British columbia institute of technology calculus for. Students study the lectures at home and do the homework assignments. Many topics in the physical sciences can be analysed mathematically using the techniques of vector calculus. Consider first a functional j fdx in which f depends only x, y and y. If p 0, then the graph starts at the origin and continues to rise to infinity. Calculus of variations and integral equations by prof. There are several ways to derive this result, and we will cover three of the most common approaches.
Vector calculus is the fundamental language of mathematical physics. Calculus of variations and integral equations math 440. This is a very condensed and simplified version of basic calculus, which is a prerequisite for many courses in mathematics, statistics, engineering, pharmacy, etc. Nptel syllabus calculus of variations and integral equations web course course outline calculus of variations. The following problems were solved using my own procedure in a program maple v, release 5. The determination of the conjugate points for discontinuous. The main body of chapter 2 consists of well known results concerning necessary or su. The calculus of structures is a prooftheoretical formalism motivated by computation. Niket kaisare, department of chemical engineering, iit madras.
If you put a dog into this machine, youll get a red. The problem of lagrange in the calculus of variations. It converts any table of derivatives into a table of integrals and vice versa. Notes on calculus of variations 5 with the domain d 1. Suppose yxis defined on the interval a,b and so defines a curve on the x,y plane. Those who took the hybrid format section in calculus i had an average of 2. Variational problems with the fixed boundaries, module 3. Differential calculus in several variables video course course outline this is part of a standard course contents in several variable calculus.
Feb 08, 2017 sign in to like videos, comment, and subscribe. Mathematics nptel online videos, courses iit video. Mathematics nptel online videos, courses iit video lectures. The idea of the course is to provide students with different backgrounds a common platform to take up further topics in mathematics, physics and engineering. There may be more to it, but that is the main point. Lecture01 calculus of variations and integral equations. Ive tried to make these notes as self contained as possible and so all the information needed to read through them is either from an algebra or trig class or contained in other sections of the notes. Calculus of variations calculus of variations is a branch of m ethematics dealing with optimizing functionals. Shevgaonkar, dept of electrical engineering, iit bombay for more details on nptel visit. Bahuguna variational problems with the fixed boundaries,variational problems with moving boundaries, sufficiency conditions, fredholms integral equations, voltera integral equations, fredholms theory hilbertschmidt theorem, fredholm and volterra integrodifferential equation. We know that systems in the sequent calculus can be. Numbers, functions, and sequences, limit and continuity, differentiation, maxima, minima and curve sketching, approximations, integration, logarithmic and exponential functions, applications of integration, series of numbers and functions, limit and continuity of scalar fields, differentiation of scalar fields, maxima. Mathematical methods in engineering and science by dr.
Our subject matter is intermediate calculus and linear algebra. In the previous section, we saw an example of this technique. The value of this will depend on the choice of the function y and the basic problem of the calculus of variations is to find the form of the. Functions for calculus chapter 1 linear, quadratic, polynomial and rational this course is intended to remind you of the functions you will use in calculus. Y ou can practice alone or in small groups explaining calculus to eac h other is a go o d idea. The preceding examples are special cases of power functions, which have the general form y x p, for any real value of p, for x 0.
Lecture notes single variable calculus mathematics mit. Bhaskar dasgupta,department of mechanical engineering,iit kanpur. Ck12 foundation is a nonprofit organization with a mission to reduce the cost of textbook materials for the k12 market both in the u. For example, you can have a machine that paints things red. It was developed in the 17th century to study four major classes of scienti. In particular, if p 1, then the graph is concave up, such as the parabola y x2. Calculus of variations and integral equations math 440 by. It is the only period of cosmic thinking in the entire. The fundamental theorem of calculus the single most important tool used to evaluate integrals is called the fundamental theorem of calculus. Basic calculus for engineers, scientists and economists video. Lecture 17, fundamental theorems of calculus, riemann sum, pdf. Continuity and limits intuitively, we think of a function f. Jahresberichtderdeutschemathematikervereinigung,56.
Video lectures for calculus with analytic geometry iii, math 2415 these lectures cover the basic material for calculus iii at an introductory level. It pro vides a way to describe physical quantities in threedimensional space and the way in which these quantities vary. There is online information on the following courses. The term continuous curve means that the graph of f can be drawn without jumps, i. All, aicte, cec, ignou, iimb, ncert, nios, nitttr, nptel, ugc. Class time will be used for problem solving and presentation by students. Lecture02 calculus of variations and integral equations. Development of control relevant dynamic models is viewed as integral part of the process of controller. Mit ocw has a huge collection of undergraduate and graduate level courses in mathematics and other subjects as well which includes audiovideo lectures, lecture notes, textbooks, assi. Calculus of variations and integral equations nptel online. Nptel provides elearning through online web and video courses various streams. We shall develop the material of linear algebra and use it as setting for the relevant material of intermediate calculus. Jan 14, 2000 vector calculus is the fundamental language of mathematical physics.
Since dis a compact set, and since is continuous, its range b d is necessarily compact. Calculus of variations solvedproblems pavel pyrih june 4, 2012 public domain acknowledgement. Mathematics calculus of variations and integral equations nptel. These top ics include fluid dynamics, solid mechanics and electromagnetism, all of which. Linear approximation and differentiability gradient. Online video lectures for calculus with analytic geometry. Convergence of a sequence, monotone sequences, pdf. Indeed, the theory of functions and calculus can be summarised in outline as the study of the doing and undoing of the processes involved figure 3. This course aims at providing the reader with basic concepts of calculus of one and several variables which find applications in physics, chemistry. Its most direct analogue is gentzens sequent calculus. Consequently the functions f00 22, f00 23 and f 00 33 are all bounded on bthey are continuous because f2c2, and it follows that the double integral is less than or equal to. Rhas a discontinuous graph as shown in the following. What are the best online, collegelevel mathematics courses.
The calculus of variations university of california, davis. Calculus of variations and integral equations nptel. It is a functional of the path, a scalarvalued function of a function variable. The calculus of variations the variational principles of mechanics are rmly rooted in the soil of that great century of liberalism which starts with descartes and ends with the french revolution and which has witnessed the lives of leibniz, spinoza, goethe, and johann sebastian bach. In simplest terms, the calculus of variations can be compared to onedimensional, standard calculus. Furthermore, we assume that it is twice di erentiable. Mathworld website variational calculus had its beginnings in 1696 with john bernoulli applicable in physics. A line passes through the point 2, 5 and has slope 0. Nptel video lectures, iit video lectures online, nptel youtube lectures, free video lectures, nptel online courses, youtube iit videos nptel courses. The history of the calculus of variations is tightly interwoven with the history of mathematics, 9. Application of vector calculus in mechanics, lines, surface and volume integrals. A biological application of the calculus of variations.
The value of this will depend on the choice of the function y and the basic problem of the calculus of variations is to find the form of the function which makes the value of the integral a. Online video lectures for calculus with analytic geometry iii. Da2 1 linearization approximating curves with a model of a line ex. In the end, calculus is learned b y doing calculus, and not b y reading, or w atc hing someone else do it.
The divergence theorem of gauss, stokes theorem, and greens theorem. Malay banerjee, department of mathematics and statistics, iit kanpur. Mod06 lec20 differentiation and integration part 1 youtube. Euler differential equation and boundary conditions 453 3. Calculus of variations 1 functional derivatives the fundamental equation of the calculus of variations is the eulerlagrange equation d dt. Calculus i or needing a refresher in some of the early topics in calculus. For the love of physics walter lewin may 16, 2011 duration. The interpretation of vector functions and how to graph vector functions. In order to prove that this function results in an extremum, we need to prove that any alternative function does not attain the extremum. Calculus of variations and integral equations free math online course on nptel by iit kanpur malay banerjee, d. Calculus of variations solvedproblems univerzita karlova. The students who took calculus 24 in fall of 2006 were tracked into spring of 2007.
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