Calculus: Basic Concepts for High Schools by L. V. Tarasov

By L. V. Tarasov

An interactive textbook of Calculus offered as a discussion among the writer and the reader.

Show description

Read or Download Calculus: Basic Concepts for High Schools PDF

Similar calculus books

Mathematica: A Problem-Centered Approach (Springer Undergraduate Mathematics Series)

Mathematica®: A Problem-Centered method introduces the immense array of good points and robust mathematical services of Mathematica utilizing a mess of truly awarded examples and labored- out difficulties. every one part starts off with an outline of a brand new subject and a few uncomplicated examples. the writer then demonstrates using new instructions via 3 different types of problems

- the 1st type highlights these crucial elements of the textual content that reveal using new instructions in Mathematica when fixing each one challenge presented;

- the second one contains difficulties that additional display using instructions formerly brought to take on various occasions; and

- the 3rd provides tougher difficulties for additional study.

The goal is to allow the reader to profit from the codes, hence averting lengthy and arduous explanations.

While according to a working laptop or computer algebra path taught to undergraduate scholars of arithmetic, technology, engineering and finance, the publication additionally comprises chapters on calculus and fixing equations, and pix, therefore protecting all of the simple issues in Mathematica. With its powerful concentration upon programming and challenge fixing, and an emphasis on utilizing numerical difficulties that don't want any specific historical past in arithmetic, this booklet can also be excellent for self-study and as an advent to researchers who desire to use Mathematica as a computational software.

Linear Differential Operators

Because the different reviewers have acknowledged, it is a grasp piece for numerous purposes. Lanczos is legendary for his paintings on linear operators (and effective algorithms to discover a subset of eigenvalues). in addition, he has an "atomistic" (his phrases) view of differential equations, very on the subject of the founding father's one (Euler, Lagrange,.

Lehrbuch der Analysis: Teil 2

F? r den zweiten Teil des "Lehrbuchs der research" gelten dieselben Prinzipien wie f? r den erste: sorgf? ltige Motivierungen der tragenden Begriffe, leicht fassliche Beweise, erhellende Bespiele ("Bruder Beispiel ist der beste Prediger. "), nicht zuletzt Beispiele, die zeigen, wie analytische Methoden in den verschiedensten Wissenschaften eingesetzt werden, von der Astronomie bis zur ?

Differential and Integral Inequalities

In 1964 the author's mono graph "Differential- und Integral-Un­ gleichungen," with the subtitle "und ihre Anwendung bei Abschätzungs­ und Eindeutigkeitsproblemen" used to be released. the current quantity grew out of the reaction to the call for for an English translation of this publication. meanwhile the literature on differential and quintessential in­ equalities elevated drastically.

Extra resources for Calculus: Basic Concepts for High Schools

Sample text

Explain in the above light which of the examples of immersed submanifolds given in [Ch. 17] are integral curves and which not, for a suitable line subbundle of the tangent bundle. We will now show that immersed integral manifolds do not admit pathologies of the kind we pointed out in [Ch. 17]. 6. Proposition. If go : N -> M is any integral manifold and L is any other manifold with a map f : L --3 N, then f is differentiable if and only if cp o f is. Proof. If f is differentiable, the composite coo f is of course differentiable.

Indeed we have f (x) - f (a) = f f i t (tx + (1 - t)a)}dt 7-{f axi f (tx + (1 - t)a). dt (txi + (1 - t)ai)dt J(xi - ai) f 1a axZ f (tx + (1 - t)a)dt. 2. Locally Free Sheaves and Vector Bundles 29 The above considerations motivate the following definition. 4. Definition. A homogeneous first order differential operator on a differential manifold M is a linear operator on A(M) satisfying the Leibniz rule. Equivalently, it is a sheaf homomorphism A -* A which satisfies the Leibniz rule. A linear differential operator of order at most one on functions is of the form f H D f + gyp.

Lemma. If w is any nonzero element of Ar(V), then the linear map V -* Ar+1(V) given by v - vnw has kernel of dimension < r. Moreover, the kernel is of dimension r if and only if w E Ar(W) for some r-dimensional subspace W of V. Proof. In fact, it is obvious that if w belongs to Ar(W), then every element of W is in the kernel of the above map. Let {ei},1 < i < n, be a basis of V such that the first r of these generate W. In other words, el A ... A er can be taken to be w. Let v = E aiei; then vnw = 0 if and only if ai = 0 for all i > r.

Download PDF sample

Rated 4.14 of 5 – based on 17 votes