Chapters and sections refer to our textbook, *APEX Calculus 1 (Version 3.0)* by Gregory Hartman.

- 1st Week, Aug. 21-25. Begin chapter 1, Limits.
- What Calculus is About.
- 1.1 An introduction to Limits
- 1.2 Epsilon Delta Definition of a Limit. (This is a long story that is covered thoroughly in MAT 401-403. We'll barely touch the surface.)
- 1.3 Finding Limits Analytically

- 2nd Week, Aug. 28 - Sept. 1. Chapter 1 (cont.)
- 1.4 One Sided Limits. Paper-and-pencil homework assignment, due Wednesday: Let \(f(x)=4x+6\) when \(x\neq 10\). Give an "\(\epsilon-\delta\)" proof showing that \(\displaystyle \lim_{x\to 10} f(x) = 46\).
- 1.5 Continuity
- 1.6 Limits Involving Infinity

- 3rd Week, Sept. 4-8. Chapter 2, Derivatives.
**Labor Day holiday, Monday Sept. 4**- 2.1 Instantaneous Rates of Change: the Derivative.
- 2.2 Interpretation of the Derivative

- 4th Week, Sept. 11-15. Chapter 2 (cont.)
- 2.3 Basic Differentiation Rules
- Supplement (not in the textbook): Exponential and Logarithm functions and their derivatives.
- 2.4 The Product and Quotient Rules

- 5th Week, Sept. 18-22. Chapter 2 (cont.)
- 2.5 The Chain Rule
- 2.6 Implicit Differentiation

- 6th Week, Sept. 25-29. Chapter 2 (cont.)
- 2.7 Derivatives of Inverse Functions
**Test Friday Sept. 29**Solutions

- 7th Week, Oct. 2-6. Chapter 3, The Graphical Behavior of Functions
- 3.1 Extreme Values
- 3.2 The Mean Value Theorem
- 3.3 Increasing and Decreasing Functions

- 8th Week, Oct. 9-13. Chapter 3 (cont.)
- 3.4 Concavity and the Second Derivative
- 3.5 Curve Sketching

- 9th Week, Oct. 16-20. Chapter 4, Applications of the Derivative
- 4.1 Newton's Method Geogebra demo
- 4.2 Related Rates

- 10th Week, Oct. 23-27. Chapter 4 (cont.)
- 4.3 Optimization

- 11th Week, Oct. 30 - Nov. 3. Chapter 4 (cont.)
- 4.4 Differentials
**Test Friday Nov. 3**Solutions

- 12th Week, Nov. 6-10. Chapter 5, Integration
- 5.1 Antiderivatives and Indefinite Integration
- 5.2 The Definite Integral
**Veterans' Day Holiday Friday Nov. 10**

- 13th Week, Nov. 13-17. Chapter 5 (cont.)
- 5.4 The Fundamental Theorem of Calculus
- 5.3 Riemann Sums. What the "\(dx\)" means in \(\int f(x)\; dx\).

- 14th Week, Nov. 20-24. Chapter 5 (cont.)
- Supplementary material: integrals of \(1/\sqrt{1-x^2}\), \(1/(1+x^2)\), and \(1/\sqrt{1+x^2}\). Hyperbolic functions.
**Thanksgiving Holiday Thursday, Friday Nov. 23-24**

- 15th Week, Nov. 27 - Dec. 1. Chapter 6 Techniques of Antidifferentiation
- 6.1 Substitution
- Another way to look at integration: slope fields

- 16th Week, Monday Dec. 4 only.
- Review

**Final Exam Monday, Dec. 11, 1-3pm**