Utkal University, Odisha, Mathematics Semester 5, Multivariate Calculus Syllabus

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Unit - 1 Functions Of Several Variables

Unit 1

Functions of several variables

1.1 Functions of several variables

1.2 Limit and continuity of functions of two variables

1.3 Partial differentiation

1.4 Total differentiability and differentiability

1.5 Sufficient condition for differentiability

1.6 Chain rule for one and two independent parameters

1.7 Directional derivatives

1.8 The gradient maximal and normal property of the gradient tangent planes

Unit - 2 Extrema Of Functions Of Two Variables

Unit 2

Extrema of functions of two variables

2.1 Extrema of functions of two variables

2.2 Method of Lagrange multipliers Constrained optimization problems

2.3 Definition of vector field divergence and curl

2.4 Double integration over rectangular region double integration over nonrectangular region

2.5 Double integrals in polar coordinates

Unit - 3 Triple Integrals

Unit 3

Triple integrals

3.1 Triple integrals

3.2 Triple integral over a parallelepiped and solid regions

3.3 Volume by triple integrals

3.4 Cylindrical and spherical coordinates

3.5 Change of variables in double integrals and Triple integrals

Unit - 4 Line Integrals

Unit 4

Line integrals

4.1 Line integrals

4.2 Applications of line integrals Mass and Work

4.3 Fundamental theorem for line integrals

4.4 Conservative vector fields independence of path

4.5 Greens theorem

4.6 Surface integrals

4.7 Integrals over parametrically defined surfaces

4.8 Stokes theorem

4.9 The Divergence theorem

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Other Subjects of Semester-5
Linear algebra
Linear programming
Probability and statistics
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