 # Engineering Maths Tuition Classes ## Engineering Mathematics-1

UNIT I DIFFERENTIAL CALCULUS 12 Representation of functions – Limit of a function – Continuity – Derivatives – Differentiation rules – Maxima and Minima of functions of one variable.

UNIT II FUNCTIONS OF SEVERAL VARIABLES 12 Partial differentiation – Homogeneous functions and Euler’s theorem – Total derivative – Change of variables – Jacobians – Partial differentiation of implicit functions – Taylor’s series for functions of two variables – Maxima and minima of functions of two variables – Lagrange’s method of undetermined multipliers.

UNIT III INTEGRAL CALCULUS 12 Definite and Indefinite integrals – Substitution rule – Techniques of Integration – Integration by parts, Trigonometric integrals, Trigonometric substitutions, Integration of rational functions by partial fraction, Integration of irrational functions – Improper integrals. UNIT IV MULTIPLE INTEGRALS 12 Double integrals – Change of order of integration – Double integrals in polar coordinates – Area enclosed by plane curves – Triple integrals – Volume of solids – Change of variables in double and triple integrals.

UNIT V DIFFERENTIAL EQUATIONS 12 Higher order linear differential equations with constant coefficients – Method of variation of parameters – Homogenous equation of Euler’s and Legendre’s type – System of simultaneous linear differential equations with constant coefficients – Method of undetermined coefficients.

## Engineering Mathematics-2

UNIT I MATRICES 12 Eigenvalues and Eigenvectors of a real matrix – Characteristic equation – Properties of Eigenvalues and Eigenvectors – Cayley-Hamilton theorem – Diagonalization of matrices – Reduction of a quadratic form to canonical form by orthogonal transformation – Nature of quadratic forms. UNIT II VECTOR CALCULUS 12 Gradient and directional derivative – Divergence and curl – Vector identities – Irrotational and Solenoidal vector fields – Line integral over a plane curve – Surface integral – Area of a curved
31

surface – Volume integral – Green’s, Gauss divergence and Stoke’s theorems – Verification and application in evaluating line, surface and volume integrals. UNIT III ANALYTIC FUNCTIONS 12 Analytic functions – Necessary and sufficient conditions for analyticity in Cartesian and polar coordinates – Properties – Harmonic conjugates – Construction of analytic function – Conformal mapping – Mapping by functions 2 1 z z czczw, += – Bilinear transformation.

UNIT IV COMPLEX INTEGRATION 12 Line integral – Cauchy’s integral theorem – Cauchy’s integral formula – Taylor’s and Laurent’s series – Singularities – Residues – Residue theorem – Application of residue theorem for evaluation of real integrals – Use of circular contour and semicircular contour.

UNIT V LAPLACE TRANSFORMS 12 Existence conditions – Transforms of elementary functions – Transform of unit step function and unit impulse function – Basic properties – Shifting theorems -Transforms of derivatives and integrals – Initial and final value theorems – Inverse transforms – Convolution theorem – Transform of periodic functions – Application to solution of linear second-order ordinary differential equations with constant coefficients.

## Engineering Mathematics-3

UNIT I PARTIAL DIFFERENTIAL EQUATIONS 12 Formation of partial differential equations – Singular integrals – Solutions of standard types of first-order partial differential equations – Lagrange’s linear equation – Linear partial differential equations of second and higher-order with constant coefficients of both homogeneous and non-homogeneous types.

UNIT II FOURIER SERIES 12 Dirichlet’s conditions – General Fourier series – Odd and even functions – Half range sine series – Half range cosine series – Complex form of Fourier series – Parseval’s identity – Harmonic analysis.

UNIT III APPLICATIONS OF PARTIAL DIFFERENTIAL EQUATIONS 12 Classification of PDE – Method of separation of variables – Fourier Series Solutions of one-dimensional wave equation – One-dimensional equation of heat conduction – Steady-state solution of two-dimensional equation of heat conduction.

UNIT IV FOURIER TRANSFORMS 12 Statement of Fourier integral theorem – Fourier transforms pair – Fourier sine and cosine transforms – Properties – Transforms of simple functions – Convolution theorem – Parseval’s identity.

UNIT V Z – TRANSFORMS AND DIFFERENCE EQUATIONS 12 Z-transforms – Elementary properties – Inverse Z-transform (using partial fraction and residues) – Initial and final value theorems – Convolution theorem – Formation of difference equations – Solution of difference equations using Z – transform.

## Engineering Mathematics-4

UNIT I SOLUTION OF EQUATIONS AND EIGENVALUE PROBLEMS 12 Solution of algebraic and transcendental equations – Fixed point iteration method – Newton Raphson method – Solution of linear system of equations – Gauss elimination method – Pivoting – Gauss Jordan method – Iterative methods of Gauss Jacobi and Gauss-Seidel – Eigenvalues of a matrix by Power method and Jacobi’s method for symmetric matrices.

UNIT II INTERPOLATION AND APPROXIMATION 12 Interpolation with unequal intervals – Lagrange’s interpolation – Newton’s divided difference interpolation – Cubic Splines – Difference operators and relations – Interpolation with equal intervals – Newton’s forward and backward difference formulae.

UNIT III NUMERICAL DIFFERENTIATION AND INTEGRATION 12 Approximation of derivatives using interpolation polynomials – Numerical integration using Trapezoidal, Simpson’s 1/3 rule – Romberg’s Method – Two-point and three-point Gaussian quadrature formulae – Evaluation of double integrals by Trapezoidal and Simpson’s 1/3 rules.

UNIT IV INITIAL VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS 12 Single step methods – Taylor’s series method – Euler’s method – Modified Euler’s method – Fourth order Runge – Kutta method for solving first-order equations – Multistep methods – Milne’s and Adams – Bash forth predictor-corrector methods for solving first-order equations. UNIT V BOUNDARY VALUE PROBLEMS IN ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS 12 Finite difference methods for solving second order two-point linear boundary value problems – Finite difference techniques for the solution of two dimensional Laplace’s and Poisson’s equations on rectangular domain – One-dimensional heat flow equation by explicit and implicit (Crank Nicholson) methods – One-dimensional wave equation by explicit method.

## Engineering Mathematics-5

UNIT I PROBABILITY AND RANDOM VARIABLES 12 Probability – The axioms of probability – Conditional probability – Baye’s theorem – Discrete and continuous random variables – Moments – Moment generating functions – Binomial, Poisson, Geometric, Uniform, Exponential and Normal distributions.

UNIT II TWO – DIMENSIONAL RANDOM VARIABLES 12 Joint distributions – Marginal and conditional distributions – Covariance – Correlation and linear regression – Transformation of random variables – Central limit theorem (for independent and identically distributed random variables).

UNIT III TESTING OF HYPOTHESIS 12 Sampling distributions – Estimation of parameters – Statistical hypothesis – Large sample tests based on Normal distribution for single mean and difference of means -Tests based on t, Chi-square and F distributions for mean, variance and proportion – Contingency table (test for independent) – Goodness of fit.

UNIT IV DESIGN OF EXPERIMENTS 12 One way and Two-way classifications – Completely randomized design – Randomized block design – Latin square design – 22 factorial design. UNIT V STATISTICAL QUALITY CONTROL `12 Control charts for measurements (X and R charts) – Control charts for attributes (p, c and np charts) – Tolerance limits – Acceptance sampling.

### Engineering Maths Tuition Classes – Credentials

• Classes are conducted by Mrs. Vanitha M.E., Power Systems.
• 8 Years of experience in Teaching Field.
• Students whom to have a willingness to join these Engineering Maths tuition classes contact us by presence.

Click to go top