Class Information
Instructor: Prof. June Amillo. Email: amillo@fi.upm.es
Office Hours: by appointment. Office: 1317.
Class Hours: Tuesday 09:0011:00, Thursday 13:0014:00 and Friday 11:0013:00. Room: Artá.
Announcements
June 12, 2017: Final Grades as they will show on records.
Course Description
This is an accelerated course of one and several variable calculus. The first part of the course is devoted to those topics of one variable calculus not covered in preuniversity math courses: applications of differential and integral calculus and the study of series. The second part deals with differential calculus of more than one variable and multiple integrals leaving out integration in vector fields.
The course is applications oriented and the presentation is not rigorous: some results are proven formally but others are only justified intuitively. The applications are drawn from the world of engineering and economics. Mathematical software will be used extensively as a tool to understand concepts and solve problems.
Learning Outcomes
By completion of the course the student will have achieved competency in the following skills:
 Use derivatives to compute differentials and approximate linearly functions of one variable.
 Apply the mean value theorem and its consequences to analyze functions of one variable.
 Apply differential calculus to solve optimization problems.
 Find anti derivatives and evaluate integrals.
 Apply integration to find the area of plane regions and volumes of revolution.
 Analyze convergence of improper integrals and evaluate them.
 Find limits of sequences and establish the order of growth.
 Analyze the convergence of series and sum geometric series.
 Find the power series expansion of functions.
 Represent two and three dimensional curves and find tangent lines.
 Calculate arc length and surface of revolution.
 Graph functions of several variables and understand contour lines.
 Compute partial derivatives of functions of several variables.
 Understand gradients and use them to find tangent planes and normal lines.
 Apply differential calculus of several variables to solve optimization problems.
 Apply the Lagrange method to solve max/min problems with constraints.
 Compute double and triple integrals and apply them to find volumes.
Syllabus
Each two hour lecture will be devoted to one of the topics listed on the syllabus but there could be some overlapping between lectures. The one hour lecture will be used to compensate for exams and festivities.
Lecture Topics

Lecture Notes

Extension of Differential Calculus

Derivatives 
Extension of Integral Calculus

Integrals 
Series

Series 
Mid Term Exam


Curves and Vector Functions

Curves 
Partial Derivatives

Partial Derivatives 
Multiple Integration

Exercise Set 7: 1.1 
End Term Exam


Textbook
There is no specific textbook. For complimentary reading you can use one of the following popular books:
 Salas S. L. & E. Hille, Calculus: One and Several Variables, 9th Edition, John Wiley, New York, 2002
 Stewart J., Calculus, 6th Edition, Brooks Cole, Toronto, 2007
 Strang G., Calculus, Online Text, http://ocw.mit.edu/resources/res18001calculusonlinetextbookspring2005/textbook/
 Thomas G. B. & R. L. Finney, Calculus and Analytic Geometry, 9th Edition, AddisonWesley Reading, Massachusetts,1999
Grading
 The final grade will be based on the following percentages:
 Exercise set assignments: 20%.
 Lab practice: 20%.
 Two 60 minute exams: 30% each.
 Class attendance is required.
 There are no makeup exams.
 Hand in only assignments in bold the rest are in class assignments.
 Do not hand in Lab practice assignments, they will be assessed in class before the midterm and endterm exams.
 Students are expected to devote 45 additional hours a week to personal study and to complete home assignments.
 Students may work by teams but must submit their work individually including their own explanations.
 Mathematical software can be used to solve exercise and lab practice sets.
Exams
EndTerm Exam 2012
July Exam 2012
EndTerm Exam 2013
July Exam 2013
MidTerm Exam 2014
EndTerm Exam 2014
MidTerm Exam 2015
EndTerm Exam 2015
MidTerm Exam 2016
EndTerm Exam 2016