| Date |
Sections |
Topics |
Prerequisite Skills |
Student Learning Outcomes
|
| Week 1
|
1.3
|
The Fundamental Theorem of Calculus
|
|
- Evaluate definite integrals using the Fundamental Theorem of Calculus
- Interpret the definite integral as the signed area under the graph of a function.
|
| Week 1
|
1.5
|
Integration by Substitution
|
|
- Use substitution to evaluate indefinite integrals.
- Use substitution to evaluate definite integrals.
|
| Week 2
|
2.1
|
Area between Curves
|
|
- Find the area of plane regions bounded by the graphs of functions.
|
| Week 2
|
2.2
|
Determining Volumes by Slicing
|
|
- Find the volume of solid regions with a known cross-sectional area.
|
|
| Week 3
|
2.3
|
Volumes of Revolution, Cylindrical Shells
|
|
- Find the volume of solid regions obtained by revolving a plane region about a line.
|
|
| Week 3
|
2.4
|
Arc Length and Surface Area
|
|
- Find the arc length of a plane curve
- The area of the surface obtained by revolving a curve about one of the coordinate axes.
|
|
| Week 4
|
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 4
|
2.6
|
Moments and Center of Mass
|
|
- Find the moments and center of mass of a thin plate of uniform density.
|
|
| Week 5
|
3.1
|
Integration by Parts
|
|
- Integrate products of certain functions.
- Integrate logarithmic and inverse trigonometric functions.
|
|
| Week 5
|
3.2
|
Trigonometric Integrals
|
|
- Integrate products of powers of sin(x) and cos(x) as well as sec(x) and tan(x).
|
|
| Week 6
|
3.3
|
Trigonometric Substitution
|
|
- Integrate the square root of a sum or difference of squares.
|
| Week 6
|
3.4
|
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 7
|
4.3
|
Separation of Variables
|
|
- Recognize and solve separable differential equations.
- Develop and analyze elementary mathematical models.
|
| Week 8
|
2.8
|
Exponential Growth and Decay
|
|
- The exponential growth model
- The concept of doubling time
- The exponential decay model
- The concept of half-life
|
| Week 8
|
4.4
|
The Logistic Equation
|
|
- Carrying capacity in the logistic model of population growth
- Interpret the solution curves of a direction field for a logistic equation
- Solve a logistic equation and interpret the results
|
| Week 9
|
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 10
|
5.2
|
Infinite Series
|
|
- Define the convergence or divergence of an infinite series.
- Find the sum of a geometric or telescoping series.
|
| Week 10
|
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 11
|
5.4
|
Comparison Tests
|
|
- Determine the convergence or divergence of a series using the Direct or Limit Comparison Tests.
|
| Week 11
|
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 12
|
5.6
|
Ratio and Root Tests
|
|
- Determine the convergence or divergence of infinite series using the ratio and root tests..
|
| Week 12
|
6.1
|
Power Series and Functions
|
|
- Recognize a power series.
- Find its interval and radius of convergence.
- Represent certain functions as power series.
|
| Week 13
|
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 14
|
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 15
|
7.1
|
Parametric Equations
|
|
- Sketch the graph of a parametric curve
|
|
| Week 15
|
7.2
|
The Calculus of Parametric Equations
|
|
- Find the slope of the tangent line to a parametric curve at a point
- Find the second derivative of a parametric curve
- Determine the area bounded by a parametric curve
- Determine the arc length of a parametric curve
- Calculating the area of a surface obtained by rotating a parametric curve about an axis
|
|
