ENGINEERING MATHEMATICS I book. Read 2 reviews from the world's largest community for readers. Engineering Mathematics. Front Cover · A. Singaravelu. Tata McGraw-Hill Education, - Engineering mathematics · 0 Reviews. Books · My library · Help · Advanced Book Search · Get print book. No eBook available Engineering Mathematics. By A. Singaravelu.
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Chapter 4: Chapter 5: Existence conditions — Transform of elementary functions — Transform of unit step function and unit impulse function — Basic properties — Shifting theorems — Transform of derivatives and integrals — Initial and final value thorems - Inverse Laplace transform — Statement of Convolution theorem — Transforms of periodic functions — Application to solution of linear ODE of second order with constant coefficients.
Differential Calculus. Representation of functions — Limit of a function — Continuity — Derivatives — Differentiation rules — Maxima and Minima of functions of one variable.
Functions of Several Variables. Integral Calculus. 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.
Multiple Integrals. 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. Differential Equations. Partial Differential Equations.
Fourier Series. Applications of Partial Differential Equations. Classification of PDE — Method of separation of variable — Solutions of one dimensional wave equation — One dimensional heat conduction — Steady state solution of two dimensional equation of heat conduction excluding insulated edges. Fourier Transforms. The Z-Transform and Difference Equations.
Random Variables. Two Dimensional Random Variables. 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. Random Processes. Correlation And Spectral Densities. Auto correlation functions - Cross correlation functions - Properties — Power spectral density — Cross spectral density - Properties.
Linear Systems With Random Inputs. Linear time invariant system - System transfer function — Linear systems with random inputs — Auto correlation and cross correlation functions of input and output.
Classification — Stationary process — Markov process —Poisson process — Discrete parameter Markov chain — Chapman Kolmogorov equations — Limiting distributions.
Queueing Models. Balking and reneging.
Advanced Queueing Models. Probability — The axioms of probability — Conditional probability — Discrete and continuous random variables — Moments - Moment generating functions — Binomial, Poisson, Geometric, Uniform, Exponential, Gamma and Normal distributions.
Two - Dimensional Random Variables. Testing of Hypothesis.
Sampling distributions — Estimation of parameters — Statistical hypothesis — Large sample test based on Normal distribution for single mean and difference of means — Test based on t, Chi — square and F distributions for mean, variance and proportion — Contingency table test for independent — Goodness of fit.
Design of Experiments.
Statistical Quality Control. Control charts for measurements X and R charts - Control charts for attributes p, c and np charts — Tolerance limits — Acceptance sampling.