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. Introduction The calculus of variations gives us precise analytical techniques to answer questions of the following type: 1. of vector, differential, and integral calculus. : Volume integrals, center of gravity and moment of Inertia. NPTEL-NOC IITM 1,683 views This course also includes the calculus of vector functions with different applications. His research expertise are Partial Differential Equations, Applied Analysis, Variational Methods, Homogenization Theory and very recently he has started working on Mathematical Biology. We’ll start with the concepts of partition, Riemann sum and Riemann Integrable functions and their properties. In this unit we describe how to write down vectors, how to add and subtract them, and how to use them in geometry. Consider the endpoints a; b of the interval [a b] from a to b as the boundary of that interval. Weâll then study improper integral, their convergence and learn about few tests which confirm the convergence. 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. 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)). The online registration form has to be filled and the certification exam fee needs to be paid. revision of problems from Integral and Vector calculus. 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. NPTEL provides E-learning through online Web and Video courses various streams. Both of these properties must be given in order to specify a vector completely. 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. VECTOR CALCULUS I YEAR B.Tech . calculus. Corollary 1.3. Let ~aand ~bbe two vectors in R3 ( more generally Rn), and let be the angle between them. Unit 1 . Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course. Got this far last time. In the next part, we’ll study the vector calculus. 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. January 2017; Edition: FIRST; Publisher: STUDERA PRESS, NEW DELHI; ISBN: 978-81-930333-8-8; Authors: Dr Bhavanari … 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. Please choose the SWAYAM National Coordinator for support. In the next part, weâll study the vector calculus. Weâll start with the concepts of partition, Riemann sum and Riemann Integrable functions and their properties. 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 course consists of topics in complex analysis,numerical analysis, vector calculus and transform techniques with applications to various engineering problems. We then move to anti-derivatives and will look in to few classical theorems of integral calculus such as fundamental theorem of integral calculus. Vector Calculus In this chapter we develop the fundamental theorem of the Calculus in two and three dimensions. 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 . We’ll start the first lecture by the collection of vector algebra results. I did not have a TA for this course. If there are any changes, it will be mentioned then. : Partition, concept of Riemann integral, properties of Riemann integrable functions, anti-derivatives, Fundamental theorem of Integral calculus, mean value theorems. Enjoy the videos and music you love, upload original content, and share it all with friends, family, and the world on YouTube. Weâll also study the concepts of conservative, irrotational and solenoidal vector fields. In Lecture 6 we will look at combining these vector operators. 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. Introduction to vectors mc-TY-introvector-2009-1 A vector is a quantity that has both a magnitude (or size) and a direction. : Curves, Arc-length, partial derivative of vector function, directional derivative gradient, divergence and curl. 40 videos Play all Multivariable calculus Mathematics Review of Vector Calculus : Common theorems in vector calculus - Duration: 32:12. This becomes relevant when studying Einstein’s theory of special relativity where space and time are united into a four dimensional space for example. I did all the work by myself. Thus, a directed line segment has magnitude as well as Toggle navigation. Week 12 : Integral definition of gradient, divergence and curl. A.3. : Double integrals. Then weâll look into the line, volume and surface integrals and finally weâll learn the three major theorems of vector calculus: Greenâs, Gaussâs and Stokeâs theorem. 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. Vector Calculus ... Collapse menu 1 Analytic Geometry. 1. line integrals independent of path. revision of problems from Integral and Vector calculus. This region might be a line, a surface or a volume. We then move to anti-derivatives and will look in to few classical theorems of integral calculus such as fundamental theorem of integral calculus. In the following weeks, weâll 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. change of order of integration, Jacobian transformations, triple integrals. 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. Geodesics on surfaces of revolution 29 1. Toggle navigation. 1. Actually, we’ll see soon that eqn(5) plays a core role in matrix calculus. Here we ﬁnd out how to. This course will offer a detailed introduction to integral and vector calculus. Theorem 1.2. There is no problem in extending any of the learnt material to higher dimensional spaces. Then ~a~b= jajjbjcos( ) Proof. Happy learning. line integrals independent of path. WEEK 1. Finally, we’ll finish the integral calculus part with the calculation of area, rectification, volume and surface integrals. The depth of this last topic will likely be more intense than any earlier experiences you can remember. Line integrals in complex plane. This chapter presents a brief review that. This course will offer a detailed introduction to integral and vector calculus. Hard copies will not be dispatched. Recommended for you Weâll look into the concepts of tangent, normal and binormal and then derive the Serret-Frenet formula. We then move to anti-derivatives and will look in to few classical theorems of integral calculus such as fundamental theorem of integral calculus. 16. cal, and spherical, then enter into a review of vector calculus. Each point within this region has associated with it a number, which might be used to describe the size or amount of something. 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. This course assumes very limited knowledge of vector calculus, ordinary differential equations and basic mechanics. 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. We borrow the Physics terminology for vectors, which mean that they have magnitude and direction. highlights the essential mathematical tools needed throughout the text. 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. Before joining here, he worked as a postdoc at the University of Georgia, USA. IIT Kharagpur. Many new applications in applied mathematics, physics, chemistry, biology and engineering are included. Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm. : Application of vector calculus in mechanics, lines, surface and volume integrals. Fundamentals of Vector Analysis Abstract The purpose of this appendix is to present a consistent but brief introduction to vector calculus. Prerequisites are calculus of functions of one variable, vector algebra and partial differentiation. 2 JOSE FIGUEROA-O’FARRILL Find the shortest path (i.e., geodesic) between two given points on a surface. Geodesics, harmonic maps and Killing vectors 27 A.4. : Area of plane regions, rectification, surface integrals. Registration url: Announcements will be made when the registration form is open for registrations. Once again, thanks for your interest in our online courses and certification. : 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. : The divergence theorem of Gauss, Stokes theorem, and Green’s theorem. Prof. Hari Shankar Mahato is currently working as an Assistant Professor in the Department of Mathematics at the Indian Institute of Technology Kharagpur. They will make you ♥ Physics. Finally, weâll finish the integral calculus part with the calculation of area, rectification, volume and surface integrals. Lectures by Walter Lewin. 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. 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. Vector calculus, or vector analysis, is concerned with differentiation and integration of vector fields, primarily in 3-dimensional Euclidean space. Contents: Vectors: Vector calculus, Gradient, Divergence and Curl in curvilinear coordinates applications to Classical mechanics and Electrodynamics. calculus rules. This begins with a slight reinterpretation of that theorem. Week 11 : The divergence theorem of Gauss, Stokes theorem, and Green’s theorem. Distance Between Two Points; Circles Triple integrals and surface integrals in 3-space: 25 Only the e-certificate will be made available. Week 10 : Application of vector calculus in mechanics, lines, surface and volume integrals. : Irrotational, conservative and Solenoidal fields, tangent, normal, binormal, Serret-Frenet formula. 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. : Beta and Gamma function, their properties, differentiation under the integral sign, Leibnitz rule. Eqn(5) is analogous to eqn(2), except the variable changes from a scalar to a vector. Afterwards weâll look into multiple integrals, Beta and Gamma functions, Differentiation under the integral sign. The topics will be complimented by many examples from different topics in Physics. Hard copies will not be dispatched. LINEAR ALGEBRA AND VECTOR CALCULUS. Afterwards we’ll look into multiple integrals, Beta and Gamma functions, Differentiation under the integral sign. NPTEL provides E-learning through online Web and Video courses various streams. vectors, how to take scalar and vector products of vectors, and something of how to describe geometric and physical entities using vectors. Numbers, Functions, Sequencs and Limits of Functions. Analytic functions. We’ll also study the concepts of conservative, irrotational and solenoidal vector fields. * : By Prof. Hari Shankar Mahato | Toggle navigation. 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. Cauchy’s integral theorem, Derivatives of analytic functions. It should be emphasized that this appendix cannot be seen as a textbook on vector algebra and analysis. Lec : 1; Modules / Lectures. The course contains vector calculus in curvilinear coordinates, linear vector spaces, tensors and complex analysis. This course will cover the following main topics.Function of complex variables. Vector Calculus In this part of the presentation, we will learn what is known as multivariable calculus. For the sake of completeness, we shall begin with a brief review of vector algebra. Lines; 2. 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. : Collection of vector algebra results, scalar and vector fields, level surfaces, limit, continuity, differentiability of vector functions. This course will offer a detailed introduction to integral and vector calculus. Weâll start the first lecture by the collection of vector algebra results. The underlying physical meaning — that is, why they are worth bothering about. dimensional vector calculus is Maxwell’s theory of electromagnetism. The exam is optional for a fee of Rs 1000/- (Rupees one thousand only). We’ll then study improper integral, their convergence and learn about few tests which confirm the convergence. Thus we want to directly claim the result of eqn(5) without those intermediate steps solving for partial derivatives separately. : Reduction formula and derivation of different types of formula, improper integrals and their convergence, tests of convergence. More details will be made available when the exam registration form is published. See the textbook. 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. Examples include velocity, force and the like. For the Love of Physics - Walter Lewin - May 16, 2011 - Duration: 1:01:26. , numerical analysis, numerical analysis, is concerned with differentiation and integration of vector algebra results, and... Of Georgia, USA solving for partial Derivatives separately role in matrix calculus you remember! Consists of topics in Physics 16, 2011 - Duration: vector calculus nptel two vectors in R3 ( more generally )... Find the shortest path ( i.e., geodesic ) between two Points ; Circles vector calculus, gradient divergence. Average of best 8 assignments out of the total 12 assignments given in the course about few tests which the. 12 assignments given in the next part, we shall begin with a brief Review of vector functions topics... 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