Engineering Mathematics III For RTU (Subject Code 3CS1)

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Cover Contents Preface Acknowledgements Roadmap to the Syllabus Symbols and Basic Formulae Chapter 1: Optimization 1.1 History of Optimization 1.2 Methods of Optimization 1.3 Applications of Optimization Techniques in Various Streams of Engineering 1.4 General Optimization Problems 1.5 Classification of Optimization Problems 1.6 Modeling of Optimization Problems 1.7 Classical Optimization Techniques 1.8 Single-variable Optimization 1.9 Multivariable Optimization with No Constraints 1.10 Multivariable Optimization with Equality Constraints 1.11 Multivariable Optimization with Inequality Constraints Exercises Chapter 2: Linear Programming 2.1 Linear Programming Problems 2.2 Formulation of an LPP 2.3 Graphical Method to Solve LPP 2.4 Canonical and Standard Forms of LPP 2.5 Basic Feasible Solution of an LPP 2.6 Simplex Method 2.7 Tabular form of the Solution 2.8 Generalization of Simplex Algorithm 2.9 Two-phase Method 2.10 Duality Property 2.11 Dual Simplex Method 2.12 Transportation Problems 2.13 Matrix form of the Transportation Problem 2.14 Transportation Problem Table 2.15 Basic Initial Feasible Solution of Transportation Problem 2.16 Test for the Optimality of Basic Feasible Solution 2.17 Degeneracy in Transportation Problem 2.18 Unbalanced Transportation Problems Exercises Chapter 3: Project Scheduling: PERT & CPM 3.1 Project Management 3.2 Network Planning and Scheduling Techniques 3.3 Network Construction 3.4 Time Estimates and Critical Path Analysis 3.5 Project Evaluation and Review Technique (PERT) Exercises Chapter 4: Sequencing Theory 4.1 General Terminology, Notations and Assumptions 4.2 Problems of N Jobs Through Two Machines 4.3 Problems of N Jobs Through Three Machines 4.4 Problems of Two Jobs Through M Machines Exercises Chapter 5: Laplace Transform 5.1 Definition and Examples of Laplace Transform 5.2 Properties of Laplace Transforms 5.3 Limiting Theorems 5.4 Miscellaneous Examples Exercises Chapter 6: Inverse Laplace Transform 6.1 Definition and Examples of Inverse Laplace Transform 6.2 Properties of Inverse Laplace Transform 6.3 Partial Fractions Method to Find Inverse Laplace Transform 6.4 Heaviside’s Expansion Theorem 6.5 Series Method to Determine Inverse Laplace Transform 6.6 Convolution Theorem 6.7 Complex Inversion Formula 6.8 Miscellaneous Examples Exercises Chapter 7: Applications of Laplace Transform 7.1 Ordinary Differential Equations 7.2 Simultaneous Differential Equations 7.3 Difference Equations 7.4 Integral Equations 7.5 Integro-differential Equations 7.6 Solution of Partial Differential Equation 7.7 Evaluation of Integrals 7.8 Miscellaneous Examples Exercises Chapter 8: Finite Differences and Interpolation 8.1 Finite Differences 8.2 Factorial Notation 8.3 Some More Examples of Finite Differences 8.4 Error Propagation 8.5 Numerical Unstability 8.6 Interpolation 8.7 Use of Interpolation Formulae 8.8 Interpolation with Unequal-spaced Points 8.9 Newton’s Fundamental (Divided Difference) Formula 8.10 Error Formulae 8.11 Lagrange’s Interpolation Formula 8.12 Error in Lagrange’s Interpolation Formula 8.13 Hermite Interpolation Formula 8.14 Throwback Technique 8.15 Inverse Interpolation 8.16 Chebyshev Polynomials 8.17 Approximation of a Function with a Chebyshev Series 8.18 Interpolation by Spline Functions 8.19 Existence of Cubic Spline Exercises Chapter 9: Numerical Differentiation 9.1 Centered Formula of Order O (h2) 9.2 Centered Formula of Order O (h4) 9.3 Error Analysis 9.4 Richardson’s Extrapolation 9.5 Central Difference Formula of Order O (h2) for f ″(x) 9.6 General Method for Deriving Differentiation Formulae 9.7 Differentiation of a Function Tabulated in Unequal Intervals 9.8 Differentiation of Lagrange’s Polynomial 9.9 Differentiation of Newton Polynomial Exercises Chapter 10: Numerical Quadrature 10.1 General Quadrature Formula 10.2 Cote’s Formulae 10.3 Error Term in Quadrature Formula 10.4 Richardson Extrapolation (or Deferred Approach to the Limit) 10.5 Simpson’s Formula with End Correction 10.6 Romberg’s Method 10.7 Euler–Maclaurin Formula 10.8 Double Integrals Exercises Chapter 11: Ordinary Differential Equations 11.1 Initial Value Problems and Boundary Value Problems 11.2 Classification of Methods of Solution 11.3 Single-step Methods 11.4 Multistep Methods 11.5 Stability of Methods 11.6 Second Order Differential Equation 11.7 Solution of Boundary Value Problems by Finite Difference Method 11.8 Use of the Formula to Solve Boundary Value Problems 11.9 Eigenvalue Problems Exercises Chapter 12: Difference Equations 12.1 Definitions and Examples 12.2 Homogeneous Difference Equation with Constant Coefficients 12.3 Particular Solution of a Difference Equation Exercises Solved Question Papers Index