Cover -- Preface -- Acknowledgement -- Contents -- Unit-l.Differential Calculus-I -- 1.1 Introduction -- 1.2 Radius of Curvature -- 1.2.1 Radius of Curvature in Cartesian Form -- 1.2.2 Radius of Curvature in Parametric Form -- Worked Out Examples -- Exercise 1.1 -- 1.2.3 Radius of Curvature in Pedal Form -- 1.2.4 Radius of Curvature in Polar Form -- Worked Out Examples -- Exercise 1.2 -- 1.3 Some Fundamental Theorem -- 1.3.1 Rolle's Theorem -- 1.3.2 Lagrange's Mean Value Theorem -- 1.3.3 Cauchy's Mean Value Theorem -- 1.3.4 Taylor's Theorem -- Worked Out Examples -- Exercise 1.3 -- Additional Problems (From Previous Years VTU Exams.) -- Objective Questions -- Unit-ll Differential Calculus-II -- 2.1 Indeterminate Forms -- 2.1.1 Indeterminate Form 0/0 -- Wroked Out Examples -- Exercise 2.1 -- 2.1.2 Indeterminate Forms ∞ - ∞ and 0 × ∞ -- Worked Out Examples -- Exercises 2.2 -- 2.1.3 Indeterminate Forms 00, 1∞, ∞0, 0∞ -- Worked Out Examples -- Exercise 2.3 -- 2.2 Taylor's Theorem for Functions of two Variables -- Worked Out Examples -- Exercise 2.4 -- 2.3 Maxima and Minima of Functions of two Variables -- 2.3.1 Necessary and Sufficient Conditions for Maxima and Minima -- Worked Out Examples -- Exercise 2.5 -- 2.4 Lagrange's Method of Undetermined Multipliers -- Working Rules -- Worked Out Examples -- Exercise 2.6 -- Additional Problems (From Previous Years VTU Exams.) -- Objective Questions -- Unit-lll Integral Calculus -- 3.1 Introduction -- 3.2 Multiple Integrals -- 3.3 Double Integrals -- Worked Out Examples -- Exercise 3.1 -- 3.3.1 Evaluation of a Double Integral by Changing the Order of Integration -- 3.3.2 Evaluation of a Double Integral by Change of Variables -- 3.3.3 Applications to Area and Volume -- Worked Out Examples -- Type 1. Evaluation over a given region -- Type 2. Evaluation of a double integral by changing the order of integration.

Type 3. Evaluation by changing into polars -- Type 4. Applications of double and triple integrals -- Exercise 3.2 -- 3.4 Beta and Gama Functions -- 3.4.1 Definitions -- 3.4.2 Properties of Beta and Gamma Functions -- 3.4.3 Relationship between Beta and Gamma functions -- Worked Out Examples -- Exercise 3.3 -- Additional Problems (From Previous Years VTU Exams) -- Objective Questions -- Unit-lV Vector Integration and Orthogonal Curvilinear Coordinates -- 4.1 Introduction -- 4.2 Vector Integration -- 4.2.1 Vector Line Integral -- Worked Out Examples -- Exercise 4.1 -- 4.3 Integral Theorem -- 4.3.1 Green's Theorem in a Plane -- 4.3.2 Surface integral and Volume integral -- 4.3.3 Stoke's Theorem -- 4.3.4 Gauss Divergence Theorem -- Worked Out Examples -- Exercise 4.2 -- 4.4 Orthogonal Curvilinear Coordinates -- 4.4.1 Definition -- 4.4.2 Unit Tangent and Unit Normal Vectors -- 4.4.3 The Differential Operators -- Worked Out Examples -- Exercise 4.3 -- 4.4.4. Divergence of a Vector -- Worked Out Examples -- Exercise 4.4 -- 4.4.5 Curl of a Vector -- Worked Out Examples -- Exercise 4.5 -- 4.4.6. Expression for Laplacian ∇2 ψ -- 4.4.7. Particular Coordinate System -- Worked Out Examples -- Exercise 4.6 -- Additional Problems -- Objective Questions -- Unit-V Differential Equations-I -- 5.1 Introduction -- 5.2 Linear Differential Equations of Second and Higher Order with Constant Coefficients -- 5.3 Solution of a Homogeneous Second Order Linear Differential Equation -- Worked Out Examples -- Exercise 5.1 -- 5.4 Inverse Differential Operator And Particular Integral -- 5.5 Special Forms of X -- Worked Out Examples -- Exercise 5.2 -- Exercise 5.3 -- Exercise 5.4 -- 5.6 Method of Undetermined Coefficients -- Worked Out Examples -- Exercise 5.5 -- 5.7 Solution of Simultaneous Differential Equations -- Worked Out Examples -- Exercise 5.6.

Additional Problems (From Previous Years VTU Exams.) -- Objective Questions -- Unit-Vl Differential Equations-II -- 6.1 Methods of Variation of Parameters -- Worked Out Examples -- Exercise 6.1 -- 6.2 Solution of Cauchy's Homogeneous Linear Equation And Lengendre's Linear Equation -- Worked Out Examples -- Exercise 6.2 -- 6.3 Solution of Initial and Boundary Value Problems -- Worked Out Examples -- Exercise 6.3 -- Additional Problems (From Previous Years VTU Exams.) -- Objective Questions -- Unit Vll Laplace Transforms -- 7.1 Introduction -- 7.2 Definition -- 7.3 Properties of Laplace Transforms -- 7.3.1 Laplace Transforms of Some Standard Functions -- Worked Out Examples -- Exercise 7.1 -- 7.3.2 Laplace Transforms of the form eat f (t) -- Worked Out Examples -- Exercise 7.2 -- 7.3.3 Laplace Transforms of the form t n f (t) Where n is a Positive Integer -- 7.3.4 Laplace Transforms of f(t)/t -- Worked Out Examples -- Exercise 7.3 -- 7.4 Laplace Transforms of Periodic Functions -- Worked Out Examples -- Exercise 7.3 -- 7.5 Laplace Transforms of Unit Step Function and Unit impulse Function -- Unit Step Function (Heaviside function) -- 7.5.1 Properties Associated with the Unit Step Function -- 7.5.2 Laplace Transform of the Unit Impulse Function -- Exercise 7.4 -- Additional Problems (From Previous Years VTU Exams.) -- Objective Questions -- Unit Vlll Inverse Laplace Transforms -- 8.1 Introduction -- 8.2 Inverse Laplace Transforms of Some Standard Functions -- Worked Out Examples -- 8.3 Inverse Laplace Transforms Using Partial Fractions -- Exercise 8.1 -- 8.4 Inverse Laplace Transforms of the Functions of the form F(s)/s -- Worked Out Example -- Exercise 8.2 -- 8.5 Convolution Theorem -- Worked out Examples -- Exercise 8.3 -- 8.6 Laplace Transforms of the Derivatives -- 8.7 Solution of Linear Differential Equations -- Worked Out Examples.

Solution of Simultaneous Differential Equations -- Exercise 8.4 -- 8.8 Applications of Laplace Transforms -- Worked Out Examples -- Exercise 8.5 -- Additional Problems (From Previous Years VTU Exams.) -- Objective Questions -- Model Question Paper-I -- Model Question Paper-Il.