MAT 1505 Syllabus

Textbook: Stewart: Calculus: Early Trancendentals, 8th Edition, Brooks/Cole(Cengage), 2015 [click link for format options]
Coordinators: Marilyn Belkin and Joyce Longman

Chapter 5: Integrals
5.4 Indefinite Integrals  

5.5 The Substitution Rule

Chapter 6: Applications of Integration
6.1 Areas Between Curves

6.2 Volumes (by cross sections)                                                               

6.4 Work                               

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
9.1 Modeling with Differential Equation

9.2 Direction Fields & Euler's Method

9.3 Separable Equations           

9.4 Models for Population Growth

A suggested schedule based on a 14 week (56 class hours) semester, is given below. It may be modified at the instructor's discretion.

Sections Approximate Time Comments
5.4,5.5
4 class hours  
6.1, 6.2, 6.4, 6.5    7 class hours 6.4 pumping problems optional
7.1-7.4, 7.7, 7.8     7 class hours 1 or 2 brief examples each from 7.2-7.4
8.1, 8.4, 8.5 3 class hours  
11.1-11.6, 11.8-11.11 15 class hours Emphasize ratio test in 11.6
10.1-10.4 7 class hours  
9.1-9.4 6 class hours
You might not have time for this.
Exam Reviews 4 class hours Includes Final Exam Review
Exams 3 class hours  

Maple or Other Computer Software
Maple or other computer software discussions should be determined by each instructor. Each student shoud master the following topics using the computer: (1) integration, (2) approximate integration, (3) solving differential equations, (4) exploring the convergence or divergence of a series, and (5) Taylor series.

Contact Information

Department of Mathematics & Statistics
SAC Room 305
Villanova University
800 Lancaster Avenue
Villanova, PA 19085 
Tel: 610.519.4850
Fax: 610.519.6928
Email: math@villanova.edu

Chair:
Dr. Douglas Norton

Staff:
Marie O'Brien, 610.519.4809
Lorraine McGraw, 610.519.4850

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