Math 1B – Final Portfolio

Math 1B – Final Portfolio

 

The purpose of this final project is to give you the opportunity to synthesize and reflect upon all of the different concepts and problem solving techniques that we’ve learned throughout the quarter. Think of this as a sort of booklet or pamphlet that is meant to highlight the different things we’ve explored. In your finished portfolio, you will have pages dedicated to each of the course objectives that we’ve learned that are fundamental/foundational in calculus and you find interesting. For example, you may have a page dedicated to limits, derivative as a limit, different derivative rules, etc. Understand that each page can have multiple course objectives within it.

 

Expectations:

• You will type (or neatly handwrite) each page. You can choose to create a physical portfolio or a digital one.
• Each chosen topic should have some relevant definitions and at least two worked out examples that illustrates YOUR understanding of the topic or problem solving technique
• Rather than copying directly from lecture notes or other sources, explain each concept in your own words. You can use examples from notes, but if you do be sure to explain each step and why each step is being done. You are encouraged to find examples from outside of lecture notes and to discuss those in your portfolio
• Each topic should have a picture, illustration, or graph that goes along with it
• The final page of the portfolio should have a list of any references used
• As a minimum, you should have all 11 course objectives represented in your portfolio.
• During our final exam time in finals week, each person will present one page of their portfolio to the class

 

I am hoping you stress out about this – think of this as an opportunity to reflect upon all that you have learned this quarter and to document your growth as a mathematician. I’m not expecting you to make a page for every single thing that we discussed (although you are more than welcome to); I’m expecting that you put in an honest effort and that you have reasons for including and excluding the topics you choose to represent in your portfolio. Please feel free to be as creative as you want and to have some fun with it! The goal is to build upon and deepen your learning.

 

Suggestion: You can start working on this immediately and add to it as the quarter progresses. We will begin weekly reflections in which you will be asked to make a list of topics that we have covered – this can serve as a starting point for you to decide what to include in your final portfolio.

 

We will have draft discussions throughout the quarter so that I can give you feedback and so that you can more concretely see my expectations.

 

 

 

Student Learning Outcomes

• Students will solve problems involving applications of integration of functions of a single variable.
• Students will develop conceptual understanding of integration of functions of a single variable. They will learn to demonstrate and communicate this understanding in a variety of ways, such as: reasoning with definitions and theorems, connecting concepts, and connecting multiple representations, as appropriate.
• Students will demonstrate the ability to compute and approximate integrals of functions of a single variable.

 

Course Objectives

The student will be able to:

1. Define the antiderivative and determine antiderivatives of simple functions.
2. Demonstrate an understanding of and evaluate and approximate definite integrals.
3. Find antiderivatives graphically and analytically.
4. Use the first and second fundamental theorems of calculus to evaluate definite integrals and construct antiderivatives.
5. Evaluate a definite integral as a limit.
6. Apply integration to find area.
7. Evaluate definite and indefinite integrals using a variety of integration formulas and techniques.
8. Apply integration to areas and volumes, and other applications such as work or length of a curve.
9. Evaluate improper integrals.
10. Graph and differentiate functions in polar and parametric form.
11. Graph and integrate functions in polar and parametric forms.
12. Solve and interpret solutions to elementary differential equations.
13. Use technology, such as graphing calculators and/or computer software to assist in solving problems involving any of the topics in (1) through (12) above.
14. Discuss mathematical problems and write solutions in accurate mathematical language and notation.
15. Interpret mathematical solutions.

 

 

Brainstorming Session – Oct 28^th

 

Pick one Course Objective that you feel confident in and write it below.

 

Write at least 3 sentences explaining what you remember about the objective above.

Create an example problem, without outside resources, that fits within the objective above.

 

Can your example use an image/graphic/graph/table? If so, explain how. If not, explain why not.