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The purpose of this course is to introduce students to the basic concepts of calculus. The emphasis will be on derivatives and its applications. It will introduce anti-derivatives at a basic level. The course will also introduce students to Fermat’s Theorem, Mean-Value Theorem, Definite Integrals, The Fundamental Theorem of Calculus and others depending on time.

University Calculus I (UC-Cal I: not for credit)

Course Credit

0

Course Price

\$ 550.00

Course Developer

My Learning Oasis

Prerequisite(s) (Text)

Grade 12 Calculus or permission of school

Course Code

UC-Cal I

Course Type

First Year University

First Year University I(Non-Credit)

Course Development Date

June 10th, 2021

## Course Outline

Week 1
Functions and graphing with a graphing calculator or a computer software (where possible
trigonometric functions, their reciprocals, and their inverses.

Week 2 Limits and Continuity
Governing laws in evaluating a limit;
Definition of a limit

Week 3 Limits and Continuity
Rates of Change
What constitutes continuity
The intermediate value theorem
limits at infinity
Applications

Week 4 Differentiation
Definition of dx versus delta x
Differentiation (derivatives, the derivative as a function, differentiation formulas)
Product, quotient, chain, and power rule for differentiation

Week 5
Derivatives of trigonometric functions
implicit differentiation

Week 6
derivatives of inverse trigonometric functions
higher order derivatives
Week 7
Derivatives of transcendental functions
Derivatives of logarithmic functions

Week 7 Applications of Differentiation
Fermat's Theorem
Rolle's Theorem
Mean Value Theorem;
Exploring how derivatives influence the shape of a graph (local extreme values, asymptotes).

Week 8 Applications of Differentiation
L’Hospital’s rule;

Week 9
optimization problems

Week 10
Introduction to anti-derivatives
Definite integrals to find the area under a curve

Week 11
indefinite integrals and the Net Change Theorem;
Fundamental Theorem of Calculus

Week 12
Basic ‘u’ substitution rule
Areas enclosed by curves.

Marks Break Down
Assignments: 10%
Project: 20%
Midterm: 30%
Final Exam: 40%

If your final mark in the final exam is better than the overall average of the course, then the better of the two will be recorded.

## Resources

Note: This course does not require or rely on any textbook.

● Every student needs access to an electronic device to communicate with their teacher
● All class notes and assignments will be provided by teachers.

## Overall Curriculum Expectations

By the end of this course students ought to have a sound knowledge of all forms of derivatives ie of all kinds of transcendental functions, traigonometric expression, radical expressions and more. They are also expected to understadn the basic concepts of integration. They will also be able to apply these concepts in real life applications.

## Special Accommodations

Only Some students are able, with accommodations, to be part of a regular course curriculum and to demonstrate independent learning. These accommodations allow access to the course without any dilution of the knowledge and skills the student is expected to demonstrate.

These required accommodations to facilitate the student’s learning will be identified in his or her IEP (see IEP Standards, 2000, page 11*). It is likely that IEP for many or all courses will reflect the same accommodations. The instructions and accommodations are geared to meet the diverse needs of learners. The three types of accommodations that are going to be used are:

i) Instructional accommodations - changes in teaching/learning strategies facilitated by different styles of presentation; methods of organization; the use of technology and multimedia.
ii) Environmental accommodations - Certain classroom settings and preferential seating may benefit these students.
iii) Assessment: assessment procedures that enable the student to demonstrate his or her learning, such as Multiple Intelligence Theory, giving more time to complete tasks (see page 29 of the IEP Resource Guide, 2004, for more examples).

For students who require accommodations for only the mathematics courses, the assessment and evaluation of their achievement will be based on the appropriate course curriculum expectations and the achievement levels outlined in this document. The IEP box on the students’ Provincial Report Cards will not be checked, and no information on the provision of accommodations will be included.

* Taken form: Ministry of Education, Ontario. Extracted from The Ontario Curriculum, Grades 11 and 12: Canadian and World Studies; Date of extraction: Sunday, March 14, 2021

## Program Considerations For English Language Learners

Students from a variety of cultural and linguistic backgrounds. For many of tStudents hese students, English is not their spoken language. They may be coming from highly sophisticated educational systems, while others may have come from regions where access to formal schooling was limited. These students offer a rich addition to the classroom experience by way of their background knowledge and experience. All teachers will assist with their English- language development. In mathematics the teachers will include appropriate adaptations and strategies in their instructions and assessments to facilitate the success of the English language learners in their classrooms. Some of these strategies and adaptations are: modification of some or all of the course expectations so that they are challenging but attainable for the learner at his or her present level of English proficiency, given the necessary support from the teacher.

## Teaching/Learning Strategy

The key learning strategy at My Learning Oasis Elite Private School is Constructivism. This format facilitates learning by many techniques, most or all of which will be adopted in the classroom. The most dominant of these is group learning. The facilitator places students of different backgrounds in the same group so that they can feed off each other. Each may bring to the table a different reasoning strategy to facilitate problem-solving. Now, each student becomes a learner and a teacher at the same time, as he/she has to communicate his/her solution. This builds the students' knowledge base and by default, increases their confidence to speak in a crowd, albeit a small group at the beginning.

The famous educationalist, Vygotsky, proved that by placing students in a group they function at the upper level of their zone of proximal development, each one scaffolding the other. This strategy is further enhanced by the teacher asking leading questions as opposed to giving the answer outright, then allowing for group discussion. The students are encouraged to make connections between what they have learnt and their life experiences, then share with the group.

The effect of this strategy is intrinsic motivation and learning. Each student develops an expanded appreciation of the topic at hand by seeing how it applies in different settings around the world by way of listening to their group members. This Constructivist approach will be further accentuated by implementing “fish-bowling”. There are many ways to implement this technique. The one that will mostly be used will be by dividing up the larger problem (technical, mathematics, science, or otherwise) into smaller bits and have each student thoughtfully master one part. That student then teaches the group and facilitates a discussion reflection about the strategy (computational or otherwise) used in the solution. Each student in turn does this. The above techniques enable students to reflect on the material learnt, make real life connections, and develop problem solving skills. One important by-product of the technique of Constructivism is that each student develops an appreciation of each other’s culture.

This cultivates healthy people’s skill, which is not only important for the professional world but for life itself. Constructivism lends itself well to students whose first language is not the language of instruction and who is new to the class. While other strategies will be used for students having difficulty with the English Language, this technique will definitely be used to enhance their English skill.

## Assessment And Evaluation

Mark breakdown
Assignments: 10%
Project: 20%
Midterm I: 30%
Final Exam: 40%

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