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(Replaced content with " = Mathematical Analysis I = * '''Course name''': Mathematical Analysis I * '''Code discipline''': * '''Subject area''': ['Differentiation', 'Integration', 'Series'] ==...")
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# Functional series. Uniform convergence
 
# Functional series. Uniform convergence
 
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== Intended Learning Outcomes (ILOs) ==
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=== What is the main purpose of this course? ===
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understand key principles involved in differentiation and integration of functions, solve problems that connect small-scale (differential) quantities to large-scale (integrated) quantities, become familiar with the fundamental theorems of Calculus, get hands-on experience with the integral and derivative applications and of the inverse relationship between integration and differentiation.
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=== ILOs defined at three levels ===
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  +
==== Level 1: What concepts should a student know/remember/explain? ====
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By the end of the course, the students should be able to ...
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* Derivative. Differential. Applications
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* Indefinite integral. Definite integral. Applications
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* Sequences. Series. Convergence. Power Series
  +
  +
==== Level 2: What basic practical skills should a student be able to perform? ====
  +
By the end of the course, the students should be able to ...
  +
* Derivative. Differential. Applications
  +
* Indefinite integral. Definite integral. Applications
  +
* Sequences. Series. Convergence. Power Series
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* Taylor Series
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  +
==== Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios? ====
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By the end of the course, the students should be able to ...
  +
* Take derivatives of various type functions and of various orders
  +
* Integrate
  +
* Apply definite integral
  +
* Expand functions into Taylor series
  +
* Apply convergence tests

Revision as of 11:43, 25 April 2022

Mathematical Analysis I

  • Course name: Mathematical Analysis I
  • Code discipline:
  • Subject area: ['Differentiation', 'Integration', 'Series']

Short Description

Prerequisites

Prerequisite subjects

Prerequisite topics

Course Topics

Course Sections and Topics
Section Topics within the section
Sequences and Limits
  1. Sequences. Limits of sequences
  2. Limits of sequences. Limits of functions
  3. Limits of functions. Continuity. Hyperbolic functions
Differentiation
  1. Derivatives. Differentials
  2. Mean-Value Theorems
  3. l’Hopital’s rule
  4. Taylor Formula with Lagrange and Peano remainders
  5. Taylor formula and limits
  6. Increasing / decreasing functions. Concave / convex functions
Integration and Series
  1. Antiderivative. Indefinite integral
  2. Definite integral
  3. The Fundamental Theorem of Calculus
  4. Improper Integrals
  5. Convergence tests. Dirichlet’s test
  6. Series. Convergence tests
  7. Absolute / Conditional convergence
  8. Power Series. Radius of convergence
  9. Functional series. Uniform convergence

Intended Learning Outcomes (ILOs)

What is the main purpose of this course?

understand key principles involved in differentiation and integration of functions, solve problems that connect small-scale (differential) quantities to large-scale (integrated) quantities, become familiar with the fundamental theorems of Calculus, get hands-on experience with the integral and derivative applications and of the inverse relationship between integration and differentiation.

ILOs defined at three levels

Level 1: What concepts should a student know/remember/explain?

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

  • Derivative. Differential. Applications
  • Indefinite integral. Definite integral. Applications
  • Sequences. Series. Convergence. Power Series

Level 2: What basic practical skills should a student be able to perform?

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

  • Derivative. Differential. Applications
  • Indefinite integral. Definite integral. Applications
  • Sequences. Series. Convergence. Power Series
  • Taylor Series

Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?

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

  • Take derivatives of various type functions and of various orders
  • Integrate
  • Apply definite integral
  • Expand functions into Taylor series
  • Apply convergence tests