Three Dimensional Coordinate Geometry
(Solid Geometry)
Lecture 10: Direction cosines and Projection
10.1 System of Co-ordinates
z
Point in 3D Space
P(x, y, z)
z
O
x
y
y
x
Any point P(x, y, z) in 3 dimensional space can be obtained by traveling the distanc
Lecture 1: Continuity and differentiability of a function
1 Definition of a Function
A function, f, with domain D, is a rule which assigns to each element x D a single real number,
f(x). The domain is usually a set of real numbers. The range R, of f consi
Lecture 6: Integration by the method of substitutions
6.1 Integration
Integration is a process of summation, or a process, which is the inverse of differentiation and
which accordingly be called anti-differentiation.
Note: Integration is a process of summ
Lecture 8: Definite integrals with properties
8.1 Definite Integrals
If a function f(x) is continuous on an interval [a, b], then f is integrable on [a, b]. If there exists a
dF
function F(x) such that
= f ( x) then
dx
b
f ( x)dx = F (b) F (a)
a
b
Here,
Lecture 3: Partial differentiation and Eulers theorem
To differentiate a function of single variable like y = f(x) we use ordinary derivative that is
dy
dx
or f ( x ) but in case of the functions of two or several variables like z = f(x,y) or u = f(x,y,z)
Lecture 12: Straight Lines and Shortest Distances
12.1 Equations of Straight lines
General Form of the equation of straight line
In three dimensional geometry a straight line can be obtained from the intersection of two nonparallel planes. So, equation st
Lecture 11: Equations of Planes and Lines
11.1 Definition of a Plane
A plane is a surface such that if any two points taken on, the straight line joining them lies wholly
in the surface i.e. every point on the line joining the points will be on the plane.
Lecture 5: Maximum and Minimum of Functions
Maxima
y
Function
y = f(x)
Minima
O
x
Figure 5.1: Maxima and Minima of the function y = f(x)
5.1 Definition
A function f(x) is said to have a maximum for a value a of x if f(a) is greater than any other value
th