MATH 1241: Calculus II
This course is intended for students who have already completed a Calculus I course in differential and integral calculus, and need to further develop their skills in this subject.
Learning outcomes
- Distinguish between the indefinite integral and the definite integral.
- Define the definite integral as a limit of Riemann sums and interpret it as area.
- Explain the Fundamental Theorem of Calculus, showing how differentiation and integration are related.
- Evaluate an integral by the method of substitution.
- Use integrals to calculate areas between curves, volumes, work, and average value of a function.
- Evaluate integrals, using the techniques of integration by parts, using trigonometric identities and trigonometric substitution, and using partial fractions.
- Use the Midpoint Rule, Simpson's Rule, and the Trapezoidal Rule to find the approximate value of certain definite integrals.
- Evaluate the two types of improper integrals.
- Solve separable first-order differential equations.
- Use integrals to find arc length and area of a surface of revolution.
- Use integrals in applications to economics and biology.
- Determine whether or not a sequence of real numbers converges.
- Test a series for convergence or divergence, using the integral, ratio, root, and comparison tests.
- Test an alternating series for absolute convergence, conditional convergence, or divergence.
- Determine the radius and interval of convergence of a power series.
Course topics
Unit 1: Integrals
Unit 2: Applications of Integration
Unit 3: Techniques of Integration
Unit 4: Further Applications of Integration
Unit 5: Sequences and Series
Required text and materials
The following textbook would have been purchased in MATH 1141. Students who did not take MATH 1141 and/or don't already own the required textbook, will need to purchase them. To do so, please contact Enrolment Services at student@tru.ca or 1.800.663.9711 (toll-free in Canada), 250.852.7000 (Kamloops, BC), and 1.250.852.7000 (International).
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Stewart, J. (2021). Single Variable Calculus: Early Transcendentals + Student Solutions Manual (9th ed.). Belmont, CA: Thomson Brooks/Cole.
Type: Textbook Bundle. ISBN: 9780357717127Note: The previous 8th edition textbook + SSM is acceptable
Additional requirements
A good-quality scientific calculator is required.
Assessments
Please be aware that should your course have a final exam, you are responsible for the fee to the online proctoring service, ProctorU, or to the in-person approved Testing Centre. Please contact exams@tru.ca with any questions about this.
To successfully complete this course, students must achieve a passing grade of 50% or higher on the overall course, and 50% or higher on the final mandatory exam.
Note: The final exam for this course is only available as a paper exam and must be taken in person at an approved Testing Centre. Please email exams@tru.ca with any questions.
| Assignment 1 | 10% |
| Assignment 2 | 10% |
| Assignment 3 | 10% |
| Assignment 4 | 10% |
| Assignment 5 | 10% |
| Final Exam (mandatory) | 50% |
| Total | 100% |
Open Learning Faculty Member Information
An Open Learning Faculty Member is available to assist students. Students will receive the necessary contact information at the start of the course.
