This Postgraduate certificate will allow you to update your knowledge in Calculus and Numerical Methods in a practical way, 100% online, without giving up the maximum academic accuracy"

This program is aimed at those interested in achieving a higher level of knowledge in Calculus and Numerical Methods. The main objective is to enable the student to apply in the real world the knowledge acquired in the Postgraduate certificate, in a work environment that reproduces the conditions that may be encountered in the future, in a rigorous and realistic manner.

This program will prepare scientifically and technologically, as well as to develop the professional practice of software engineering, with a transversal and versatile approach adapted to the new technologies and innovations in this field. You will obtain extensive knowledge in Calculus and Numerical Methods from professionals in the sector.

The students will be able to take the opportunity and study this program in a 100% online format, without neglecting their obligations.

Learn the latest techniques and strategies with this program and achieve success as a computer engineer"

This Postgraduate certificate in Calculus and Numerical Methods contains the most complete and up-to-date program on the market. The most important features include:

• Development of 100 simulated scenarios presented by experts in Calculus and Numerical Methods
• Its graphic, schematic and eminently practical contents provide scientific and practical information on Calculus and Numerical Methods
• News on the latest advances in Calculus and Numerical Methods
• It contains practical exercises where the self-assessment process can be carried out to improve learning
• Interactive learning system based on the case method and its application to real practice
• All of this will be complemented by theoretical lessons, questions to the expert, debate forums on controversial topics, and individual reflection assignments
• Content that is accessible from any fixed or portable device with an Internet connection

Get trained in Calculus and Numerical Methods with this intensive program, from the comfort of your home"

It includes in its teaching staff professionals belonging to the field of education, who bring to this program their work experience, in addition to recognized specialists belonging to reference societies and prestigious universities. 

Thanks to its multimedia content developed with the latest educational technology, this Postgraduate certificate will allow the professional a situated and contextual learning, that is to say, a simulated environment that will provide an immersive learning programmed to learn in real situations. 

This program is designed around Problem-Based Learning, whereby the students must try to solve the different professional practice situations that arise throughout the program. For this purpose, the professional will be assisted by an innovative interactive video system created by renowned experts in Calculus and Numerical Methods with extensive teaching experience. 

Benefit from the latest educational technology to get up to date in Calculus and Numerical Methods without leaving home"

Learn the latest techniques in Calculus and Numerical Methods from experts in the field"

The structure of the contents has been designed by a team of Computer Engineering professionals, aware of the relevance of the current specialization in order to deepen in this area of knowledge with the aim of humanistically enriching the student and raising the level of knowledge in Calculus and Numerical Methods by means of the latest educational technologies available. 

This Postgraduate certificate in Calculus and Numerical Methods contains the most complete and up-to-date learning program on the market"

Module 1. Calculus and Numerical Methods 

1.1. Introduction to Analysis 

1.1.1. Function Concept 
1.1.2. Limit Concept 
1.1.3. Limit Calculation 
1.1.4. Function Continuity 

1.2. Derivation of Functions and its Applications 

1.2.1. Derivative of a Function 
1.2.2. Geometric Interpretation 
1.2.3. Physical Interpretation 
1.2.4. Derivative Calculation 
1.2.5. Successive Derivatives 
1.2.6. Derivable Functions Lateral Derivatives 
1.2.7. Theorems of Derivable Functions 
1.2.8. L'Hôpital Rule 
1.2.9. Relative Extremes and Monotony 
1.2.10. Inflection Points and Curvature 
1.2.11. Optimization Problems 

1.3. Study and Graphical Representation of One-Variable Functions 

1.3.1. Function Study 
1.3.2. Polynomial Functions Study 
1.3.3. Rational Functions Study 
1.3.4. Study of Irrational Functions 
1.3.5. Exponential Functions Study 
1.3.6. Logarithm Functions Study 
1.3.7. Trigonometric Functions Study 
1.3.8. Construction of Functions from Other Known Functions 

1.4. Definite Integral 

1.4.1. The Definite Integral as Limit of a Sum 
1.4.2. Properties of Definite Integral 
1.4.3. Immediate Integrals 
1.4.4. Mean Value Theorem of Integral Calculus 
1.4.5. Fundamental Theorem of Calculus. Barrow's Rule 
1.4.6. Flat Enclosures Areas 
1.4.7. Curve Arc Length 
1.4.8. Solid Body Volumes 

1.5. Indefinite Integral 

1.5.1. Concept of Primitive of a Function 
1.5.2. Properties of Indefinite Integral 
1.5.3. Integration by Parts 
1.5.4.  Rational Functions Integration 
1.5.5. Integration by Variable Change 
1.5.6. Integration by Trigonometric Substitutions 
1.5.7. Non-Elementary Integrals 

1.6. Finite Sequences and Series 

1.6.1. Real Number Sequences 
1.6.2. Sets 
1.6.3. The Integral Criterion and the Comparison Criterion 
1.6.4. Alternating Series 
1.6.5. Absolute Convergence and Quotient Criterion 

1.7. Fundamental Counting Principles 

1.7.1. Partitioning of a Set 
1.7.2. Addition Principle 
1.7.3. Multiplication Principle 
1.7.4. Inclusion- Exclusion Principle 
1.7.5. Distribution Principle 

1.8. Numerical and Error Analysis 

1.8.1. Origin and Evolution of Numerical Analysis 
1.8.2. Algorithms 
1.8.3. Error Types 
1.8.4. Convergence 

1.9. Numbering Systems 

1.9.1. Information Representation 
1.9.2. Introduction to Numerical Systems 
1.9.3. Conversion from Decimal System to Base B 
1.9.4. Arithmetic Operations in Base B 
1.9.5. Conversion from b1 to b2 System 
1.9.6. Number Representation 
1.9.7. Floating Point Arithmetic 
1.9.8. Error Propagation 

1.10. Root Computation and Interpolation, Solving Algorithms and Acceleration Techniques 

1.10.1. Bisection Algorithm 
1.10.2. Fixed Point Algorithm 
1.10.3. Secant Method 
1.10.4. Newton-Raphson Algorithm 
1.10.5. Modified Secant Algorithm 
1.10.6. Modified Newton's Algorithm 
1.10.7. ∆2 of Aitken 
1.10.8. Steffensen's Algorithm 

A unique, key, and decisive educational experience to boost your professional development”