**Textbook:** Stewart: *Calculus: Early Trancendentals,* 8th Edition, Brooks/Cole(Cengage)

**Course Coordinator:** Dr.Kathleen Acker

**Chapter 5: Integrals**

5.3 Fundamental Theorem of Calculus, Review

5.4 Indefinite Integrals

5.5 The Substitution Rule

**Chapter 6: Applications of Integration**

6.1 Areas Between Curves

6.2 Volumes

6.4 Work (Optional)

6.5 Average Value of a Function

**Chapter 7: Techniques of Integration**

7.1 Integration by Parts

7.2 Trigonometric Integrals (Optional)

7.3 Trigonometric Substitution (Optional)

7.4 Int. of Rational Fns by Partial Frac. (Optional)

7.7 Approximate Integration

7.8 Improper Integrals

**Chapter 8: Further Applications of Integration**

8.1 Arc Length

8.4 Applications to Economics and Biology

8.5 Probability

**Chapter 11: Infinite Sequences and Series**

11.1 Sequences

11.2 Series (emphasize geometric series)

11.3 The Integral Test & Estimates of Sums

11.4 The Comparison Test

11.5 Alternating Series

11.6 Absolute Convergence, Ratio & Root Tests

11.8 Power Series**

11.9 Representations of Functions as Power Series**

11.10 Taylor and Maclaurin Series**

11.11 Application of Taylor Polynomials

* ** emphasize these sections*

**Chapter 10: Parametric Equations and Polar Coordinates**

10.1 Curves Defined by Parametric Equations

10.2 Calculus with Parametric Equations

10.3 Polar Coordinates

10.4 Areas and Lengths in Polar Coordinates

**Chapter 9: Differential Equations **(if time allows)

9.1 Modeling with Differential Equation (Optional)

9.2 Direction Fields & Euler's Method (Optional)

9.3 Separable Equations (Optional)

9.4 Models for Population Growth (Optional)

This material is covered over a 14 week (56 class hours) semester.

**WebAssign**

Faculty have the option of utilizing WebAssign, a web-based supplement to our textbook. This portal provides graded and practice homework problems, online quizzes, video instruction and an eBook. WebAssign registration requires an access code, which is included with the text purchased from the Villanova Bookstore.

Note: If you choose to rent/purcase a book that comes without a WebAssign code, you will be required to purchase the registration code separately if your instructor uses WebAssign.

Upon the start of each semester, students will received a second code, called a class enrollment code, from their instructor. This code enrolls them into the specific course set up by their instructor for that semester.

**Computer Algebra System (CAS)**

Instructors will be using Maple or a comparable Computer Algebra System in the course. Students will work with the software interface to integrate numerically and symbolically, to solve differential equations, to explore the convergence or divergence of a series, as well as understand Taylor series.