# Course Name

Calculus II

Session: VSOU1722

3 Credits

# Prerequisites & Language Level

Taught In English

• There is no language prerequisite for courses at this language level.

# Overview

Course Description:

Integration techniques and applications, series and approximations. Students are expected to have completed a Calculus I course. This is the second course of a calculus sequence for STEM (Science, Technology, Engineering, Mathematics) majors. The approach is more computational than theoretical. Mathematics is the basic language for STEM fields. Understanding the language, the basic ideas and results, and the computational techniques of calculus is prerequisite to any advanced learning in a STEM field.

Lectures will be based on University Calculus (Alternate Edition) by J. Hass, M. Weir, and G. Thomas, Addison Wesley, current edition. It is not necessary for students to purchase the text, though it is strongly recommended that each student arranges access to some calculus textbook. The text University Calculus will not be available for sale at Korea University, although a copy is expected to be available for short-term borrowing. Students may want to make arrangements for the text before coming to the Summer Campus. The text is available, for example, from amazon.com.

Course Outline:

Review: We will begin with a brief review of integration, including use of the Fundamental Theorem of Calculus to find the area between graphs of functions.

Chapter 6: Applications of the integral. Volumes by slicing and rotation about axes (6.1), volumes via shells (6.2).

Chapter 7: Transcendental Functions. Inverse functions and their derivatives (7.1), natural logarithms (7.2), exponential functions (7.3), inverse trigonometric functions (7.4), exponential growth and separable differential equations (7.5), indeterminate forms and L’Hˆopital’s Rule (7.6)

Chapter 8: Techniques of Integration. Integration by parts (8.1), trigonometric integrals (8.2)

Exam 1.

Chapter 8: Techniques of Integration; continued. Trigonometric substitution (8.3), integration of rational functions by partial fractions (8.4), improper integrals (8.7).

Chapter 9: Infinite sequences and series. Sequences (9.1), infinite series (9.2), the integral test (9.3), comparison test (9.4), ratio and root test (9.5), alternating series, absolute and conditional convergence (9.6), power series (9.7), Taylor and Maclaurin series (9.8), convergence of Taylor series (9.9), the binomial series (9.10).

Exam 2.

*Course content subject to change