# MATH 1241: Calculus II

This is the second course in calculus, intended for students who have already completed a Calculus I course in differential and integral calculus and need to extend their skills in this subject.

## Objectives

By the end of this course, students should be able to:

• 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 outline

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

This is a companion course to MATH 1141. Therefore, the materials listed below would have been purchased with your enrollment in MATH 1141.

If you did not take MATH 1141 and do not already own the required materials, you will need to purchase them. To do so, 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).

Listed below are the two textbooks that would have been purchased when taking MATH 1141.

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

A good-quality scientific calculator is required.

## Assessments

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

 Assignment 1 8% Assignment 2 8% Assignment 3 8% Assignment 4 8% Assignment 5 8% Final Exam 60% Total 100%

## Open Learning Faculty Member

An Open Learning Faculty member is available to assist students throughout the course. Primary communication is through the Learning Environment's "Mail" tool or by phone. Students will receive the necessary contact information at the start of the course.

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