Date |
Sections |
Topics |
Prerequisite Skills |
Student Learning Outcomes
|
Week 1
|
1.3
|
Three-Dimensional Coordinate Systems
|
|
- Three-dimensional coordinate systems
- Distance Formula in R3
- Standard Equation for a Sphere
|
Week 1 and 2
|
12.2
|
Vectors
|
|
- Vector Algebra Operations
- Magnitude of a vector
- Unit Vectors
- Midpoint of a Line Segment
- Angle between vectors
- Definition of Dot product
- Orthogonal vectors
- Vector projection
|
Week 3
|
12.3
|
The Dot Product
|
|
- Find the area of plane regions bounded by the graphs of functions.
|
Week 3/4
|
12.4
|
The Cross Product
|
|
- Define the cross product
- Properties of the cross product
- Area of a parallelogram
- Cross product as a determinant
|
|
Week 4
|
12.5
|
Cylinders and Quadratic Surfaces
|
|
- 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 4/5
|
13.1
|
Curves in Space
|
|
- Vector functions
- Limits of vector functions
- Continuity of vector functions
- Differentiation of vector functions
- Differentiation rules for vector functions
- Curves and paths in space
|
|
Week 5/6
|
2.5
|
Physical Applications
|
|
- Find the mass of an object with a given density function.
- Find the work done by a variable force
- Find the work done in pumping fluid from a tank
- Find the hydrostatic force on a vertical plate.
|
|
Week 6/7
|
2.6
|
Moments and Center of Mass
|
|
- Find the moments and center of mass of a thin plate of uniform density.
|
|
Week 6
|
3.1
|
Integration by Parts
|
|
- Integrate products of certain functions.
- Integrate logarithmic and inverse trigonometric functions.
|
|
Week 7
|
3.2
|
Trigonometric Integrals
|
|
- Integrate products of powers of sin(x) and cos(x) as well as sec(x) and tan(x).
|
|
Week 7/8
|
3.3
|
Trigonometric Substitution
|
|
- Integrate the square root of a sum or difference of squares.
|
Week 6/7
|
3.8
|
Partial Fractions
|
|
- Integrate rational functions whose denominator is a product of linear and quadratic polynomials.
|
Week 7
|
3.7
|
Improper Integrals
|
|
- Recognize improper integrals and determine their convergence or divergence.
|
Week 8
|
4.1
|
Basics of Differential Equations
|
|
- Classify an Ordinary Differential Equation according to order and linearity.
- Verify that a function is a solution of an Ordinary Differential Equation or an initial value problem.
|
Week 8/9
|
4.2
|
Direction Fields and Numerical Methods
|
|
- Sketch the direction field of a first-order ODE(Ordinary Differential Equation) by hand
- Using direction field, find equilibria of an autonomous ODE.
- Determine the stability of equilibria using a phase line diagram.
|
Week 9
|
4.3
|
Separable Equations
|
|
- Recognize and solve separable differential equations
- Develop and analyze elementary mathematical models.
|
Week 10/11
|
4.4
|
Exponential Growth and Decay, The Logistic Equation
|
|
- Solve the exponential growth/decay equations and the logistic equation.
- Describe the differences between these two models for population growth.
|
Week 11
|
5.1
|
Sequences
|
|
- Find the formula for the general term of a sequence.
- Discuss the convergence or divergence of a sequence.
- Find the limit of a convergent sequence.
- Determine whether a sequence is monotone.
|
Week 11/12
|
5.2
|
Series
|
|
- Define the convergence or divergence of an infinite series.
- Find the sum of a geometric or telescoping series.
|
Week 12
|
5.3
|
The Divergence and Integral Tests
|
|
- Determine the convergence or divergence of a series using the Divergence or Integral Tests.
- Estimate the sum of a series using the Remainder Estimate Theorem.
|
Week 13/14
|
5.4
|
Comparison Tests
|
|
- Determine the convergence or divergence of a series using the Direct or Limit Comparison Tests.
|
Week 14
|
5.5
|
Alternating Series
|
|
- Determine the convergence or divergence of alternating series.
- Estimate the sum of an alternating series.
- Describe the difference between conditional and absolute convergence.
|
Week 15
|
5.6
|
Ratio and Root Tests
|
|
- Determine the convergence or divergence of infinite series using the ratio and root tests..
|
Week 15/16
|
6.1
|
Power Series and Functions
|
|
- Recognize a power series.
- Find its interval and radius of convergence.
- Represent certain functions as power series.
|
Week 16
|
6.2
|
Properties of Power Series
|
|
- Differentiate and integrate power series term-by-term.
- Recognize certain continuous functions as power series on their radius of convergence.
|
Week 17
|
6.3
|
Taylor and Maclaurin Series
|
|
- Find the Taylor or Maclaurin series representation of a function.
- Find the radius of convergence of a Taylor Series.
- Estimate the remainder in a Taylor polynomial approximation.
|
Week 17/18
|
7.1
|
Parametric Equations
|
|
- Sketch the graph of a parametric curve
|
|