New York University Skopje
COURSE SYLLABUS
CALCULUS 2
Spring 2008
Instructor: Magdalena Ivanovska
Class Hours: Tuesday, 14:00-17:00
Classroom: Cl.6
Office Hours: Monday, 13:00-
E-mail address: mivanovska@nyus.edu.mk
Phone Number: +389 (0)2 20 34 600, +389 (0)70 915 897
Prerequisite(s): Algebra, Calculus 1
Textbook(s): Calculus, Early Transcendentals (7th Edition) by H. Anton,
I. Bivens, and S. Davis, John Wiley & Sons Inc, 2002
Course Description and Related Requirements
v Course Description
The course involves techniques of integral evaluation, introduces basic differential equations and initial-value problems, provides a treatment of infinite series, functions of two or more variables, partial derivatives, double and triple integrals.
v Course Objectives
Upon successful completion of the course the student will be able:
- to evaluate indefinite integrals of different types using various techniques;
- to evaluate definite integrals and apply it in Geometry, Science and Engineering problems;
- to solve and apply first-order differential equations;
- to work with polar coordinates;
- to understand functions with two variables and evaluate partial derivatives;
- to evaluate double and triple integrals;
v Course Structure
The course is structured as follows:
Integration
Applications of the Definite Integral in Geometry, Science and Engineering
Principles of Integral Evaluation
Mathematical Modeling with Differential Equations
Infinite Series
Analytic Geometry in Calculus
Partial Derivatives
Multiple Integrals
v Grading
The grade depends on the following:
Attendance and Participation: 10%
Homework and Projects: 15%
Mid-Term Exam 35%
Final Exam 40%
Weekly Plan
|
Week (1x3 classes) |
Theme |
Chapter |
|
1 |
An Overview of the Area Problem The Indefinite Integral; Integral Curves and Direction Fields Integration by Substitution |
Chapter 6: Integration
|
|
2 |
Sigma Notation; Area as a Limit The Definite Integral The Fundamental Theorem of Calculus
|
Chapter6: Integration
|
|
3 |
Area between Two Curves Volumes by Slicing; Disks and Washers Volumes by Cylindrical Shells |
Chapter 7: Applications of the Definite Integral in Geometry, Science and Engineering |
|
4 |
Integration by parts Trigonometric Integrals |
Chapter 8: Principles of Integral Evaluation |
|
5 |
Trigonometric Substitutions Integrating Rational Functions by Partial Fractions |
Chapter 8: Principles of Integral Evaluation |
|
6 |
First-Order Differential Equations and Applications
|
Chapter 9: Mathematical Modeling with Differential Equations |
|
7 |
Sequences Infinite Series Convergence Tests |
Chapter 10: Infinite Series
|
|
8 |
Mid Term Exam |
Mid Term Exam |
|
9 |
Taylor and Maclaurin Series The Comparison, Ratio, and Root Tests Alternative Series; Conditional Convergence Power Series |
Chapter 10: Infinite Series
|
|
10 |
Polar Coordinates |
Chapter 11: Analytic Geometry in Calculus |
|
11 |
Functions of Two or More Variables Limits and Continuity Partial Derivatives |
Chapter 14: Partial Derivatives
|
|
12 |
Differentiability and Chain Rules Total Differentials for Functions in Two Variables
|
Chapter 14: Partial Derivatives
|
|
13 |
Double Integrals Double Integrals over Nonrectangular Regions |
Chapter 15: Multiple Integrals
|
|
14 |
Double Integrals in Polar Coordinates Triple Integrals
|
Chapter 15: Multiple Integrals
|
|
15 |
Final Exam |
Final Exam |
v Grading Scale
Grade |
Percentage |
Quality Points |
A |
96-100 |
4.00 |
|
A- |
90-95 |
3.67 |
|
B+ |
87-89 |
3.33 |
|
B |
83-86 |
3.00 |
|
B- |
80-82 |
2.67 |
|
C+ |
77-79 |
2.33 |
|
C |
73-76 |
2.00 |
|
C- |
70-72 |
1.67 |
|
D+ |
67-69 |
1.33 |
|
D |
63-66 |
1.00 |
|
D- |
60-62 |
0.67 |
F |
0 -59 |
0.00 |