Checkpoint Exam, Final Exam |
SI6 |
Divergence Theorem: Use the Divergence Theorem to calculate surface integrals. |
16.9 |
HW SI6, Checkpoint Exam, Final Exam |