Online Teaching And Academics Courses & Certifications

The Ordinary and Partial Differential Equations and Applications certification course is designed with complete overview of the differential equations and its relative significance. This course is a standard curriculum that is offered to UG/PG engineering or science students. It requires the presence and uniqueness of an ODE solution, homogeneous and non-homogeneous linear differential equation systems, second-order homogeneous differential equation power series solution. 

The Ordinary and Partial Differential Equations and Applications training will undertake both aspects of the curriculum in an analytical and practical manner that will help the candidate to be more productive and effective in their respective major. This course has considerable applications in numerous engineering and science areas, such as control theory, numerical analysis, dynamic systems, etc. The main motive will be focused towards the core elements of the major that have a significant role in the functioning of the problem-solving areas. 

This course will provide a quick overview of the whole curriculum in the beginning and then later it will be directed to the new modules, framework, theorems, challenges and limitations that are associated with this particular programme along with that, the candidate will be provided Ordinary and Partial Differential Equations and Applications certification that will help them to pursue further courses in same field. 

The Numerical Linear Algebra online course has been structured as a basic and fundamental course for the students who are pursuing their postgraduate or undergraduate level degree course from the stream of science or engineering. 

The Numerical Linear Algebra certification benefits the registered students by providing them the core concepts regarding- stability of numerical algorithms, matrix algebra, stability of nonlinear systems, conditioning and condition number,  vector and matrix norms, convergent matrices, computer arithmetic, sensitivity analysis, singular value decomposition (SVD), least square solutions, algebraic and geometric properties of SVD, Power method and applications, Householder matrices and applications, QR method, Jacobi method for finding the eigenvalues of a given matrix. 

The Numerical Linear Algebra certification course will be dealing with all the real world applications of the numerical linear algebra concept in the diverse fields of - sciences and engineering. The twelve weeks course will be emphasised on topics like- control theory, numerical analysis, image processing and dynamical systems.

Probabilistic Methods in PDE by Swayam is designed by IISER Pune and verified by NPTEL. Professor Anindya Goswami instructs this ongoing elective program that spans 12 weeks. The course falls under the purview of Mathematics and is based on two books, namely: Semigroup Theory and Stochastic Calculus. Candidates seeking certificates can also acquire them by paying and registering for the proctored evaluation. 

The Probabilistic Methods in PDE certification syllabus introduces you to a potent research tool related to the differential equations theory. The curriculum aims to offer expertise on probability theory and PDE, considering the absence of extensive learning material on this topic. Young researchers who have to undergo time-consuming research with scattered references have easy access to the course’s compiled information, offering in-depth insights.

The Probabilistic Methods in PDE program is an advanced curriculum but is also ideal for mathematical finance, probability theory, PDE, or mathematical physics aspirants. The instructor will explain several complex theorems from the books mentioned above during the course lectures to facilitate a comprehensive approach towards the subject.

The Optimization from Fundamentals certification course is a structural framework set for improving the learning of the field in a more effective way. From its fundamentals, this course will cover the subject of Optimization. A summary of actual analysis and convexity will begin with it. Linear programming, convex optimization and nonlinear programming, complementarity concerns and algorithms for the same will cover this basis. 

With dynamic optimization, the Optimization from Fundamentals training will stop. The course will give a complete framework of what's the level of optimization in different sectors and now where it stands and what are the problems and challenges, it suffers.  

The Optimization From Fundamentals certification will give an assurance that the candidate is more effective in the respective field, which will help him to undertake the same major in their respective upcoming future. The course is more tilted towards the understanding of the core elements that play the main role in the functioning of optimization principle. The students who will get enrolled in the programme will study various elements that are so vital for the functioning of the fundamentals and Optimization from Fundamentals certification syllabus will mainly consulate with that only. 

SageMath is a python based, free and open-source computer algebra system (CAS). The software is being used widely to explore applied linear algebra, calculus, and numerical methods. The Computational Mathematics with SageMath course by Swayam aims to deep dive give practical learning to the applications of SageMath in the concepts mentioned earlier.

The Computational Mathematics with SageMath certification syllabus covers a range of topics like python, classes in python, use of NumPy, SciPy, and SymPy, exploring SageMath, local maximum and minimum, and the like. The AICTE verified course is perfectly suited to students wishing to pursue their careers in the data science or numerical computations industry.

Besides, the Computational Mathematics with SageMath online course is taught by an experienced professor from chemical technology, Mumbai, called Prof. Ajit Kumar. The 12-week course will contain weekly assignments for evaluation through which the students will be able to track their progress.

The Transform Calculus and its applications in Differential Equations online course will help candidates learn about the basic techniques involved in the integral. The simpler ways of dealing out with the equations and coming up with the solution in a quick span of time will be taught to the candidates.

The candidates will be exposed to high-level concepts as well so that there is no difficulty in the process of learning. The course will train the students with the basic Integral Transform techniques. The candidates will be learning everything this topic covers within this time. The high-level concepts will also be touched by the experts.

The Transform Calculus and its applications in Differential Equations training come with certification, so the learning is a fun process. The candidates will have all the learning materials with them prior to the starting of the course and can carry on with their learning anytime they wish to.

The Fourier Analysis and Its Applications online course has been selected as the basic theoretical applications and aspects of the topics that are directly or indirectly related to the topic of Fourier. 

The Fourier Analysis and Its Applications certification syllabus will be conducted for a total of 12 weeks and will be covering the topics namely- The space S of rapidly decreasing functions, Application to PDEs, Fourier transform as an operator from S to S, and the Plancherel's theorem, Cesaro summability - Fejer's theorem and its applications, Basic convergence theorem of Fourier series and its applications and Sturm-Liouville problems and its applications. 

With the help of lecture videos, assignments, tests, and case study guides, the students will be taught the basics of the concept of  Fourier. The diverse applications of the subject of mathematics will also be covered in a descriptive way in the online course on Fourier Analysis and Its Applications by Swayam.

The Linear Algebra online program is a Swayam course provided by the Ministry of Education(Government of India) and is designed by the National Programme on Technology Enhanced Learning(NPTEL) and the Indian Institute of Science in Bangalore. This course is part of the mathematics domain and will take twelve weeks for the students to complete the training.

The course instruction is done by Prof. Dilip. P. Patil, a faculty member of the department of mathematics in IISC. The course materials that include books, references, and assignments will be a source of extensive learning of the subject. 

The Linear Algebra training provides expertise that enables students to equip themselves with valuable mathematical insights that improve their job skills. The students of this course will develop their knowledge of the geometric concepts involved in mathematical applications and other algebraic principles. This core course will fetch the candidates three credit points and a certificate from Swayam that is recognized by NPTEL and IISC Bangalore.

The ‘Advanced Engineering Mathematics’ online course is a study about the analytical functions and applications of the various concepts and ideas that form the core of engineering mathematics. The National Program for Technology Enhanced Learning program (NPTEL) free online course is offered on the Swayam education platform for the undergraduate and postgraduate students of engineering and science.

The course curriculum is designed and provided by the Indian Institute of Technology Roorkee for twelve weeks. This certification course is a core course for undergraduate-level students. The course educator for this program is Dr. P. N. Agarwal from the department of mathematics at IIT Roorkee. The students of the ‘Advanced Engineering Mathematics online training program can earn three credit points. The candidates will also receive a course certificate that is e-verifiable with the authenticated logos of NPTEL and IIT Roorkee. The twelve weeks of training on the theoretical principles of the mathematical aspects of engineering and sciences enables the students to develop expertise in this domain.

The ‘Algebra - I’ online certification program is a core course for the students of mathematics that is focused on delivering the students insights on the foundational concepts of algebra. This free online course is provided by Swayam educational platform in collaboration with the National Programme on Technology Enhanced Learning (NPTEL). The course classes are held online in a virtual environment through videos, lectures, online resources, and assessments. The students of this course will take about twelve weeks to complete the course.

The instructors for this online training program are mathematics faculties from The Institute of Mathematical Sciences in Chennai, Prof. S Viswanath, and Prof. Amritanshu Prasad. The candidates of this mathematics course will gain a comprehensive understanding of the theoretical and practical aspects of algebra in this course.

By the end of this postgraduate level course, the students of the ‘Algebra - I’ training program will be given E-Certificate with the credit points. 

The ‘Combinatorics’ online certification course is created for the students to engage and discuss the various aspects of counting and the study of patterns in this course. The students of this course will engage in enhancing their knowledge of mathematics and algebra. The free online learning course is provided by Swayam in collaboration with the National Program for Technology Enhanced Learning (NPTEL). The classes for this program are conducted online aided by lectures, videos, books, and reference materials for about twelve weeks.

The instructor for this program is Prof. Narayanan N from the department of physics at the Indian Institute of Technology Madras. The students of this undergraduate level mathematics and algebra course will gain insights into the concepts of combinatorics.

The ‘Combinatorics’ online training program equips students with the E-Certificate and credits points after successfully completing this core course approved by the All India Council for Technical Education. The students are evaluated based on their weekly assignments and final examination for the certification.

The ‘Complex Analysis’ online certification course enables students to learn about the foundational level mathematics focussing on complex numbers and the complex analysis functions. This online course attempts to discuss the implications of complex numbers that offer the spectral theorem for matrices. This free National Program for Technology Enhanced Learning (NPTEL) course is provided by the Swayam education portal. It is a core course for undergraduate and postgraduate level students and is scheduled for twelve weeks. The classes are held online through videos, lectures, weekly assignments, and other online resources.

The instructor for this online training is Dr. Pranav Haridas, assistant professor at the Kerala school of mathematics. The students of this course are given an opportunity to explore the theoretical and practical implications of complex numbers in the mathematics domain.

The ‘Complex Analysis’ certification course ensures a course certificate and credit points after successfully completing this AICTE recognized course and the certification exam.

The ‘Computational Commutative Algebra’ certification course is an elective course for the students to develop their understanding of the computation of the rings, ideals, and modules with the help of a computer. This course enables students to get an overview of commutative algebra with a focus on the computations and the techniques behind them. This free online training course is provided by the Swayam education portal along with the National Program for Technology Enhanced Learning (NPTEL). The classes for this course are conducted online for a period of twelve weeks.

The students of this program are led by the instructor, Prof. Manoj Kummini from the Chennai Mathematical Institute (CMI). In this course, candidates will get a theoretical and hands-on experience with the computational tool Macaulay2. This program can be downloaded and installed locally or can also be worked with the online version for smaller computations.

The ‘Computational Commutative Algebra’ online training program ensures an E-Certificate and credit points after completing the course and the assessments successfully.

An invitation to Topology certification by IMSC via Swayam is a 12-week online course. Through this online certification course, students will be exposed to the investigation and formalization of the abstract notion of a “space” under a minimum set-theoretic structure, known as a topology. An invitation to Topology certification syllabus provides foundational theory in topology which plays a crucial role in modern mathematics, and by extension, other mathematical sciences. This is a free course and anyone interested in learning topology can enrol in this online course offered by the Institute of Mathematical Sciences, Chennai (IMSC) via Swayam. 

Spread across 12 weeks, An invitation to Topology online course equips learners with the concepts of Topological spaces, Subspace Topology, Box and Product topology, and Metric topology. The course also provides a certificate on the completion of the exam which is conducted at the designated exam centres.

An introduction to Point-Set-Topology Part-I certification by IIT Bombay via Swayam explores the definition of metric spaces and topological spaces. This is a 12-week online course that deals with topological aspects of metric spaces. An introduction to Point-Set-Topology Part-I certification course will expose students to three crucial theorems on complete metric spaces while providing them with the structure of completion of metric spaces. Through An introduction to Point-Set-Topology Part-I online course, students will get familiar with topological spaces, building new topologies from the old, Bases and subbases, I and II countability, connected and path connectedness, separability, and others.

An introduction to Point-Set-Topology Part-I certification syllabus discusses the meaningful study of analysis and further topology. In the end, the course gives outstanding results such as Urysohn’s lemma and Titze’s extension theorem and some applications. An introduction to Point-Set-Topology Part-I classes are backed up by a strong team of tutors solving all the queries. The classes also include several online interactive sessions.

The Algebraic Combinatorics certification by the Institute of Mathematical Sciences (IMSc), Chennai is designed to introduce students to some influential paradigms in modern combinatorics. They are combinatorial classes and combinatorial species, Möbius inversion on partially ordered sets, and the Lindström-Gessel-Viennot lemma. The Algebraic Combinatorics training course is a 12-week online course delivered via Swayam. The Algebraic Combinatorics certification syllabus also provides learners with the theory of symmetric functions.

Students from science and engineering backgrounds having studied mathematics and computer science are best suited for the Algebraic Combinatorics certification course. The course will be taught by two instructors covering powerful paradigms in modern combinatorics. There are three credit points in the Algebraic Combinatorics online course that will be awarded to students after completion of the course. Students will also receive a certificate upon successful completion of the final exam. 

The completion of a Discrete Mathematics Certification will lay the groundwork for enrolling in higher-level maths courses like real analysis, abstract algebra, maths modelling, geometry, and topology. 

Discrete Mathematics Classes shall discuss the symbolic logic techniques which are required for the algebraic understanding of circuits and computer logic and layer introduce you to Boolean algebras with the help of certain examples based on objects.

Discrete Mathematics Certification Syllabus will discuss how to express the overall functioning of a circuit mathematically in terms of certain suitably defined functions called Boolean functions and also consider a simple circuit design problem to illustrate the applications of the relationship between Boolean functions and circuits. 

All students get a Discrete Mathematics Certification by MPSTME, NMIMS Deemed University, Vile Parle West, Mumbai under the Swayam Initiative by the Government of India. 

Experimental Physics I Certification is a core course at the undergraduate level, which is offered online. It belongs to the category of Physics. The course will help students understand the working principle of common devices, their applications in different types of experiments. The course is also ideal for students who are preparing for GATE, NET, JAM, and JEST exams conducted by reputed institutes. There are three modules in the course and each module is 30 hours. 

Prof. Amal Kumar Das is the instructor for Experimental Physics I Certification course on the NPTEL website. Prof. Amal Kumar Das has a PhD in material science and experimental physics from the Institute of Physics, at Bhubaneswar. Each module is a 30 hours course. Currently, only module – I is discussed in this online course. Modules - II and III may be discussed in upcoming semesters. 

In this universe, we can observe matter in our everyday lives, existing in four states - the solid, liquid, gaseous, and plasma state. Other forms of matter exist as well, but only under specific and extreme conditions. Regardless of its existing structure, all matter is made up of atoms. The atomic arrangement, interatomic distances, and atomic ionization in matter determine its state. 

In the solid-state, atoms arrange themselves in a particular structure, which further imparts materials different properties such as thermal, electrical, optical, magnetic, and dielectric properties, among others. In the Solid State Physics online programme, candidates will learn about the structure of solids, their physical properties, and the underlying Physics.

The Solid State Physics online course is a 12-week programme at the undergraduate level. It is intended for B.Sc. (Physics, Chemistry, and Electronics), B.E., and B.Tech. (Electronics, Metallurgy, Metallic Science, Cryogenics) students.

The X-ray Crystallography and Diffraction online training is an undergraduate-level core course. The programme belongs to the category of metallurgy and material science and mining engineering. Students in similar fields and domains such as physics, chemistry, and biological sciences will benefit from this course.

The X-ray Crystallography and Diffraction undergraduate course focuses on the properties, functions of the internal structure, and arrangement of atoms in a crystalline material. It offers an insight into how x-ray diffraction can solve crystallographic issues related to single and poly-crystalline material, right from the base.

The X-ray Crystallography and Diffraction online course require candidates to hand in 12 assignments out of which Swayam will consider a 25 percent average of the best eight as part of the final score. Candidates also have to answer an external proctored exam, and a total of 75 percent of this score will be added to the final score. Upon acquiring 40 percent in the final score, candidates will be eligible to get a certificate.

The Waves and Oscillations course is designed to help candidates understand one of the most important concepts in physics, waves, and oscillations. The course gives insights into how this theory can be applied to understand how specific applications like communication gadgets, musical instruments, and other electronic devices work. 

The Waves and Oscillations certification course emphasises the current trends and practices of why and how devices rely on this concept. The course also deep dives into different aspects of wave phenomenon. Furthermore, the method of teaching is not only theoretical. Candidates will gain in-depth insights into the practical application of the theory as well. 

Moreover, Professor M S Santhanam from the prestigious IISER, who has conducted various researches on the same, teaches the Waves and Oscillations online programme. The course is perfect for students who want to specialise in Physics as it will help you to evolve your thinking about the concept of waves and oscillations and their future uses. 

The Introduction to LASER certification course provides a great deal of exposure to the scientists, teachers, working engineers, or anybody interested in knowing how LASERS work. Spread over 12 weeks, this elective course is offered by Prof. M. R Shenoy, a faculty of IIT Delhi.  He joined IIT Delhi in 1988 and is known for his collaborative research on Integrated Optical Devices. 

The Introduction to LASER certification syllabus gives students deep insights into the principle functioning behind the lasers. It also deals with the issues concerned with the design and output characteristics of the Lasers along with resonator physics. 

The Introduction to LASER training is an ‘applied’ course in nature. It could be opted by students studying B.E/B.Tech (3rd/4th year)/M.Sc (2nd year)/M.Tech (1st year). Moreover, the course is approved by the AICTE as an FDP course. It mandates a sincere and regular effort on the part of the student to obtain expertise in the subject. 

The course on Fluid Dynamics for Astrophysics by Swayam provides a comprehensive overview of the concept of fluid phenomena in the subject of Astrophysics. The programme over the initial few weeks will cover the fundamentals of fluid dynamics with a special emphasis on compressible phenomena. The basic concepts hence learnt by the students will help them to understand the core concepts that pertain to astrophysics in a more comprehensive way. In the Fluid Dynamics for Astrophysics certification module, the students will elaborate cover the topics of- magnetic field, black hole accretion, solar wind power, magnetohydrodynamics and more. 

The students after completing the online certification programme will be equipped to pursue a career as a research worker in the subject of astrophysics. Thus, after completing the twelve week programme the students will learn to understand the concepts of dynamos that are used in jets. They will also learn to work with the concepts of classical mechanics.

The Electronic Theory of Solids programme by Swayam is a 12-week course that begins with a straightforward example of a two-atom solid. This course builds on this example and discusses the theory of electrons in an N-atom solid. The application to thermal and electrical properties in solids is also discussed.

The Electronic Theory of Solids training explains symmetries and how they relate to emergent electronic properties. Next, the course introduces the magnetism of solids to the students, and the origin and types of magnetic states are outlined. Students also learn about the concept of magnetic long-range order with examples.

Furthermore, the Electronic Theory of Solids certification course introduces the historical developments and basic superconductivity concepts. Students learn how to work out the BCS theory and the Cooper problem. Additionally, all successful participants of the course receive a certificate of completion to highlight their advanced skills.

The Experimental Physics II certification course throws light on the wide range of experiments in physics that form an important part of the knowledge base to be acquired by the students of engineering and science. Since there are no books available to elaborate on these experiments, we can understand why the course is highly reputed for a reason. 

The Experimental Physics II certification syllabus extensively covers all the experiments ranging from reflection, refraction, and dispersion to quantum and atomic physics. The training spans over 12 weeks and Professor Amal Kumar Das from IIT Kharagpur teach it. He has completed his Ph.D. in experimental physics and material sciences from the autonomous Institute of Physics, (IOPB) Bhubaneswar and is currently working as a faculty in the Department of Physics at IIT Kharagpur.

The Experimental Physics II training helps the students in understanding the core concepts of each of the experiments. This simplified training is made available in the form of video lectures over the NPTEL platform. Thus, the online course not only imparts knowledge but also ensures that the evaluation of the same is done in an effective manner. The course sees to that the absence of specialized teachers to simplify the subject is compensated in our country.

The Experimental Physics certification course enables students to understand and grasp all the concepts used in the experiments of mechanics, sound, magnetism, electricity, optics, quantum physics, modern physics, and solid-state physics. The course has been conveniently divided into modules that come with 30 hours of lessons each. The training is also preceded by two other courses which deal with different modules of experiments. 

Currently, the Experimental Physics III certification syllabus comprises the third module of experiments which deals with the topics of solid-state physics and modern physics. The course is spread over 12 weeks and is taught by Professor Amal Kumar Das who is currently working as a faculty in the physics department of IIT Kharagpur. Students can apply this knowledge in securing higher scores in national level exams like NET, JAM, GATE, and JEST which are conducted by UGC/CSIR, IIT, IIT, and SERB respectively.   

The Experimental Physics III training comes with a curriculum that is not only ideal for undergraduate students of physics but also mandatory for undergraduates of engineering, technology, and science. Since these students are required to deal with instruments at different points of time through their courses, this program can easily prove beneficial to them. It will enable them to understand the working principles behind several common devices in experiments.

The Group Theory Methods In Physics Training course will provide the candidate an understanding of basic group theory methods in physics within a systematic manner. The course will cover the topics like Mulliken notation, great orthogonality theorem, and character tables, root vector diagrams, conjugacy classes, and unitary groups, subgroups and generators, weight vector diagrams, and basic introduction to discrete groups, su(2), su(3). 

The Group Theory Methods In Physics Programme will be having an instructor from IIT Bombay where the course e-certificate will be provided to candidates with the logo of NPTEL and IIT Bombay. The duration will be 12 weeks with online learning.

The participants' Group Theory Methods In Physics by Swayam will provide the candidate to go in-depth knowledge of orthogonal groups and lie algebra with continuous groups, generators, Lorentz transformation and quark model, su(3) baryons, mesons, Wigner-Eckart theorem, a hydrogen atom, dynamical symmetry. The experience of the instructor will help the candidate in solving the problems in a proper manner.

The Introduction to Astrophysical Fluids program is an elective course under the discipline of Physics. This AICTE approved FDP course will be held for 12 weeks and instructed by Prof Supratik Banerjee. The course is suitable for students pursuing any advanced UG or PG degrees.

The domain discussed in the Introduction to Astrophysical Fluids certification course has been under active research for the past 70 years. Candidates will learn about magnetospheric plasmas and solar wind, and how large interstellar clouds are borne out of the astrophysical fluid expansion. The course thoroughly explains phenomena such as solar flares, sunspots, stellar winds, accretion disks, star formation, supernovae explosions, and much more.

Derived from the IIT Kanpur course, the Introduction to Astrophysical Fluids training explicates astrophysical theories with an analytical, research-oriented, and systematic approach. Candidates will understand these concepts through phenomenological descriptions and by using specific mathematic tools taught throughout the course.