About the course
This course is a continuation of university calculus I. It picks up from an introduction to integration and goes into various techniques in integration. It introduces differential equations and various series (Maclauren and Taylor). It also introduces tests for convergence of a series. The course then delves into volumes of revolution and lengths of arcs. It then looks at parametric equations, partial derivatives and functions with two or more variables. The students will also be introduced to double and triple integrals and their applications.

University Calculus II (UC-Cal II, Not for credit)
Course Credit
0
Course Price
$ 550.00
Course Developer
My Learning Oasis
Prerequisite(s) (Text)
Completion of University Calculus I
Course Code
Department Head & Contact Information
UC-Cal II
Ravi Sharma (ravi@mylearningoasis.com)
Course Type
First Year University
Grade Level
First Year University II (Non-Credit)
Course Development Date
June 10th, 2021
Course Outline
Prerequisite: Completion of University Calculus I
Suggested Textbook
Required reading Calculus: Early Transcendentals, James Stewart, Brooks/Cole, 6th edition,
ISBN/ISSN: 0-495-42969-4 (or 0-495-01166-5 is equivalent)
Student Solutions Manual (for Stewart's Calculus: Early Transcendentals),
Brooks/Cole , 6th Edition. The bookstore offers the option of buying the solutions
Purpose of Course
By popular demand, My Learning Oasis created this course to give students a head start in university, regardless of their discipline. As such, it is not meant to replace a university course and is not intended to be valued as a university credit, although the content is well in tune with the second course in calculus in most universities. As such, students may, on their own volition, seek a credit from the university.
Course Description
This course is a continuation of university calculus I. It picks up from an introduction to integration and goes into various techniques in integration. It introduces differential equations and various series (Maclauren and Taylor). It also introduces tests for convergence of a series. The course then delves into volumes of revolution and lengths of arcs. It then looks at parametric equations, partial derivatives and functions with two or more variables. The students will also be introduced to double and triple integrals and their applications.
Week 1
Review of integration by ‘u’ substitution
Integration of trigonometric functions
Integration by parts
Week 2
Integration by trigonometric substitution
Introduction to partial fractions
Week 3
Integration using partial fractions
Introduction to numerical integration (trapezoidal rule)
Week 4
improper integrals
Week 5
Volumes of revolution
Arc length
Week 6
Surface area
hydrostatic pressure on a dam
Week 7
Differential Equations
modelling with differential equations.
Week 8
Separable differential equations
Further modelling with differential equations
Week 9
Parametric and Polar Coordinates
exponential growth and decay
parametric curves and their derivatives
Week 10
polar coordinates and polar curves
Several variable Calculus
Partial derivatives.
Week 11
chain rule
Gradient vector operator
max/min.
Week 12
double integrals over rectangles
iterated integrals
Week 13
Sequences and Series
Taylor and Maclaurin Series
.
Week 14
tests for divergence/convergence;
ratio and root tests;
power series of functions.
Mark breakdown
Assignments: 10%
Project: 20%
Midterm I: 30%
Final Exam: 40%
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 the course, it is expected that students will be able to apply different techniques of intetration to evalute various types of expressions. They will also be expected to understand and apply MacLaurin and Taylor series. They will model real life situations with differential equations and solve them to see the behavior of the modelled situation. They will be expected to test a series for convergence and divergence and apply them to real life situations.
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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