## Math 221. Calculus I

Lecture Syllabus

**Textbook: Stewart, Calculus: Early Transcendentals,
7th edition, with Enhanced Webassign**,

**Thomson Brooks/Cole**.

This syllabus assumes 29 lecture hours in the semester. It includes 24 to 25 lectures with 5 or 4 hours left for leeway and exams. Note that 3 one-hour exams are recommended for Math 221.

It is assumed that the Teaching Assistants in this course may need to do some lecturing in their discussion sections so as to keep the timeline for the syllabus on track.

### Chapter 2: Limits and Derivatives (4 lectures)

2.1 The Tangent and Velocity Problems

2.2 The Limit of a Function

2.3 Calculating Limits Using the Limit Laws

2.4 The Precise Definition of a Limit (optional)

2.5 Continuity

2.6 Limits at Infinity; Horizontal Asymptotes

2.7 Derivatives and Rates of Change

2.8 The Derivative as a Function

### Chapter 3: Differentiation Rules (6 lectures)

3.1 Derivatives of Polynomials and Exponential Functions

3.2 The Product and Quotient Rules

3.3 Derivatives of Trigonometric Functions

3.4 The Chain Rule

3.5 Implicit Differentiation

3.6 Derivatives of Logarithmic Functions

3.7 Rates of Change in the Natural and Social Sciences

3.8 Exponential Growth and Decay

3.9 Related Rates

3.10 Linear Approximations and Differentials

3.11 Hyperbolic functions (optional)

### Chapter 4: Applications of Differentiation (5-6 lectures)

4.1 Maximum and Minimum Values

4.2 Mean Value Theorem

4.3 How Derivatives Affect the Shape of a Graph

4.4 Indeterminate Forms and L'Hospital's Rule

4.5 Summary of Curve Sketching

4.7 Optimization Problems

4.8 Newton's Method

4.9 Antiderivatives

### Chapter 5: Integrals (5 lectures)

5.1 Areas and Distances

5.2 The Definite Integral

5.3 The Fundamental Theorem of Calculus

5.4 Indefinite Integrals and the Net Change Theorem

5.5 The Substitution Rule

### Chapter 6: Applications of Integration (4 lectures)

6.1 Areas Between Curves

6.2 Volumes

6.3 Volumes by Cylindrical Shells

6.4 Work

6.5 Average Value of a Function

Revised January 18, 2011; approved by Joseph Miles.