# Mathematical Analysis flashcards, diagrams and study guides

Discover popular Mathematical Analysis study sets on Quizlet. Study Mathematical Analysis topics like Real Analysis, Complex Analysis and Fourier Analysis. Learn what you need to get good grades in Mathematical Analysis classes. Memorize important Mathematical Analysis terms, definitions, equations and concepts. Prepare for Mathematical Analysis homework and exams with free online flashcards, diagrams, study guides and practice tests.

## Top 20 sets of about 5,520

#### MATH 312 Exam 1

collection of objects

Y is a subset of X if for every y in Y there is a y in X

contains no elements

#### Classifying Real Numbers, Classifying numbers

Integer, Rational, Real

Irrational & Real

Rational & Real

#### 12 basic Functions

f(x)= x D: all real R: all real

f(x)= x^2 D: all real R: [0, infinity)

f(x)= x^3 D: all real R: all real

#### Figure 28.3

atrial depolarization

ventricular depolarization

#### ECG/EKG

Atrial Depolarization

Ventricular Depolarization

SA ---> AV Node

#### Chapter 2.1

a way of writing the set of all real numbers between two endpoints. the symbols [ and ] are used to include an endpoint in an interval, and the symbols ( and ) are used to exclude an endpoint from an interval

denoted by [a,b] which contains all real numbers and a≤x≤b

denoted by (a,b) which contains all real numbers x and a<x<b

#### Optical Isomers (idk if these are real)

5 bonds (expanded octet)

#### Math 312

We define |a| = a if a ≥ 0 and |a| = −a if a ≤ 0. |a| is called the absolute value of a.

For numbers a and b we define dist(a, b) = |a−b|; dist(a, b) represents the distance between a and b.

(i) |a| ≥ 0 for all a ∈ R. (ii) |ab| = |a|·|b| for all a, b ∈ R. (iii) |a + b|≤|a| + |b| for all a, b ∈ R.

#### Complex numbers

Complex number z a = real b= real bi=imaginary

sqr -1

B=0

#### ophiolite complex

1

2a & b

2c

#### EPHS Precalculus Honors Chandra - 2.4 (Complex Numbers)

b^2 - 4ac (What's under the square root in the quadratic formula)

a + bi

2 real zeros

#### Exam 2

A infinite sequence is a function from the ℕ into all R.

A sequence converges in R if ∃a∈R s.t. for every ε>0 ∃N∈ℕ s.t. whenever n≥ℕ it follows that |a_n - a|<ε

The limit of a sequence, when it exists, must be unique. In other words, if lim n→∞ a_n = L1 and lim n→∞ a_n = L2, then L1 = L2. lim n→∞ a_n = L means ∀ε > 0 ∃N ∈ ℕ s.t. n ≥ N → | a_n - a | < ε lim n → ∞ a_n ≠ L means ∃ε > 0 s.t. ∀n ∈ ℕ s.t. |a_n - a|≥ ε.

#### Label Shoulder Complex

radius

ulna

#### Real Analysis Midterm 2

a set where a notion of distance between elements of the set is defined 1. d(p,q) ≥ 0 2. d(p,q) = 0 <==> p=q 3. d(p,q) = d(q,p) 4. d(p,r) ≤ d(p,q) + d(q,r)

A subset S of a metric space E is open if, for each p e S, S contains some open ball of center p

A subset S of a metric space E is closed if, it's compliment, cS (that is, all points in E which are not in S) is open

#### Math 172 Exam 1

A sequence of real numbers (xn)∞n=1 is said to converge to a real number l ∈ R, if for every ε > 0 there exists a natural number N := N(ε) ∈ N such that for all n ≥ N, |xn − l| < ε. If (xn)∞n=1 converges to l, we write lim xn = l n→∞

Let f be a function defined on a closed interval [a, b] and let (xi)n i=0 be the regular partition of [a, b], i.e. xi = a + i ((b−a)/n) for all i ∈ {0, 1, . . . , n}. If lim Σ exists and gives the n→∞ same value for all possible choices of points x*i ∈ [xi−1, xi], then we say that f is integrable on [a, b]. If f is integrable on [a, b] we denote the definite integral of f on [a, b] by ∫b f(x)dx := lim Σi+1 f(x*i) (b-a)/n a n→∞

Let f : [a, b] → R be continuous on [a, b]. Then, F(x) = ∫x f(t)dt is a well-defined for all x ∈ [a, b]. More- over, the function F is differentiable on [a, b], and F' is continuous on [a, b] with F'(x) = f(x) for all x ∈ [a, b]

#### PQRST complex

#### Chpt 2: Argand Diagrams

The real axis

The imaginary axis

(x,y)

#### aug 27-oct 22 (1st partial)

Given f: A ⊆ R-->R and g: B ⊆ R-->R, such that f(A) ⊆ B, the function h: A ⊆ R-->R which associates each element of A with the element g(f(x)) is called composite functions.

a function whose expression varies with the domain

{0, 1, 2, ...n}

#### EKG

Atrial Depolarization

#### Analysis Midterm Review

A division of Q into two nonempty subsets L and U, with property that x < y for all x ϵ L and y ϵ U, and such that U has no smallest element

If A ⊆ R, A =/= Ø, then A is bounded above if there is a b ϵ R such that x <= b for all x ϵ A. Any such b is called an upper bound for A. Note that b is not necessarily in A

Every nonempty subset of R which is bounded above has a least upper bound, (supremum), denoted lub(A) or sup(A)