# Course Name

Calculus I

Session: VSOU1222

3 Credits

# Prerequisites & Language Level

Taught In English

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

# Overview

Course Description:

This introductory course will cover the basic concepts of one vari-
able calculus, including limits, di erentiation 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.

Text:

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:

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 de nition of limit.
2.4: One-sided limits and limits at in nity.
2.5: In nite limits and asymptotes.
2.6: Continuity.
Chapter 3: Derivatives.
3.1: De nition of the derivative, calculation of derivatives using rst principles, and
di erentiability on an open interval.
3.2: Calculate derivatives, linearity, product and quotient rule. Higher order deriva-
tives.
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 di erentiation.
3.7: Related rates.
3.8: Di erentials and linear approximation.
Exam 1.
Chapter 4: Applications of di erentiation.
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.
4.7 Antiderivatives.
Chapter 5: Integration.
5.1: Area estimates with nite sums.
5.2: Sigma Notation and Riemann sums.
5.3: The de nite integral and its basic properties
5.4: The Fundamental Theorem of Calculus.
5.5: Inde nite integrals and substitution.
5.6: Areas between curves.
Exam 2.

*Course content subject to change