Math 111 Calculus I

Textbook: 

• Calculus: Early Transcendentals by James Stewart, 8th Edition.

Software:

None

Topics:

Chapter 2 Limits and Derivatives

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
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

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
3.9 Related Rates
3.10 Linear Approximations and Differentials

Chapter 4 Applications of Differentiation

4.1 Maximum and Minimum Values
4.2 The Mean Value Theorem
4.3 How Derivatives Affect the Shape of a Graph
4.5 Summary of Curve Sketching
4.7 Optimization Problems
4.9 Antiderivatives

Chapter 5 Integrals

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

6.1 Areas Between Curves
6.5 Average Value of a Function

Chapter 9 Differential Equations

9.1 Modeling with Differential Equations
9.5 Linear Equations