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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

  1. Unit 1: Integrals
  2. Unit 2: Applications of Integration
  3. Unit 3: Techniques of Integration
  4. Unit 4: Further Applications of Integration
  5. 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 it. 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).

  1. Stewart, J. Single Variable Calculus: Early Transcendentals. 8th edition. Boston, MA: Cengage Learning (This is referred to as SVC in the course.), 2016.
    Type: Textbook: ISBN: 978-1-305-27033-6
  1. Anders, D., Cole, J.A., & Drucker, D. Student Solutions Manual for Stewart's Single Variable Calculus: Early Transcendentals. 8th edition. Boston, MA: Cengage Learning, 2016.
    Type: Textbook: ISBN: 978-1-305-27242-2

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.

In order to successfully complete this course, students must obtain at least 50% on the final mandatory examination and 50% overall.

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.

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