Engineering Mathematics - I

Simple notes for engineering mathematics-I.It almost cover important topics chapter wise

Chapter 1 DIFFERENTIAL CALCULUS

1. Expansion of functions by Maclaurin's and Taylor's theorem. Partial differentiation
2. Euler's theorem and its application in approximation and errors
3. Maxima and Minima of function of two variables
4. Radius of curvature
5. centre of curvature

Chapter 2 INTEGRAL CALCULUS

1. Definite Integrals as a limit of a sum
2. Beta and Gamma Functions
3. double integrals
4. Triple Integrals
5. Change of Order of Integration
6. Area,Volume and Surfaces using double and triple Integral

Chapter 3 DIFFERENTIAL EQUATIONS

Solution of Ordinary Differential Equation of first order and first degree for Exact differential Equations
1. III Exact differential equations
2. Linear Differential Equations with Constant Coefficients
3. Cauchy's Homogeneous differential Equation
4. Simultaneous differential Equations
5. Method of Variation of Parameters

Chapter 4 MATRICES

1. matrices rank
2. Matrix Determinants
3. Matrix Inverse
4. Solution of Simultaneous equation by elementary transformation
5. matrices transformation
6. Consistency of System of Simultaneous Linear Equation
7. Consistency of System of Simultaneous Linear Equation
8. Eigen Values and Eigen Vectors
9. Cayley-Hamilton Theorem and its Application to find the inverse

Chapter 5 ALGEBRA AND GRAPH THEORY

1. Boolean Algebra
2. Principle of Duality
3. Basic Theorems
4. Boolean Expressions and Functions
5. Elementary Concept of Fuzzy Logic
6. Graph thoery