• Basic information
• Learning outcomes
• Contents
• Assessment
• Workload

Learning outcomes

Upon successful completion of this course, students will be able to:

1. Solve integral problems related to multivariable functions

   Contribution to Program Outcomes

   1. Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
   2. Describing, formulating, and analyzing real-life problems using mathematical and statistical techniques.
   3. Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.
   4. Exhibiting professional and ethical responsibility.

   Method of assessment

   1. Homework assignment
2. Identify advanved integral theorems

   Contribution to Program Outcomes

   1. Describing, formulating, and analyzing real-life problems using mathematical and statistical techniques.
   2. Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.

   Method of assessment

   1. Written exam
3. Interpret curvilinear integral

   Contribution to Program Outcomes

   1. Communicating between mathematics and other disciplines, and building mathematical models for interdisciplinary problems.
   2. Describing, formulating, and analyzing real-life problems using mathematical and statistical techniques.
   3. Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.

   Method of assessment

   1. Written exam

Contents
Week 1:	Multiple Integrals. Double Integrals and their properties.
Week 2:	Iterated Integrals. Fubini's Theorem.
Week 3:	Applications of Double Integrals.
Week 4:	Triple Integrals.
Week 5:	Change of Variables.
Week 6:	Multiple Improper Integrals.
Week 7:	Line Integrals.
Week 8:	Fundamental Theorem for Line Integrals. Midterm Exam.
Week 9:	Green's Theorem.
Week 10:	Surface Integrals and applications.
Week 11:	Divergence and Stokes Formulas.
Week 12:	Path Independence. Scalar and vector fields.
Week 13:	Vector forms of Divergence and Stokes Formulas.
Week 14:	Application of Stokes and Divergence Formulas.
Week 15*:	-
Week 16*:	Final Exam.
Textbooks and materials:	1. W. R. Wade; An Introduction to Analysis, Pearson Prentice Hall, 3rd Edition 2. Thomas’ Calculus, Pearson Addison-Wesley, Eleventh Edition.
Recommended readings:	Schaums Outline of Advanced Calculus, Second Edition: Robert C. Wrede, Murray Spiegel / Paperback / McGraw-Hill Professional / March 2002
	* Between 15th and 16th weeks is there a free week for students to prepare for final exam.

Assessment
Method of assessment	Week number	Weight (%)
Mid-terms:	8	40
Other in-term studies:	0	0
Project:	0	0
Homework:	2,4,7,9,12	10
Quiz:		0
Final exam:	16	50
	Total weight:	(%)

Workload
Activity	Duration (Hours per week)	Total number of weeks	Total hours in term
Courses (Face-to-face teaching):	3	14
Own studies outside class:	10	7
Practice, Recitation:	2	14
Homework:	2	5
Term project:	0	0
Term project presentation:	0	0
Quiz:	0	0
Own study for mid-term exam:	10	1
Mid-term:	2	1
Personal studies for final exam:	10	1
Final exam:	2	1
		Total workload:
		Total ECTS credits:	*
	* ECTS credit is calculated by dividing total workload by 25. (1 ECTS = 25 work hours)