## Department of Mathematics - RHIT Topics Outline for MA111 - Calculus I - 2010-11

last posted to site: 08/19/10

### Textbook and other required materials

Text: Thomas' Calculus - Early Transcendentals Twelfth Edition - Weir, Hass
Supplement: Just in Time - bundled with text.

### Approximate Timing and Pace

There should be 3 or 4 tests, perhaps a final review day or two.

 Chapter Sections Topic Time First Chapter and other review, including Precalculus gateway Maple Introduction 1.5, 1.6 Review Material 1 week and interspersed through out term as needed 2.1, 2.2, 2.3, 2.4, 2.5, 2.6 Limits and Continuity 1.5 weeks or so 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, 3.9 , 3.10, 3.11 Derivatives 2 .5 weeks 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7 Applications of Derivatives 2 to 2 .5 weeks 4.8, 5.1, 5.2, 5.3, 5.4 Intro to Integration 1.5 to 2 weeks

### Text Topics - Optional topics in italics

1. Functions

1.1 Functions and Their Graphs (optional)

1.2 Combining Functions; Shifting and Scaling Graphs (optional)

1.3 Trigonometric Functions

1.4 Graphing with Calculators and Computers

1.5 Exponential Functions

1.6 Inverse Functions and Logarithms

2. Limits and Continuity

2.1 Rates of Change and Tangents to Curves

2.2 Limit of a Function and Limit Laws

2.3 The Precise Definition of a Limit

2.4 One-Sided Limits

2.5 Continuity

2.6 Limits Involving Infinity; Asymptotes of Graphs

3. Differentiation

3.1 Tangents and the Derivative at a Point

3.2 The Derivative as a Function

3.3 Differentiation Rules

3.4 The Derivative as a Rate of Change

3.5 Derivatives of Trigonometric Functions

3.6 The Chain Rule

3.7 Implicit Differentiation

3.8 Derivatives of Inverse Functions and Logarithms

3.9 Inverse Trigonometric Functions

3.10 Related Rates

3.11 Linearization and Differentials

4. Applications of Derivatives

4.1 Extreme Values of Functions

4.2 The Mean Value Theorem

4.3 Monotonic Functions and the First Derivative Test

4.4 Concavity and Curve Sketching

4.5 Indeterminate Forms and L'Hopital's Rule

4.5 Applied Optimization Problems

4.7 Newton's Method

4.8 Antiderivatives

5. Integration

5.1 Area and Estimating with Finite Sums

5.2 Sigma Notation and Limits of Finite Sums

5.3 The Definite Integral

5.4 The Fundamental Theorem of Calculus