Unit 1
Algebra
Course Outcome: Apply the concepts of algebra to solve engineering related problems.
Unit outcome:
a) Solve the given simple problem based on laws of logarithm.
b) Calculate the area of the given triangle by determinant method.
c) Solve given system of linear equations using matrix inversion method and by Cramer’s rule.
d) Obtain the proper and improper partial fraction for the given simple rational function.
Introduction: Algebra is a simple language, used to create mathematical models of real world
situations and to handle problems. The algebraic need of engineering and technology is to solve
simple engineering problems using algebra. Some of the main topics coming algebra includes
Logarithms, Determinants, Matrix and Partial fractions.
Logarithm
Significance of Logarithms: Logarithm is one of the best tools to simplify engineering
problems.
Content of Logarithms:
Definition:
If y = ax , a > 0, a 1, a R, then x is called logarithm of y to the base a and it is written as
x = log𝑎𝑦.
For example,
1) If 8 = 23 then 3 = log28
2) If 34=81 then log381=4
Note: i) ax = y is called Exponential form or Index form and
x = loga y is called Logarithmic form of the same expression.
ii) Logarithm of negative number and zero are not defined
LAWS OF LOGARITHM:
1. loga (m n) = loga m + loga n
2. loga
m
n = loga m
loga n
