# Course Description

# Course Name

**Calculus I**

**Session: VSOU1222**

# Hours & Credits

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, 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.

**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 denition of limit.

2.4: One-sided limits and limits at innity.

2.5: Innite limits and asymptotes.

2.6: Continuity.

*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-

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 dierentiation.

3.7: Related rates.

3.8: Dierentials and linear approximation.

*Exam 1.*

*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.

4.7 Antiderivatives.

*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.

*Exam 2.*

*Course content subject to change