MI1026 Calculus II
MI1026 Calculus II
MI1026 Calculus II
MI1026 Calculus II
This is the second course in calculus. It covers basic notions of multiple integrals: double integrals,
double integrals in polar coordinates, triple integrals, triple integrals in cylindrical and spherical
coordinates, line integrals, surface integrals, with variety applications in vector field studies, in mechanics,
in electrics, in physics, ...
8. Description
The definite integral and applications to area, volume, work, differential equations, etc. Sequences and
series, vectors and analytic geometry in 2 and 3-space, polar coordinates, and parametric equations.
9. Student Duties
Class attendance: ≥ 80%
Homework:
Lab work:
...
10. Assessment
Mid-term grade: 0.4 (40%)
- Home exercise grading
- Project
- Lab work and reports
- Mid-tem test
Final exam: 0.6 (60%)
11. Course Materials
Textbook: James Stewart, Calculus, fourth edition, Brooks/Cole Publishing Company
12. Course Topics
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Calculus II
Course Developer: Prof. Dr. Nguyen Van Ho
Chapter 1: Vectors and the Geometry of Space
1. Vectors
Definitions and properties
The dot product
The cross product.
2. Equations of lines and planes.
Equations of lines.
Equations of planes.
3. Cylinder and quadric surfaces
Cylinder
Quadric surfaces
4. Cylindrical and spherical coordinates
Cylindrical coordinates
Spherical coordinates
Chapter 2: Vector Functions
1. Vector functions
2. Space curves
3. Derivatives and Integrals of vector functions
Derivatives.
Integrals
3. Arc Length and Curvature.
Arc Length.
Curvature.
The normal and binormal vectors.
4. Motion in space.
Velocity.
Acceleration
Curvature
1. Vector fields.
2. Line integrals.
Line integrals in plane.
Line integrals in space.
3. Line integrals of vector fields.
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