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Applications of Calculus

创建日期：2024-08-30 17:48:12

所属分类：数学mathematics

标签： Calculus

Applications of Calculus

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Overall Curriculum Expectations :

1. demonstrate an understanding of rate of change by making connections between average rate of change over an interval and instantaneous rate of change at a point, using the slopes of secants and tangents and the concept of the limit;

2. graph the derivatives of polynomial, sinusoidal, and exponential functions, and make connections between the numeric, graphical, and algebraic representations of a function and its derivative;

3. verify graphically and algebraically the rules for determining derivatives; apply these rules to determine the derivatives of polynomial, sinusoidal, exponential, rational, and radical functions, and simple combinations of functions; and solve related problems.

4. make connections, graphically and algebraically, between the key features of a function and its first and second derivatives, and use the connections in curve sketching;

5. solve problems, including optimization problems, that require the use of the concepts and procedures associated with the derivative, including problems arising from real-world applications and involving the development of mathematical models.

1. demonstrate an understanding of vectors in two-space and three-space by representing them algebraically and geometrically and by recognizing their applications;

2. perform. operations on vectors in two-space and three-space, and use the properties of these operations to solve problems, including those arising from real-world applications;

3. distinguish between the geometric representations of a single linear equation or a system of two linear equations in two-space and three-space, and determine different geometric configurations of lines and planes in three-space;

4. represent lines and planes using scalar, vector, and parametric equations, and solve problems involving distances and intersections.

Objective:

Create a project that demonstrates a thorough understanding of one particular aspect of Calculus. Ideally, this project will extend the knowledge you have acquired during the course.

Possible Topics:

Please choose from the below given topics :

- Build 5 optimization problems used in geometry , finance, and other sectors

· Demonstrate how derivatives can be used in the field of chemistry, physics , biology , medicine engineering, economics, environmental studies, or any other scientific discipline of interest to you

· Demonstrate the application of vectors in the real life in 5 examples

· Build 5 examples stating the use of the rate of change in the field of physics, chemistry, biology , medicine engineering, economics, environmental studies, or any other scientific discipline of interest to you

Format:

The format of this project is flexible; choose a format that best allows you to demonstrate your understanding of your chosen topic. Options include (but are not limited to):

· Written report with graphs and diagrams

· Visual and/or audio presentation (Prezi/PowerPoint slides, video, etc.)

· Creation of physical models with supporting written work

References:

Any references that are used in the completion of your project must be cited using APA format. Include references somewhere near the end of your project/report

Evaluation Rubrics


Category	Description	Grade
Knowledge and Understanding Background	A brief opening paragraph (or 2) should introduce the chosen topic and clearly explain its place in (or connection to) the study of Calculus.	/3
Knowledge and Understanding Calculus Content	Content is presented in a way that shows you clearly understand the material and could explain it to me or to a classmate. Marking scheme is based on the level of calculus content as follows: Level 4 (11–12): Project’s content is beyond level of course. Level 3 (9–10): Project’s content is similar to level of course. Level 2 (6–8): Project’s content is slightly below level of course. Level 1 (0–6): Project’s content is significantly below level of course.	/12
Thinking & Inquiry Graphs, Diagrams & Models	Any graphs used in the report are accurately drawn and clearly described. Any diagrams included in report are well-constructed, clearly labeled, and relevant to the chosen topic. Any models created are precisely constructed and clearly demonstrate the chosen concept.	/15
Communication Organization & Format	Submitted work is very well-organized, well presented, using clear language that is easy to follow (assume that your target audience is one of your classmates) Use of correct mathematical units, formula and show the steps	/10 /5
Application References	All materials must be cited in APA format. Plagiarism will be penalized. Use of the correct language as required . Use of correct mathematical notations	/5 /5 /5
	Total:	/30

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