Applied Mathematics‐IV Notes
₹250.00

Notes
 Complex Integration Notes
 Matrices Notes
 Probability Notes
 Sampling Theory Notes
 Mathematical Programming ( LPP ) Notes
 Calculus of Variation (EXTC, Electrical , Electronics Notes)
 Linear Algebra Vector Space (EXTC, Electrical , Electronics Notes )
 Correlation,Regression and Curve Fitting (EXTC, Electrical , Electronics Notes )
 Graph and Group theory (IT)
 Lattice theory (IT)

Solution Keys
Applied Mathematics‐IV Notes
Applied Mathematics‐IV Notes is semester 4 subject of computer engineering in Mumbai University. Prerequisite for studying this subject are Engineering MathematicsI, Engineering MathematicsII, Engineering MathematicsIII, Binomial Distribution. Course Objectives of Engineering MathematicsIV aims to learn Matrix algebra to understand engineering problems. Line and Contour integrals and expansion of a complex valued function in a power series. ZTransforms and Inverse ZTransforms with its properties. The concepts of probability distributions and sampling theory for small samples. Linear and Nonlinear programming problems of optimization. Course Outcomes Engineering MathematicsIV On successful completion, of course, learner/student will be able to Apply the concepts of eigenvalues and eigenvectors in engineering problems. Use the concepts of Complex Integration for evaluating integrals, computing residues & evaluate various contour integrals. Apply the concept of Z transformation and inverse in engineering problems. Use the concept of probability distribution and sampling theory to engineering problems. Apply the concept of Linear Programming Problems to optimization. Solve NonLinear Programming Problems for optimization of engineering problems.
Module Linear Algebra (Theory of Matrices) consists of the following subtopics Characteristic Equation, Eigenvalues and Eigenvectors, and properties (without proof). CayleyHamilton Theorem (without proof), verification and reduction of higher degree polynomials. Similarity of matrices, diagonalizable and nondiagonalizable matrices. Selflearning Topics: Derogatory and nonderogatory matrices, Functions of Square Matrix, Linear Transformations, Quadratic forms.
Module Complex Integration consists of the following subtopics Line Integral, Cauchy‟s Integral theorem for simple connected and multiply connected regions (without proof), Cauchy‟s Integral formula (without proof). Taylor‟s and Laurent‟s series (without proof). Definition of Singularity, Zeroes, poles off(z), Residues, Cauchy‟s Residue Theorem (without proof). Selflearning Topics: Application of Residue Theorem to evaluate real integrations.
Module Z Transform consists of the following subtopics Definition and Region of Convergence, Transform of Standard Functions: {𝑘𝑛𝑎𝑘}, {𝑎𝑘}, { +𝑛𝐶. 𝑎𝑘}, {𝑐 𝑘sin(𝛼𝑘 + 𝛽)}, {𝑐 𝑘 sinh 𝛼𝑘}, {𝑐 𝑘 cosh 𝛼𝑘}. Properties of Z Transform: Change of Scale, Shifting Property, Multiplication, and Division by k, Convolution theorem. Inverse Z transform: Partial Fraction Method, Convolution Method. Selflearning Topics: Initial value theorem, Final value theorem, Inverse of Z Transform by Binomial Expansion.
Module Probability Distribution and Sampling Theory consists of the following subtopics Probability Distribution: Poisson and Normal distribution. Sampling distribution, Test of Hypothesis, Level of Significance, Critical region, Onetailed, and twotailed test, Degree of freedom. Students‟ tdistribution (Small sample). Test the significance of mean and Difference between the means of two samples. ChiSquare Test: Test of goodness of fit and independence of attributes, Contingency table. Selflearning Topics: Test significance for Large samples, Estimate parameters of a population, Yate‟s Correction.
Module Linear Programming Problems consists of the following subtopics Types of solutions, Standard and Canonical of LPP, Basic and Feasible solutions, slack variables, surplus variables, Simplex method. Artificial variables, BigM method (Method of penalty). Duality, Dual of LPP and Dual Simplex Method Selflearning Topics: Sensitivity Analysis, TwoPhase Simplex Method, Revised Simplex Method.
Module Nonlinear Programming Problems consists of the following subtopics NLPP with one equality constraint (two or three variables) using the method of Lagrange‟s multipliers. NLPP with two equality constraints. NLPP with inequality constraint: KuhnTucker conditions. Selflearning Topics: Problems with two inequality constraints, Unconstrained optimization: Onedimensional search method (Golden Search method, Newton‟s method). Gradient Search method.
Suggested Reference books for subject Engineering MathematicsIV from Mumbai university are as follows Erwin Kreyszig, “Advanced Engineering Mathematics”, John Wiley & Sons. R. K. Jain and S. R. K. Iyengar, “Advanced Engineering Mathematics”, Narosa. Brown and Churchill, “Complex Variables and Applications”, McGrawHill Education. T. Veerarajan, “Probability, Statistics and Random Processes”, McGrawHill Education. Hamdy A Taha, “Operations Research: An Introduction”, Pearson. S.S. Rao, “Engineering Optimization: Theory and Practice”, WileyBlackwell. Hira and Gupta, “Operations Research”, S. Chand Publication.
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Course Features
 Lectures 15
 Quizzes 0
 Duration 50 hours
 Skill level All levels
 Language English
 Students 2
 Certificate No
 Assessments Yes