**Content :-**

**Unit-1 Differential Calculus**

1.1.Introduction.

1.2.Radius of Curvature.

1.3.Some Fundamental Theorem.

**Unit-2 Differential Calculus**

2.1.Indeterminate Form 0/0.

2.2.Taylor's Theorem For Functions Of Two Variables.

2.3.Maxima and Minima of Functions of Two Variables.

2.4.Lagrange's Method of Undetermined Multipliers.

**Unit-3 Integral Calculus**

3.1 Introduction.

3.2 Multiple Integrals .

3.3 Double Integrals.

3.4 Beta and Gamma Functions.

**Unit-4 Vector Integration and Orthogonal Curvilinear Coordinates**

4.1 Introduction .

4.2 Vector Integration.

4.3 Integral Theorem.

4.4 Orthogonal Curvilinear Coordinates.

**Unit-5 Differential Equations**

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.

5.4 Inverse Differential Operator and Particular Integral.

5.5 Special Forms of x.

5.6 Method of Undetermined Coefficients.

5.7 Solution of Simultaneous Differential equations.

**Unit-6 Differential Equations**

6.1 Method of Variation of Parameters.

6.2 Solution of Cauchy’s Homogeneous Linear Equation and Lengendre’s.

6.3 Solution of Initial and Boundary Value Problems.

**Unit-7 Laplace Transforms**

7.1 Introduction.

7.2 Definition .

7.3 Properties of Laplace Transforms.

7.4 Laplace Transforms of Periodic Functions.

7.5 Laplace Transforms of Unit Step Function and Unit Impulse Function.

Unit-8 Inverse Laplace Transforms

8.1 Introduction.

8.2 Inverse Laplace Transforms of Some Standard Functions.

8.3 Inverse Laplace Transforms using Partial Fractions.

8.4 Inverse Laplace Transforms of the Functions of the Form F(s)/s.

8.5 Convolution Theorem.

8.6 Laplace Transforms of the Derivatives.

8.7 Solution of Linear Differential Equations.

8.8 Applications of Laplace Transforms.

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