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Unit - 1 CALCULUS

Unit 1Calculus

1.1 Evolutes and Involutes

1.2 Evaluation of Definite and Improper Integrals

1.3 Beta and Gamma Functions and Their Properties

1.4 Applications of Definite Integrals to Evaluate Surface Areas and Volumes of Revolutions

1.5 Rolle’s Theorem

1.6 Mean Value Theorems

1.7 Taylor’s and Maclaurin Theorems with Remainders

1.8 Indeterminate Forms and Lhospitals Rule

1.9 Maxima and Minima

Unit - 2 SEQUENCES AND SERIES

Unit 2Sequence and series

2.1 Convergence of Sequence and Series

2.2 Tests for Convergence Power Series

2.3 Taylors Series

2.5 Trigonometric and Logarithmic Functions

2.6 Fourier Series Half Range Sine and Cosine Series

2.7 Parseval’s Theorem

Unit - 3 MULTIVARIABLE CALCULUS: DIFFERENTIATION

Unit 3Multivariable calculus Differentiation

3.1 Limit Continuity and Partial Derivatives

3.2 Directional Derivatives

3.3 Total Derivative

3.4 Tangent Plane and Normal Line

3.5 Maxima Minima and Saddle Points

3.6 Method of Lagrange Multipliers

3.7 Gradient Curl and Divergence

Unit - 4 MULTIVARIABLE CALCULUS: INTEGRATION

Unit 4Multivariable calculus Integration

4.1 Multiple Integration Double and Triple Integrals Cartesian and Polar

4.2 Change of Order of Integration in Double Integrals

4.3 Change of Variables Cartesian to Polar

4.5 Center of Mass and Gravity Constant and Variable Densities

4.6 Theorems of Green Gauss and Stokes

4.7 Orthogonal Curvilinear Coordinates

4.8 Simple Applications Involving Cubes Sphere and Rectangular Parallelepipeds

Unit - 5 FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS

Unit 5First order ordinary differential equations

5.1 Exact Linear and Bernoulli’s Equations

5.2 Euler’s Equations

5.3 Equations Not of First Degree Equations Solvable For P Equations Solvable For Y Equations Solvable for X And Clairaut’s Type

Unit - 6 ORDINARY DIFFERENTIAL EQUATIONS OF HIGHER ORDER

Unit 6Ordinary differential equations of higher order

6.1 Second Order Linear Differential Equations with Variable Coefficients

6.2 Method of Variation of Parameters

6.3 CauchyEuler Equation

6.4 Power Series Solutions

6.5 Legendre Polynomials

6.6 Bessel Functions of The First Kind and Their Properties

Unit - 7 ORDINARY DIFFERENTIAL EQUATIONS OF HIGHER ORDER

Unit 7Partial differential equations First Order

7.1 First Order Partial Differential Equations

7.2 Solutions of First Order Linear and NonLinear PDES

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