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Math 221. Calculus I
Lecture Syllabus

Textbook: Stewart, Calculus: Early Transcendental Functions, 6th edition, Thomson Brooks/Cole.

25 lectures, with 3 left over for exams.

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 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 (3-4 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

Chapter 8: Further Applications of Integration (1-2 lectures)

8.1 Arc Length
8.2 Area of a Surface of Revolution (optional)
8.3 Applications to physics and engineering (optional)
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Last modified August 3, 2009