UNIT-I
Evaluating Algebraic Expressions
Order of operations
Evaluating algebraic expressions
Linear Equations
Translating algebraic expressions
Combining like terms
Solving linear equations: Addition property
Solving linear equations: Multiplication property
Combining rules
Literal equations
Solving linear inequalities
Graphing Linear Equations
Linear equations in two variables
The Cartesian coordinate system
The graph of a linear equation
Slope
Point-slope form of a line
Graphing linear inequalities
UNIT-II
Systems of Linear Equations
Systems of equations in two variables (addition/elimination)
Operations with polynomials
Positive integer exponents
Zero and negative integer exponents
Definition of polynomials
Addition and subtraction of polynomials
Multiplying polynomials
Factoring polynomials
Introduction to factoring
Difference of squares
Quadratic trinomials
Solving equations by factoring
Some word problems involving quadratic equations
UNIT-III
Radical expressions and complex numbers
Introduction to roots and radicals
Simplifying radical expressions [No variables]
Operations with radical expressions [No rationalizing binomials]
Complex numbers [ notation only, no operations]
Quadratic equations and some conics
Special methods, completing the square
The quadratic formula
Parabolas [Graph by table]
UNIT-IV
SETS: Sets,subsets,equal sets,null set,universal set,finite & infinite sets,open & closed sets etc.,
operations on sets, partition of sets, cartesian product.
DIFFERENTIATION: Derivative, derivatives of sum, differences, product & quotients, chain rule, derivatives of composite functions .
UNIT-V
INTEGRATION Integral as limit of a sum, indefinite & definite integrals, methods of integration substitution, by parts, partial fractions, integration of algebraic and transcedental functions
PLANE CURVES & POLAR COORDINATES: Polar coordinates, curve tracing in polar coordinates, area in polar coordinates, Arc length, area & volume of surface of revolution in Cartesian and polar coordinates.
Text/Reference Books
1. C. L. Liu.: Elements of Discrete Mathematics , Tata Mac-Graw Hill.
2. Thomas, G.B. and R. L. Finney: Calculus & Analytical Geometry, Addison-Wesley , 9th edition.
3. Chandrika Prasad : Mathematics for Engineers, Prasad Mudranalaya, Allahabad, 19th edition
4. Shanti Narayan: Differential Calculus, S.Chand & Co.
5. Shanti Narayan: Integral Calculus, S.Chand & Co.
