1. Students are able to find general terms and their sums in arithmetic sequences and geometric sequences, and are able to calculate Σ.
2. Students are able to perform basic vector calculations.
3. Students are able to show the components of planar and spatial vectors and perform basic calculations.
4. Students are able to find the inner product of plane and space vectors.
5. Students are able to find the equations of lines, planes, circles, and spheres in planes and spaces.
Outline:
Mathematics is a fundamental subject in technical colleges. In this class, students will learn the concepts of numerical sequences, their sums, and recurrence formulas. In addition, students learn the concept of vectors in the plane and in space, and master the basic calculations of vectors.
Style:
[Class time: 60 hours]
Notice:
1. Establish methods that allow you to concentrate in class and learn efficiently. Preparation and review are essential.
2. Studying for regular examinations is, of course, important, but do not neglect the normal quizzes and submissions.
3. Strictly adhere to submission deadlines for submitted materials such as assignments.
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Theme |
Goals |
| 1st Semester |
| 1st Quarter |
| 1st |
Sequences and general terms |
Understand the terms and notations of sequences, and be able to infer their regularity from the arrangement of numbers, and consider general terms in sequences.
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| 2nd |
arithmetic progression |
Understand the common difference, general term, etc. of arithmetic sequence, and be able to determine the general term of the sequence from the conditions.
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| 3rd |
sum of arithmetic progressions |
Able to find the sum of a sequence by using the formula for the sum of arithmetic sequences.
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| 4th |
geometric progression |
Understand the common ratio, general term, etc. of geometric sequence, and be able to determine the general term of the sequence from the conditions.
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| 5th |
sum of geometric progressions |
Able to find the sum of a sequence by using the formula for the sum of geometric sequences.
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| 6th |
Sum symbol Σ |
Understand the meaning and properties of the symbol Σ, and find the sum of sequences.
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| 7th |
summation calculation |
Able to obtain the sum of the first term to the n-th term by expressing the k-th term with the expression for k.
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| 8th |
recurrence formula |
Understand the meaning of recurrence formulas and obtain specific terms.
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| 2nd Quarter |
| 9th |
Midterm exam |
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| 10th |
Vectors on a plane |
Understand the concept of vectors, as well as the basic terms and symbols related to vectors.
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| 11th |
Operations on vectors |
Able to calculate sums, differences, and constant multiple of arrow vectors on a plane.
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| 12th |
Vector Parallelism and Vector Decomposition |
Able to represent a vector using unit vector of the same direction. Able to represent a vector represented by an arrow as the sum or difference of two vectors.
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| 13th |
Components of vectors |
Understand that a vector on the plane is represented as a pair of two real numbers, and be able to calculate magnitude, sum, difference, and real number multiples.
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| 14th |
Inner product of vectors (１) |
Able to calculate the inner product of vectors and find the angle between vectors.
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| 15th |
Exercises |
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| 16th |
Return of the final exam of the first semester |
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| 2nd Semester |
| 3rd Quarter |
| 1st |
Inner product of vectors (2) |
Able to handle vector magnitudes by replacing them with inner products.
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| 2nd |
Position vector |
Understand that the position of a point can be represented using a reference point and a vector.
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| 3rd |
Vectors and plane figures |
Able to represent internally dividing point and externally dividing pointpoint of a segment using position vectors.
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| 4th |
Straight line on a plane (1) |
Able to find the equation of a line on a plane.
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| 5th |
Straight line on a plane (2) |
Able to find the equation of a line from a passing point and a normal vector.
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| 6th |
Equation of a line in coordinates |
Able to use the formulas to find the equation of a line.
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| 7th |
Circles |
Able to find the equation of a circle.
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| 8th |
Midterm exam |
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| 4th Quarter |
| 9th |
Coordinates in space |
Understand coordinate space and able to find the coordinates of a point and the distance between two points.
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| 10th |
Space vectors |
Able to calculate magnitudes, sums, differences, and real multiples of vectors represented by their components.
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| 11th |
Inner product of space vectors |
Able to find the inner product of space vectors, and use parallel and perpendicular conditions.
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| 12th |
Vectors and spatial figures |
Understands the meaning of position vectors, and able to find internally dividing point and externally dividing pointpoint of a segment.
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| 13th |
Lines in space |
Able to find the equation of a line in space.
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| 14th |
Planes in space |
Able to find the equation of a plane in space.
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| 15th |
Sphere |
Able to find the equation of a sphere.
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| 16th |
Return of the final exam |
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