Seoul, South Korea
Area of Study
Taught In English
Course Level Recommendations
ISA offers course level recommendations in an effort to facilitate the determination of course levels by credential evaluators.We advice each institution to have their own credentials evaluator make the final decision regrading course levels.
Recommended U.S. Semester Credits3
Recommended U.S. Quarter Units4
Hours & Credits
This introductory course will cover the basic concepts of one vari-
able calculus, including limits, dierentiation with applications, and integration. The
approach is more computational than theoretical. The course material is fundamental for
majors in mathematics, the physical sciences, and engineering. Students enrolling in the
course are assumed to have basic knowledge of algebra and trigonometry.
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.
Chapter 1: Precalculus material. A quick review only, with most of the chapter left as a reference for students to use as needed.
Chapter 2: Tangent lines, limits, and continuity.
2.1: Tangent lines to curves.
2.2: Limits of functions and limit laws.
2.3: Precise denition of limit.
2.4: One-sided limits and limits at innity.
2.5: Innite limits and asymptotes.
Chapter 3: Derivatives.
3.1: Denition of the derivative, calculation of derivatives using rst principles, and
dierentiability on an open interval.
3.2: Calculate derivatives, linearity, product and quotient rule. Higher order deriva-
3.3: Applications and interpretation of the derivative as rate of change 3.4: Derivatives of trigonometric functions.
3.5: Chain Rule.
3.6: Implicit dierentiation.
3.7: Related rates.
3.8: Dierentials and linear approximation.
Chapter 4: Applications of dierentiation.
4.1: Absolute and local extrema and critical points.
4.2: Mean Value Theorem and some of its corollaries.
4.3 and x4.4: Monotonicity, concavity, and sketching of curves.
4.5 Applied optimization problems.
4.6 Newton's method.
Chapter 5: Integration.
5.1: Area estimates with nite sums.
5.2: Sigma Notation and Riemann sums.
5.3: The denite integral and its basic properties
5.4: The Fundamental Theorem of Calculus.
5.5: Indenite integrals and substitution.
5.6: Areas between curves.
Courses and course hours of instruction are subject to change.