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AU Mathematics IV Sem IV
 No Units Titles Sub Titles Chapters 1 Unit 1 Functions of a Complex Variables Continuity concept of f(z), Derivative of f(z), Cauchy - Riemann Equations, Analytic Functions, Harmonic Functions, Orthogonal Systems, Applications to Flow Problems, Integration of Complex Functions, Cauchys Theorem, Cauchys Integral Formula, Statements of Taylors and Laurents Series without Proofs, Singular Points, Residues and Residue Theorem, Calculations of Residues, Evaluation of Real Definite Integrals, Geometric Representation of f(z), Conformal Transformation, Some Standard Transformations:- (1) w = z∫c, (2) w = 1/z, (3) w = (az∫b) (4) w = z2, (5) w = e2 VIEW CHAPTERS 2 Unit 2 Statistical Methods Review of Probability theory (not be examined), Addition law of probability, Independent events, Multiplication law of probability, Bays theorem, Random variable, Discrete probability distribution, Expectation, Moment generation function, repeated trails, Binomial distribution, Poission distribution, Normal distribution, Prabable error, Normal approximation to binomial distribution, Sampling Theory: Sampling Distribution, Standard Error, Testing of Hypothesis, Level of Significance, Confidence Limits, Simple Sampling of Attributes, Sampling of Variables - Large Samples and Small Samples, Students T-distribution, x2 -Distribution, F - Distribution, Fishers Z - Distribution VIEW CHAPTERS 3 Unit 3 Difference Equations and Z-Transforms Z-transforms - Definition, Some Standard Z-transforms, Linear Property, Sampling Rule, Some Standard Results, Shifting Rules, Initial and Final Value Theorems, Convolution theorem, Evaluation of inverse transforms, definition, Order and Solution of Difference Equations, Formation of Difference Equations, Linear Difference Equations, Rules for finding C,F,, Rule for finding P,L,, Difference Equation Reducible to Linear Form, Simultaneous Difference Equations with Constant Coefficients, Application to Deflection of a Loaded String, Applications of Z-transform to Difference Equations VIEW CHAPTERS