This document provides an introduction and overview of key concepts in mathematics that are important for engineering, including algebra, geometry, trigonometry, and calculus. It defines each area of math and outlines prerequisites. Algebra concepts like properties of equality, exponents, polynomials, and solving equations are explained. The document also covers lines and their standard form, noting that slope indicates whether a line rises or falls and what a zero slope represents. The overall goal is to help students understand what each math concept involves and how they are applied in engineering problems.

1. Introduction to Engineering
Mathematics
Prof.V.Mahadevan
AP-Mathematics
GCE-Salem

2. Objectives for Algebra, Geometry,
Trigonometry, and Calculus.
Algebra,Geometry,Trigonometry, andCalculus,but
rather to give you a sound understanding of what
each of these are and how, and why, they are
used.My hope is that this will allow you to make
informed decisions in the future when choosing math
classes.

3. Definitions
 Algebra – the study of mathematical operations and their application to solving equations
 Geometry – the study of shapesAlgebra is a prerequisiteTrigonometry – the study of
triangles and the relationships between the lengths of their sides and the angles between
those sides.Algebra and Geometry are prerequisites
 Calculus – the mathematical study of changeDifferential Calculus – concerning rates of
change and slopes of curvesIntegral Calculus – concerning accumulation of quantities and
the areas under curves
 Algebra, Geometry, and Trigonometry are prerequisites

4. Algebra Properties
 Commutative Property a + b = b + a , ab = ba
 Associative Property (a + b) + c = a + (b + c),(ab)c = a(bc)
 Distributive Property a(b + c) = ab + ac

5. Rules of signs Order of Operations
Negative (-) can go anywhere.
 Two negatives = positiveOrder of Operations
 Parenthesis and Exponents first, thenMultiply and Divide, thenAdd and Subtract

6. Exponents and Polynomials
 𝒙 𝟐
= x times x
 𝒙 𝟑 = x times x times x times
 Polynomials 𝒙 𝟐
+ 4x + 37𝒙 𝟑
- 5𝒙 𝟐
+ 12x – 7
 Factoring 𝒙 𝟐 + 4x + 3 = (x + 1)(x + 3)

7. Solving Equations – Keep Balance
 Try to get to form: x = value

8. Solving Equations 3x + 3 = 2x + 6 solve
for x
 Subtract 2x from each side
 3x + 3 – 2x = 2x + 6 – 2x
 x + 3 = 6
 Subtract 3 from each side
 x = 6 – 3X = 3 (answer)

9. Equations of Lines Standard Form:
y = mx + b, where
 m is slope of line and
 Positive slope = ___
 Negative slope = ___
 Zero slope = ___
 b is the y-axis intercept

10. THANK YOU