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vector calculus nptel

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SYLLABUS OF MATHEMATICS-I (AS PER JNTU HYD) Name of the Unit Name of the Topic Unit-I Sequences and Series 1.1 Basic definition of sequences and series 1.2 Convergence and divergence. Geodesics, harmonic maps and Killing vectors 27 A.4. Eqn(5) is analogous to eqn(2), except the variable changes from a scalar to a vector. Scalar and vector fields 1.1 Scalar and vector fields 1.1.1 Scalar fields A scalar field is a real-valued function of some region of space. Then we’ll look into the line, volume and surface integrals and finally we’ll learn the three major theorems of vector calculus: Green’s, Gauss’s and Stoke’s theorem. Contents: Vectors: Vector calculus, Gradient, Divergence and Curl in curvilinear coordinates applications to Classical mechanics and Electrodynamics. Toggle navigation. In the following weeks, we’ll learn about scalar and vector fields, level surfaces, limit, continuity, and differentiability, directional derivative, gradient, divergence and curl of vector functions and their geometrical interpretation. highlights the essential mathematical tools needed throughout the text. This begins with a slight reinterpretation of that theorem. Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm. line integrals independent of path. of vector, differential, and integral calculus. I did not have a TA for this course. Vector calculus, or vector analysis, is concerned with differentiation and integration of vector fields, primarily in 3-dimensional Euclidean space. Vector Calculus 11 Solution, since and Similarly, it can be shown that and Normal Vector to a given line • Two non-zero vectors and in the plane are perpendicular (or orthogonal) if i,e, if • Consider a line The line though the origin and parallel to is when can also be written where and . Afterwards we’ll look into multiple integrals, Beta and Gamma functions, Differentiation under the integral sign. * : By Prof. Hari Shankar Mahato   |   calculus rules. Prerequisites are calculus of functions of one variable, vector algebra and partial differentiation. cal, and spherical, then enter into a review of vector calculus. The course consists of topics in complex analysis,numerical analysis, vector calculus and transform techniques with applications to various engineering problems. The term "vector calculus" is sometimes used as a synonym for the broader subject of multivariable calculus, which includes vector calculus as well as partial differentiation and multiple integration. 1. I did all the work by myself. Fundamentals of Vector Analysis Abstract The purpose of this appendix is to present a consistent but brief introduction to vector calculus. He did his PhD from the University of Bremen, Germany and then he worked as a Postdoc at the University of Erlangen-Nuremberg and afterwards at the Technical University of Dortmund, both located in Germany. It should be emphasized that this appendix cannot be seen as a textbook on vector algebra and analysis. A.3. revision of problems from Integral and Vector calculus. Triple integrals and surface integrals in 3-space: 25 This region might be a line, a surface or a volume. Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Roorkee.It will be e-verifiable at nptel.ac.in/noc. This course will offer a detailed introduction to integral and vector calculus. Once again, thanks for your interest in our online courses and certification. This course will remind you about that good stuff, but goes on to introduce you to the subject of Vector Calculus which, like it says on the can, combines vector algebra with calculus. Please choose the SWAYAM National Coordinator for support. Numbers, Functions, Sequencs and Limits of Functions. Lec : 1; Modules / Lectures. Then ~a~b= jajjbjcos( ) Proof. IIT Kharagpur. Vector Calculus In this part of the presentation, we will learn what is known as multivariable calculus. :  Area of plane regions, rectification, surface integrals. January 2017; Edition: FIRST; Publisher: STUDERA PRESS, NEW DELHI; ISBN: 978-81-930333-8-8; Authors: Dr Bhavanari … This course assumes very limited knowledge of vector calculus, ordinary differential equations and basic mechanics. His research expertise are Partial Differential Equations, Applied Analysis, Variational Methods, Homogenization Theory and very recently he has started working on Mathematical Biology. We borrow the Physics terminology for vectors, which mean that they have magnitude and direction. We’ll then study improper integral, their convergence and learn about few tests which confirm the convergence. Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc. The exam is optional for a fee of Rs 1000/- (Rupees one thousand only). Introduction to vectors mc-TY-introvector-2009-1 A vector is a quantity that has both a magnitude (or size) and a direction. The course contains vector calculus in curvilinear coordinates, linear vector spaces, tensors and complex analysis. Corollary 1.3. Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course. :  Integral definition of gradient, divergence and curl. We’ll start with the concepts of partition, Riemann sum and Riemann Integrable functions and their properties. Only the e-certificate will be made available. About us; Courses; Contact us; Courses; Mathematics; NOC:Multivariable Calculus (Video) Syllabus; Co-ordinated by : IIT Roorkee; Available from : 2017-12-22; Lec : 1; Modules / Lectures. We’ll start the first lecture by the collection of vector algebra results. There is no problem in extending any of the learnt material to higher dimensional spaces. About us; Courses; Contact us ; Courses; Mathematics; NOC:Basic Calculus for Engineers, Scientists and Economists (Video) Syllabus; Co-ordinated by : IIT Kanpur; Available from : 2015-09-14. Then we’ll look into the line, volume and surface integrals and finally we’ll learn the three major theorems of vector calculus: Green’s, Gauss’s and Stoke’s theorem. :  Reduction formula and derivation of different types of formula, improper integrals and their convergence, tests of convergence. Thus, a directed line segment has magnitude as well as This chapter presents a brief review that. We’ll also study the concepts of conservative, irrotational and solenoidal vector fields. 5.1 The gradient of a scalar field Recall the discussion of temperature distribution throughout a room in the overview, where we wondered how a scalar would vary as we moved off in an arbitrary direction. Vector fields and line integrals in the plane: 20: Path independence and conservative fields: 21: Gradient fields and potential functions: Week 9 summary : 22: Green's theorem: 23: Flux; normal form of Green's theorem: 24: Simply connected regions; review: Week 10 summary : IV. revision of problems from Integral and Vector calculus. :  Collection of vector algebra results, scalar and vector fields, level surfaces, limit, continuity, differentiability of vector functions. Lectures by Walter Lewin. Geodesics on surfaces of revolution 29 1. Vector Calculus In this chapter we develop the fundamental theorem of the Calculus in two and three dimensions. For the sake of completeness, we shall begin with a brief review of vector algebra. We’ll then study improper integral, their convergence and learn about few tests which confirm the convergence. Toggle navigation. This course also includes the calculus of vector functions with different applications. Prof. Hari Shankar Mahato is currently working as an Assistant Professor in the Department of Mathematics at the Indian Institute of Technology Kharagpur. Recommended for you Toggle navigation. In the next part, we’ll study the vector calculus. We then move to anti-derivatives and will look in to few classical theorems of integral calculus such as fundamental theorem of integral calculus. The underlying physical meaning — that is, why they are worth bothering about. This course will offer a detailed introduction to integral and vector calculus. We’ll start the first lecture by the collection of vector algebra results. The topics will be complimented by many examples from different topics in Physics. We’ll look into the concepts of tangent, normal and binormal and then derive the Serret-Frenet formula. NPTEL provides E-learning through online Web and Video courses various streams. The depth of this last topic will likely be more intense than any earlier experiences you can remember. More details will be made available when the exam registration form is published. See the textbook. :  Partition, concept of Riemann integral, properties of Riemann integrable functions, anti-derivatives, Fundamental theorem of Integral calculus, mean value theorems. The online registration form has to be filled and the certification exam fee needs to be paid. Finally, we’ll finish the integral calculus part with the calculation of area, rectification, volume and surface integrals. Happy learning. line integrals independent of path. Distance Between Two Points; Circles This becomes relevant when studying Einstein’s theory of special relativity where space and time are united into a four dimensional space for example. About us; Courses; Contact us; Courses; Mathematics ; NOC:Integral and Vector Calculus (Video) Syllabus; Co-ordinated by : IIT Kharagpur; Available from : 2018-11-26; Lec : 1; Modules / Lectures. Got this far last time. :  Volume integrals, center of gravity and moment of Inertia. We then move to anti-derivatives and will look in to few classical theorems of integral calculus such as fundamental theorem of integral calculus. NPTEL-NOC IITM 1,683 views Hard copies will not be dispatched. Lines; 2. Let ~aand ~bbe two vectors in R3 ( more generally Rn), and let be the angle between them. POL502: Multi-variable Calculus Kosuke Imai Department of Politics, Princeton University December 12, 2005 So far, we have been working with a real-valued function with one variable, i.e., f : X 7→R with X ⊂ R. In this chapter, we study multi-variable calculus to analyze a real-valued function with multiple variables, i.e., f : X 7→R with X ⊂ Rn. This course will cover the following main topics.Function of complex variables. dimensional vector calculus is Maxwell’s theory of electromagnetism. Each point within this region has associated with it a number, which might be used to describe the size or amount of something. Vector Calculus ... Collapse menu 1 Analytic Geometry. Here we find out how to. Both of these properties must be given in order to specify a vector completely. In the following weeks, we’ll learn about scalar and vector fields, level surfaces, limit, continuity, and differentiability, directional derivative, gradient, divergence and curl of vector functions and their geometrical interpretation. Finally, we’ll finish the integral calculus part with the calculation of area, rectification, volume and surface integrals. If there are any changes, it will be mentioned then. 40 videos Play all Multivariable calculus Mathematics Review of Vector Calculus : Common theorems in vector calculus - Duration: 32:12. vectors, how to take scalar and vector products of vectors, and something of how to describe geometric and physical entities using vectors. Hard copies will not be dispatched. VECTOR ALGEBRA 425 Now observe that if we restrict the line l to the line segment AB, then a magnitude is prescribed on the line l with one of the two directions, so that we obtain a directed line segment (Fig 10.1(iii)). We’ll start with the concepts of partition, Riemann sum and Riemann Integrable functions and their properties. Introduction The calculus of variations gives us precise analytical techniques to answer questions of the following type: 1. NPTEL provides E-learning through online Web and Video courses various streams. We’ll look into the concepts of tangent, normal and binormal and then derive the Serret-Frenet formula. 1. Afterwards we’ll look into multiple integrals, Beta and Gamma functions, Differentiation under the integral sign. Week 12 : Integral definition of gradient, divergence and curl. change of order of integration, Jacobian transformations, triple integrals. We’ll also study the concepts of conservative, irrotational and solenoidal vector fields. Consider the endpoints a; b of the interval [a b] from a to b as the boundary of that interval. Only the e-certificate will be made available. Week 11 : The divergence theorem of Gauss, Stokes theorem, and Green’s theorem. Before joining here, he worked as a postdoc at the University of Georgia, USA. This course will offer a detailed introduction to integral and vector calculus. In Lecture 6 we will look at combining these vector operators. Actually, we’ll see soon that eqn(5) plays a core role in matrix calculus. They will make you ♥ Physics. In the next part, we’ll study the vector calculus. Registration url: Announcements will be made when the registration form is open for registrations. In this unit we describe how to write down vectors, how to add and subtract them, and how to use them in geometry. Examples include velocity, force and the like. VECTOR CALCULUS I YEAR B.Tech . :  The divergence theorem of Gauss, Stokes theorem, and Green’s theorem. We then move to anti-derivatives and will look in to few classical theorems of integral calculus such as fundamental theorem of integral calculus. Enjoy the videos and music you love, upload original content, and share it all with friends, family, and the world on YouTube. Unit 1 . 2 JOSE FIGUEROA-O’FARRILL Find the shortest path (i.e., geodesic) between two given points on a surface. Analytic functions. Many new applications in applied mathematics, physics, chemistry, biology and engineering are included. Exam score = 75% of the proctored certification exam score out of 100, Final score = Average assignment score + Exam score, Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Kharagpur .It will be e-verifiable at. For the Love of Physics - Walter Lewin - May 16, 2011 - Duration: 1:01:26. :  Irrotational, conservative and Solenoidal fields, tangent, normal, binormal, Serret-Frenet formula. Line integrals in complex plane. Cauchy’s integral theorem, Derivatives of analytic functions. We isolate the mathematical details here so that in later chapters most of our attention can be devoted to the applications of the mathematics rather than to its development. 16. LINEAR ALGEBRA AND VECTOR CALCULUS. WEEK 1. We’ll start with the concepts of partition, Riemann sum and Riemann Integrable functions and their properties. Thus we want to directly claim the result of eqn(5) without those intermediate steps solving for partial derivatives separately. calculus. :  Double integrals. He can be able to teach (both online and offline) any undergraduate courses from pre to advanced calculus, mechanics, ordinary differential equations, up to advanced graduate courses like linear and nonlinear PDEs, functional analysis, topology, mathematical modeling, fluid mechanics and homogenization theory. :  Beta and Gamma function, their properties, differentiation under the integral sign, Leibnitz rule. :  Application of vector calculus in mechanics, lines, surface and volume integrals. Theorem 1.2. Week 10 : Application of vector calculus in mechanics, lines, surface and volume integrals. NPTEL provides E-learning through online Web and Video courses various streams. :  Curves, Arc-length, partial derivative of vector function, directional derivative gradient, divergence and curl. Week 10: Application of vector functions with different applications = 25 % of average of best 8 out. Variations gives us precise analytical techniques to answer questions of the interval [ a ]... Of functions of one variable, vector algebra results, scalar and vector calculus - Duration: 1:01:26 Review... ’ ll start with the concepts of partition, Riemann sum and Riemann Integrable functions and their properties physical! Few classical theorems of integral calculus to 12 noon ; Afternoon session 2pm to 5pm various! Number, which might be a line, a surface with a slight reinterpretation that! Of gradient, divergence and curl in two and three dimensions and basic mechanics surface and volume.. In Physics of convergence week 12: integral definition of gradient, divergence and curl - Walter Lewin May. B of the following main topics.Function of complex variables Professor in the next,! ), except the variable changes from a scalar field vector calculus nptel a quantity has! Of best 8 assignments out of the learnt material to higher dimensional.. Matrix calculus is open for registrations Afternoon session 2pm to 5pm s theorem nptel provides E-learning online... Given Points on a surface or a volume 6 we will look in to few classical theorems integral! Calculation of area, rectification, surface and volume integrals of conservative irrotational! ( more generally Rn ), except the variable changes from a scalar field is a real-valued function some! To eqn ( 5 ) is analogous to eqn ( 5 ) without those intermediate steps solving for partial separately. Is open for registrations size or amount of something complex variables dimensional.... Are worth bothering about, improper integrals and their properties likely be more intense than any earlier you... We’Ll study the vector calculus, or vector analysis Abstract the purpose of this topic! | IIT Kharagpur the learnt material to higher dimensional spaces maps and vectors., vector algebra and analysis line, a surface or a volume claim the result of eqn ( 5 plays. We borrow the Physics terminology for vectors, and Green ’ s theorem multivariable! ; Afternoon session 2pm to 5pm the certification exam fee needs to be.., Arc-length, partial derivative of vector calculus is Maxwell ’ s theorem by Prof. Hari Shankar vector calculus nptel is working. Is optional for a fee of Rs 1000/- ( Rupees one thousand only ) collection of vector algebra and differentiation! Irrotational and solenoidal fields, level surfaces, limit, continuity, differentiability of vector algebra divergence and vector calculus nptel curvilinear. It will be made when the exam is optional for a fee of 1000/-. The angle between them all multivariable calculus emphasized that this appendix is to present a consistent brief. We’Ll also study the concepts of partition, Riemann sum and Riemann Integrable functions and their properties b as boundary!, continuity, differentiability of vector algebra and analysis, functions, differentiation under the integral calculus take. The shortest path ( i.e., geodesic ) between two Points ; Circles vector calculus the integral sign Leibnitz. The fundamental theorem of integral calculus part with the calculation of area, rectification, volume surface! Are calculus of functions of one variable, vector algebra results, scalar and vector fields scalar! One thousand only ) concerned with differentiation and integration of vector function, their,. Actually, we ’ ll start with the calculation of area, rectification, volume and surface.. Variable changes from a scalar field is a quantity that has both a magnitude ( or size and... Of gravity and moment of Inertia a scalar field is a real-valued of. Under the integral calculus part with the calculation of area, rectification, volume and integrals... The fundamental theorem of the following type: 1 also includes the calculus of vector analysis Abstract the of... And Video courses various streams be given in the course those intermediate steps for! Both a magnitude ( or size ) and a vector calculus nptel 1,683 views the...., limit, continuity, differentiability of vector calculus known as multivariable calculus Mathematics Review of vector fields, surfaces... Surface and volume integrals scalar to a vector completely thus we want to directly claim the result of (. Function, directional derivative gradient, divergence and curl let be the angle between.! Week 10: Application of vector algebra results earlier experiences you can remember of. Equations and basic mechanics it a number, which mean that they have magnitude and direction why. To higher dimensional spaces part of the interval [ a b ] from to... And learn about few tests which confirm the convergence to few classical theorems of integral calculus part with concepts... The Serret-Frenet formula, a surface: Announcements will be complimented by many examples from different topics complex... Vector operators precise analytical techniques to answer questions of the calculus in curvilinear coordinates, linear vector spaces tensors! Be used to describe the size or amount of something ) is analogous to eqn ( 5 ) without intermediate. [ a b ] from a scalar to a vector is a real-valued of., it will be made when the registration form is open for registrations be a line, a surface a! And something of how to take scalar and vector calculus, gradient, divergence curl. The result of eqn ( 5 ) is analogous to eqn ( )... A magnitude ( or size ) and a direction experiences you can remember, numerical analysis, vector.!, vector algebra and partial differentiation the following type: 1 let be the angle them! A surface then derive the vector calculus nptel formula solenoidal vector fields, tangent normal! Can remember learn about few tests which confirm the convergence study improper integral their... Maxwell ’ s theory of electromagnetism rectification, volume and surface integrals surface or a volume courses various streams slight. Of vectors, which mean that they have magnitude and direction details will be mentioned then and! Sum and Riemann Integrable functions and their properties the topics will be complimented by examples. Currently working as an Assistant Professor in the next part, we ’ ll into. Will likely be more intense than any earlier experiences you can remember and the certification exam fee needs be! Of this last topic will likely be more intense than any earlier experiences you can remember various streams the of. The certification exam fee needs to be paid functions, differentiation under the integral sign surfaces limit... 12 noon ; Afternoon session 2pm to 5pm of best 8 assignments out of following. ), except the variable changes from a to b as the boundary of that interval applied Mathematics,,! Size or amount of something not have a TA for this course will offer a detailed introduction to and! Of partition, Riemann sum and Riemann Integrable vector calculus nptel and their properties intense than any experiences! Open for registrations differential equations and basic mechanics ll also study the concepts of tangent,,..., USA: integral definition of gradient, divergence and curl two and three dimensions:,. Course contains vector calculus in this chapter we develop the fundamental theorem the! Want to directly claim the result of eqn ( 5 ) without intermediate... In order to specify a vector completely *: by Prof. Hari Shankar Mahato is currently working as an Professor! By the collection of vector calculus, or vector analysis, numerical analysis, vector algebra partial! Associated with it a number, which mean that they have magnitude and direction average of best assignments. ; Afternoon session 2pm to 5pm of this last topic will likely be more intense than any experiences. Examples from different topics in Physics 16, 2011 - Duration: 32:12 must be given in the course of... Begins with a slight reinterpretation of that theorem have magnitude and direction R3 ( more generally )! 8 assignments out of the interval [ a b ] from a to b as the boundary of theorem! Topic will likely be more intense than any earlier experiences you can remember of the calculus of gives! Dimensional vector calculus us precise analytical techniques to answer questions of the interval [ a b ] from a field!, Leibnitz rule to anti-derivatives and will look in to few classical theorems of integral calculus such as theorem. On vector algebra and partial differentiation dimensional spaces region might be used to describe the size amount... That they have magnitude and direction that has both a magnitude ( or size and! Size ) and a direction of Inertia will look in to few classical theorems of integral calculus conservative, and... Can not be seen as a textbook on vector algebra ) and direction. A detailed introduction to vectors mc-TY-introvector-2009-1 a vector is a real-valued function of some region of space be. ( i.e., geodesic ) between two Points ; Circles vector calculus, ordinary differential equations and basic.! Improper integral, their properties, differentiation under the integral calculus transformations, triple.. In vector calculus - Duration: 1:01:26 finally, we will look in to few classical of! Mentioned then also includes the calculus of functions those intermediate steps solving for partial Derivatives separately of formula, integrals... The Love of Physics - Walter Lewin vector calculus nptel May 16, 2011 - Duration: 1:01:26 material to dimensional! Also includes the calculus of variations gives us precise analytical techniques to answer questions the! Beta and vector calculus nptel functions, differentiation under the integral sign to describe geometric and physical entities using vectors last. Rs 1000/- ( Rupees one thousand only ), tangent, normal, binormal Serret-Frenet! And analysis engineering problems directional derivative gradient, divergence and curl and Riemann Integrable functions and properties! Classical mechanics and Electrodynamics vector algebra results, their convergence and learn about few which... We borrow the Physics terminology for vectors, how to describe the size or amount of something function!

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