MAT 1505 Syllabus

Textbook: Stewart: Calculus: Early Trancendentals, 7th Edition, Brooks/Cole(Cengage), 2012
Coordinators: Marilyn Belkin and Joyce Longman

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 Representation 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 Equations
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
Review Ch. 5
4 class hours 5.4 ref. 4.10
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
9.1-9.4 6 class hours
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

*The Villanova Edition can be bought new or used through our bookstore. You also have the option to rent the full version of the textbook through any online vendor.

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