Advanced Calculus

Description

Book description:

• Author's name: Dr. Ruhi Al-Khatib

• Number of pages: 764 pages

• The subject of the book: Advanced Calculus

Scientific books and works:

1. Vectors in two- and three-space

• Arithmetic expressions

• Multiplying a vector by a scalar

• Summation of two “resultant” vectors”

• Vector Length, Vector Magnitude, or Vector Scale“

• The distance between two vectors

• Standard multiplication

• The angle between two vectors

• Muscat Vector on another vector

• Directional multiplication

• Parametric equations of a line passing through two points

• The vector equation of a straight line

• The equation of the plane in triangular space

• The distance from a point to a known plane

2. Functions of Multiple Variables  

• Real functions in more than one real variable

• Endings

• Connection

3. Differentiation of real functions of multiple variables

• Fractional derivatives

• Higher-order partial derivatives

• Perfect differentiation and differentiability

• Derivation of the function

• The derivative of implicit functions

• Jacobean

• Higher-order exact differentials

4. Applications of partial derivatives

• Homogeneous functions

• Taylor expansion in two variables

• The maximum and minimum points of the function in two variables

• Conditional Maximum and Minimum Points

• Calculus under the integral sign

• Scaling, Spacing, and Rotation

• The equation of the normal vector, tangent plane, and normal plane

• Curvature in Binary Space

• Bending and Torsion in Triangular Space

5. Bilateral integration

• Binomial finite integral calculus

• Setting the limits of bilateral integration

• Change the order of binary integration

• Change of coordinates in a double integral

• Calculating the area of an area

• Calculating volume using binary integration

• Calculating the area of surfaces using binary integration

• Surface integration

6. Triple integrals

• Definition of Triple Integration

• Trigonometric Integral

• Calculating volumes using the triple integral

• Change of coordinates in the triple integral

• Gauss's Divergence Theorem

7. Linear integrals

• Linear integration in the plane

• Linear integral with respect to arc length

• Non-path-dependent linear integration

• Green's theory

• Linear Integration in Triangular Space

• Estoux's theory

8. Supplements

9. References

Also browse:

• A special collection of books Ruhi Al-Khatib

• Calculus (2)