## Department of Mathematics - RHIT Topics Outline for MA102 - Differential Calculus - 2010-11

last posted to site: 08/19/10

MA101 and MA102 combined are equivalent to MA111, except that more that usual attention is paid to review and practice. Depending on the class the amount of MA111 material covered will vary though it is expected that the non-italicized Course Topics, given below, will be covered if not already covered in MA101. The instructors for MA101 and MA102 will collaborate on which set of topics will be covered in each course.

### Textbook and other required materials

Textbook: Thomas' Calculus - Early Transcendentals Twelfth Edition - Weir, Hass
Supplement: Just in Time - bundled with text.
Computer Usage:  Maple14 must be available on your laptop

### Approximate Timing and Pace

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

 Chapter Sections Topic Time 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, 3.9 Derivatives 4 weeks 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7 Applications of Derivatives 3 weeks 4.8, 5.1, 5.2, 5.3, 5.4 Intro to Integration 3 weeks

### Text Topics - Optional topics in italics

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