Calicut University Engineering Lecture Notes

I have taken admission in Calicut University Institute of Engineering and Technology for Civil Engineering course . From where I can get the Civil Engineering Study Material and lecture notes of Calicut University Institute of Engineering and Technology ?

I have taken admission in B.Tech Civil Engineering Course from Calicut University. I am in 1st Semester. I am searching for lecturer notes of 1st semester course. So someone is here who will provide link to download lecturer notes of B.Tech Civil Engineering 1st Semester Course of Calicut University?

[pooja]

As you are looking for lecturer notes of 1st Semester B.Tech Civil Engineering Course of Calicut University, so here I am providing curriculum of 1st Semester Course along with notes:

Calicut University B.Tech Civil Engineering 1st Semester Curriculum
EN14 101 Engineering Mathematics I
EN14 102 Engineering Mathematics II
EN14 103 Engineering Physics
EN14 103(P) Engineering Physics Lab
EN14 104 Engineering Chemistry
EN14 104(P) Engineering Chemistry Lab
EN14 105 Engineering Mechanics
EN14 106 Engg. Basics of Civil and Mechanical
EN14 107 Basics of Electrical and Electronics & Communication Engg.
EN14 108 Engineering Graphics
EN14 109 Skills Humanities and Communication
EN14 110 (P) Mechanical Workshops
EN14 111 (P) Electrical & Civil Workshops

Notes of EN14 101 Engineering Mathematics I

Limit of function:
Let f be a real-valued function defined for all points in a neighbourhood N of a point c except
possibly at the point c itself. Recall that any open set containing the element a is called the
neighbourhood of a. In particular N(a, ) = (a, a+), > 0 is called the δ-neighbourhood
of a and N∗(a, ) = N(a, ) {a} = (a , a)∪(a, a + ) is called the deleted neighbourhood
of a. We are assuming that f is defined in the deleted neighbourhood of a in the following
definition of limit.

Definition 1 The function f is said to tend to + as x tends to c (or in symbols, limx→c
f(x) = +) if for each G > 0 (however large), there exists a δ > 0 such that
f(x) > G, whenever |x − c| <

Definition 2 The function f is said to tend to a limit l as x tends to (or in symbols,
limx→ f(x) = l) if for each ε > 0, there exists a k > 0 such that
|f(x) − l| < ε, whenever x > k.

Left hand and right hand limits
While defining the limit of a function f(x) as x tends to c, we consider the values of f(x)
when x is very close to c. he values of x may be greater or less than c. If we restrict x to
values less than c, then we say that x tends to c from below or from the left and write it
symbolically as x → c − 0 or simply x → c−. he limt of f(x) with this restriction on x, is
called the left hand limit. Similarly, if x takes only the values greater than c, then x is said to
tend to c from above or from the right, and is denoted symbolically as x → c + 0 or x → c+.
The limit of f(x) with this restriction on x, is called the right hand limit.

Definition 3 A function f is said to tend to a limit l as x tends to c from the 
left, if for each ε > 0, there exists a δ > 0 such that
|f(x) − l| < ε, whenever c − δ < x < c.

Definition 4 A function f is said to tend to a limit l as x tends to c from the right, if for
each ε > 0, there exists a δ > 0 such that
|f(x) − l| < ε, whenever c < x < c + δ.

Limit of a function by sequential approach
Definition 7 Let J ⊂ R be an interval. Let a ∈ J. Let f : J\{a} → R be given. Then
limx→a f(x) = l iff for every sequence {xn} with xn ∈ J\{a} with the property that xn → a, we
have f(xn) → l.

Theorem 2 A function f tends to finite limit as x tends to c if and only if for every ε > 0
∃ a neighbourhood N(c) of c such that |f(xm) − f(xn)| < ε for all xm, xn ∈ N(c); xm, xn ̸= c.

Similarly, a function f tends to a finite limit as x tends to ∞ if and only if for every ε > 0,
there exists G > 0 such that |f(xm) − f(xn)| < ε, for all xm, xn > G.

Continuity
Let f be a real-valued function defined on an interval J ⊂ R. We shall now consider the
behaviour of f at points on J.

Definition (ε− definition of continuity) Let f : J → R be given and a ∈ J. We say that
f is continuous at a if for any given ε > 0, there exists > 0 such that x ∈ J and |x−a| < δ
⇒ |f(x) − f(a)| < ε.

A function f is said to be continuous in an interval J, if it continuous at every point of the interval.
A function is said to be discontinuous at a point x = c of its domain, if it is not continuous at x = c. The point x = c is called a point of discontinuity of the function.