Difference between revisions of "IU:TestPage"

From IU
Jump to navigation Jump to search
Line 85: Line 85:
 
== Course Sections ==
  
== Course Sections ==
 
The main sections of the course and approximate hour distribution between them is as follows:
  
The main sections of the course and approximate hour distribution between them is as follows:
  +
=== Section 1 ===
  +
  +
==== Section title ====
  +
Sequences and Limits
  +
  +
==== Topics covered in this section ====
  +
* Sequences. Limits of sequences
  +
* Limits of sequences. Limits of functions
  +
* Limits of functions. Continuity. Hyperbolic functions
  +
  +
==== What forms of evaluation were used to test students’ performance in this section? ====
  +
{| class="wikitable"
  +
|+
  +
|-
  +
! Form !! Yes/No
  +
|-
  +
| Development of individual parts of software product code || 1
  +
|-
  +
| Homework and group projects || 1
  +
|-
  +
| Midterm evaluation || 1
  +
|-
  +
| Testing (written or computer based) || 1
  +
|-
  +
| Reports || 0
  +
|-
  +
| Essays || 0
  +
|-
  +
| Oral polls || 0
  +
|-
  +
| Discussions || 1
  +
|}
  +
  +
==== Typical questions for ongoing performance evaluation within this section ====
  +
# A sequence, limiting value
  +
# Limit of a sequence, convergent and divergent sequences
  +
# Increasing and decreasing sequences, monotonic sequences
  +
# Bounded sequences. Properties of limits
  +
# Theorem about bounded and monotonic sequences.
  +
# Cauchy sequence. The Cauchy Theorem (criterion).
  +
# Limit of a function. Properties of limits.
  +
# The first remarkable limit.
  +
# The Cauchy criterion for the existence of a limit of a function. \item Second remarkable limit.
  +
  +
==== Typical questions for seminar classes (labs) within this section ====
  +
# Find a limit of a sequence
  +
# Find a limit of a function
  +
  +
==== Tasks for midterm assessment within this section ====
  +
  +
  +
==== Test questions for final assessment in this section ====
  +
# Find limits of the following sequences or prove that they do not exist:
  +
# $a_n=n-\sqrt{n^2-70n+1400}$;
  +
# $d_n=\left(\frac{2n-4}{2n+1}\right)^{n}$;
  +
# $x_n=\frac{\left(2n^2+1\right)^6(n-1)^2}{\left(n^7+1000n^6-3\right)^2}$.

Revision as of 10:50, 2 December 2021

Calculus I

  • Course name: Calculus I
  • Course number: XYZ

Course Characteristics

Key concepts of the class

  • Calculus for the functions of one variable: differentiation
  • Calculus for the functions of one variable: integration
  • Basics of series
  • Multivariate calculus: derivatives, differentials, maxima and minima
  • Multivariate integration
  • Functional series. Fourier series
  • Integrals with parameters

What is the purpose of this course?

The course is designed to provide Software Engineers the knowledge of basic (core) concepts, definitions, theoretical results and techniques of calculus for the functions of one and several variables. The goal of the course is to study basic mathematical concepts that will be required in further studies. 

This calculus course will provide an opportunity for participants to understand key principles involved in differentiation and integration of functions: solve problems that connect small-scale (differential) quantities to large-scale (integrated) quantities,
get hands-on experience with the integral and derivative applications and of the inverse relationship between integration and differentiation.

All definitions and theorem statements (that will be given in lectures and that are needed to explain the keywords listed above) will be formal, but just few of these theorems will be proven formally. Instead (in the tutorial and practice classes) we will try these definitions and theorems on work with routine exercises and applied problems.

Course objectives based on Bloom’s taxonomy

- What should a student remember at the end of the course?

By the end of the course, the students should be able to

  • what the partial and directional derivatives of functions of several variables are
  • basic techniques of integration of functions of one variables
  • how to calculate line and path integrals
  • distinguish between point wise and uniform convergence of series and improper integrals
  • decompose a function into Fourier series
  • calculate Fourier transform of a function

- What should a student be able to understand at the end of the course?

By the end of the course, the students should be able to

  • how to find minima and maxima of a function of various orders
  • how to represent double integrals as iterated integrals and vice versa
  • what the length of a curve and the area of a surface is
  • properties of uniformly convergent series and improper integrals
  • how to find Fourier transform of a function

- What should a student be able to apply at the end of the course?

By the end of the course, the students should be able to

  • take derivatives of various type functions and of various orders
  • integrate the functions of one and several variables
  • apply definite integration
  • expand functions into Taylor series
  • find multiple, path, surface integrals
  • find the range of a function in a given domain
  • decompose a function into Fourier series

Course evaluation

Course grade breakdown
Type Points
Labs/seminar classes 12
Interim performance assessment 48
Exams 140

Grades range

Course grading range
Grade Points
A [180, 200]
B [150, 179]
C [120, 149]
D [0, 119]

Resources and reference material

  • Claudio Canuto, Anita Tabacco Mathematical Analysis I (Second Edition), Springler
  • Claudio Canuto, Anita Tabacco Mathematical Analysis II (Second Edition), Springler
  • Jerrold Marsden, Alan Weinstein Calculus (in three volumes), Springer
  • Demidovich, B. Problems in mathematical analysis. Translator: G. Yankovsky, Mir publisher
  • Zorich, V. A. Mathematical Analysis I, Translator: Cooke R.

Course Sections

The main sections of the course and approximate hour distribution between them is as follows:

Section 1

Section title

Sequences and Limits

Topics covered in this section

  • Sequences. Limits of sequences
  • Limits of sequences. Limits of functions
  • Limits of functions. Continuity. Hyperbolic functions

What forms of evaluation were used to test students’ performance in this section?

Form Yes/No
Development of individual parts of software product code 1
Homework and group projects 1
Midterm evaluation 1
Testing (written or computer based) 1
Reports 0
Essays 0
Oral polls 0
Discussions 1

Typical questions for ongoing performance evaluation within this section

  1. A sequence, limiting value
  2. Limit of a sequence, convergent and divergent sequences
  3. Increasing and decreasing sequences, monotonic sequences
  4. Bounded sequences. Properties of limits
  5. Theorem about bounded and monotonic sequences.
  6. Cauchy sequence. The Cauchy Theorem (criterion).
  7. Limit of a function. Properties of limits.
  8. The first remarkable limit.
  9. The Cauchy criterion for the existence of a limit of a function. \item Second remarkable limit.

Typical questions for seminar classes (labs) within this section

  1. Find a limit of a sequence
  2. Find a limit of a function

Tasks for midterm assessment within this section

Test questions for final assessment in this section

  1. Find limits of the following sequences or prove that they do not exist:
  2. $a_n=n-\sqrt{n^2-70n+1400}$;
  3. $d_n=\left(\frac{2n-4}{2n+1}\right)^{n}$;
  4. $x_n=\frac{\left(2n^2+1\right)^6(n-1)^2}{\left(n^7+1000n^6-3\right)^2}$.
Retrieved from "https://eduwiki.innopolis.university/index.php?title=IU:TestPage&oldid=1479"