The purpose of this set of examples is to learn both Vector Analysis and SymPy. As starting skills you need basic knowledge of Jupyter, Python, SymPy and Matplotlib. An excellent resources of theory, examples and practice problems:

• Paul Dawkins: https://tutorial.math.lamar.edu/
• Youtube Mr.P Solver: '2nd Year Calculus, But in PYTHON'
• Youtube Dr. Trefor Bazett: Playlist Vector Calculus
• Youtube Dr. Bevin Maultsby: Playlist Multivariable Calculus

The problems come from the resources above and from the book 'Theory and problems of Vector Analysis', Schaum's: 1959.

You can find more vector analysis problems solved with Python in my other repository Hese49/CALCULUS-III-Lamar

1. Vector Basics VecAnal_1.ipynb:

1. Angle between two vectors
2. Perpendicularity
3. Projection of a vector $\vec{A}$ on the vector $\vec{B}$
4. Line through two given points
5. Area of the triangle
6. Volume of the parallelepiped
7. Equation of the plane
8. Work done in moving an object along a vector by a force
9. Rotating body, angular and linear velocity
10. Moment of a force

2. Parametric curve

• VecAnal_2a. Unit tangent of the curve
• VecAnal_2b. Tangent, principal normal, binormal, curvature and torsion.
• VecAnal_2c. TNB-FUNKTIO: Tangent, Normal, Binormal, Curvature, Radius of curvature, Torsion
• VecAnal_2d. MECHANICS: Tangential and normal components of acceleration
• VecAnal_2e. Parametric curve (trigonometric)
• VecAnal_2f. Unit tangent vector, unit normal vector, curvature, (matrix representation)
• VecAnal_2g. The angle between the velocity and acceleration

3. Tangent plane

• VecAnal_3a. Equation of a plane
• VecAnal_3b. Equation of a plane perpendicular to a given vector
• VecAnal_3c. Parametric surface, partial derivatives, normal to the surface, TP-equation
• VecAnal_3d. Parametric surface, partial derivatives, normal to the surface, TP-equation
• VecAnal_3e. Implicit form of surface equation, gradient, unit normal, TP-equation

4. Del operator

• VecAnal_4a. Gradient

1. Unit normal to the surface
2. Directional derivative
3. Max directional derivative
4. The angle between the surfaces
5. The distance from the origin to the plane
6. Plotting gradient field with NumPy

• VecAnal_4b. Divergence

1. Calculate divergence
2. Solenoidal vectorfield
3. Laplace's operator

• VecAnal_4c. Curl

1. Calculate curl
2. Irrotational vectorfield
3. Scalar potential of a conservative vector field

5. Vector integration

• VecAnal_5a. Single integrals
• VecAnal_5b. Double integrals
• VecAnal_5c. Triple integrals
• VecAnal_5d. Line integrals
• VecAnal_5e. Surface integrals
• VecAnal_5f. Stoke's theorem
• VecAnal_5g. Divergence theorem