# Handbook of Mathematical Functions by Gisselle Eagle, Gabriella Durand By Gisselle Eagle, Gabriella Durand

Desk of Contents:
Chapter 1 – advent to Function
Chapter 2 – Inverse Function
Chapter three – specific features & Implicit and particular Functions
Chapter four – functionality Composition
Chapter five – non-stop Function
Chapter 7 – Algebraic Function
Chapter eight – Analytic Function
Chapter nine – thoroughly Multiplicative functionality and Concave Function
Chapter 10 – Convex Function
Chapter eleven – Differentiable Function
Chapter 12 – basic functionality and whole Function
Chapter thirteen – Even and atypical Functions
Chapter 14 – Harmonic Function
Chapter 15 – Holomorphic Function
Chapter sixteen – Homogeneous Function
Chapter 17 – Indicator Function
Chapter 18 – Injective Function
Chapter 19 – Measurable functionality

Similar mathematics books

Calculus II For Dummies (2nd Edition)

An easy-to-understand primer on complex calculus topics

Calculus II is a prerequisite for plenty of well known collage majors, together with pre-med, engineering, and physics. Calculus II For Dummies deals professional guide, suggestion, and the right way to aid moment semester calculus scholars get a deal with at the topic and ace their exams.

It covers intermediate calculus themes in undeniable English, that includes in-depth assurance of integration, together with substitution, integration innovations and while to take advantage of them, approximate integration, and flawed integrals. This hands-on consultant additionally covers sequences and sequence, with introductions to multivariable calculus, differential equations, and numerical research. better of all, it contains sensible workouts designed to simplify and increase realizing of this advanced subject.

creation to integration
Indefinite integrals
Intermediate Integration issues
limitless sequence
complicated subject matters
perform exercises

Confounded through curves? at a loss for words through polynomials? This plain-English advisor to Calculus II will set you straight!

Didactics of Mathematics as a Scientific Discipline

This booklet describes the cutting-edge in a brand new department of technology. the elemental concept was once to begin from a normal standpoint on didactics of arithmetic, to spot sure subdisciplines, and to signify an total constitution or "topology" of the sphere of analysis of didactics of arithmetic. the amount presents a pattern of 30 unique contributions from 10 diverse nations.

Additional resources for Handbook of Mathematical Functions

Sample text

Preimages If ƒ: X → Y is any function (not necessarily invertible), the preimage (or inverse image) of an element y ∈ Y is the set of all elements of X that map to y: The preimage of y can be thought of as the image of y under the (multivalued) full inverse of the function f. Similarly, if S is any subset of Y, the preimage of S is the set of all elements of X that map to S: For example, take a function ƒ: R → R, where ƒ: x → x2. This function is not invertible for reasons discussed above. Yet preimages may be defined for subsets of the codomain: The preimage of a single element y ∈ Y – a singleton set {y} – is sometimes called the fiber of y.

Facts about continuous functions If two functions f and g are continuous, then f + g, fg, and f/g are continuous. (Note. The only possible points x of discontinuity of f/g are the solutions of the equation g(x) = 0; but then any such x does not belong to the domain of the function f/g. ) The composition f o g of two continuous functions is continuous. If a function is differentiable at some point c of its domain, then it is also continuous at c. The converse is not true: a function that is continuous at c need not be differentiable there.

If the function ƒ is differentiable, then the inverse ƒ−1 will be differentiable as long as ƒ′(x) ≠ 0. The derivative of the inverse is given by the inverse function theorem: If we set x = ƒ–1(y), then the formula above can be written This result follows from the chain rule. The inverse function theorem can be generalized to functions of several variables. Specifically, a differentiable function ƒ: Rn → Rn is invertible in a neighborhood of a point p as long as the Jacobian matrix of ƒ at p is invertible.