# 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

A good-quality scientific calculator is required.