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

Learning outcomes

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

1. Solve derivative problems related to multivariable functions

   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.
   4. Exhibiting professional and ethical responsibility.

   Method of assessment

   1. Written exam
2. Identify differential operators

   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.

   Method of assessment

   1. Written exam
3. Find out extremum points

   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

Contents
Week 1:	Euclidean Spaces. Topology of R^n.
Week 2:	Convergence in R^n.
Week 3:	Functions of Several Variables. Definition of the Limit .
Week 4:	Continuity and Uniform Continuity.
Week 5:	Partial Derivatives.
Week 6:	Higher Order Partial Derivatives.
Week 7:	Definition of differentiability.
Week 8:	Tangent planes and Differentials.
Week 9:	The Chain Rule.
Week 10:	Directional Derivatives and Gradient Vectors. Midterm Exam.
Week 11:	Taylor's Formula for multivariable functions.
Week 12:	Implicit Function Theorem.
Week 13:	Extrema of functions of several variables.
Week 14:	Lagrange Multipliers.
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:	1. W.Kaplan; Advanced Calculus, Pearson Addison-Wesley, 1973 2nd Edition. 2. Apostol, Tom M. ; Calculus, Vol. 2: Multi-Variable Calculus and Linear Algebra with Applications to Differential Equations and Probability. Wiley, 1969. ISBN: 9780471000075.
	* 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:	10	40
Other in-term studies:	0	0
Project:	0	0
Homework:	0	0
Quiz:	0	0
Final exam:	16	60
	Total weight:	(%)

Workload
Activity	Duration (Hours per week)	Total number of weeks	Total hours in term
Courses (Face-to-face teaching):	5	14
Own studies outside class:	10	5
Practice, Recitation:	2	14
Homework:	0	0
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)