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向量微积分I(4学分)

建议准备:m 253．

向理工科学生介绍向量演算的概念。包括向量和向量函数、参数曲线、多元函数、偏导数、梯度、方向导数和优化问题。使用绘图技术。

向量微积分I

https://catalog.cocc.edu/course-outlines/mth-254/

成绩单标题向量微积分I学分4评分模式标准书信评分总接触时数60课程时数30实验时数30推荐准备MTH 253。向理工科学生介绍向量演算的概念。包括向量和向量函数、参数曲线、多元函数、偏导数、梯度、方向导数和优化问题。使用绘图技术。课程学习成果在二维和三维中分析向量和向量的组合，用向量运算进行几何和代数运算。2.用图形和分析的方法对直线、平面、圆柱和二次曲面进行分类。3.用微积分技术分析向量值函数。 4. Categorize functions of several variables. 5. Analyze multivariable functions with partial derivatives. Content outline Vectors, and vector operations of addition, subtraction, scalar multiplication, dot-and-cross products, algebraically, and geometrically in two- and three-dimensional space Equations and graphs of lines, planes, cylinders, and quadric surfaces in three-dimensional space Vector-valued functions in one variable and space curves Derivatives and integrals of vector-valued functions to find, with respect to the space curve: Tangent and normal vectors Arc-length Curvature Motion in space: position, velocity and acceleration Differentiate functions of several variables by partial differentiation Find and apply directional derivatives and the gradient of a function of two or three variables Use partial derivatives to find tangent planes, normal lines, and extrema of functions of two variables Use Lagrange multipliers to solve optimization problems Required materials This class requires a textbook and access to graphing technology. General education/Related instruction lists Mathematics

数学

https://catalog.cocc.edu/programs/mathematics/

学习数学可以培养分析和量化的能力，这在当今数据驱动的经济中是很有价值的。数学专业的学士学位是进入研究生院(如法学院、医学院、教育学院或商学院)以及在工业、政府、研究和商业中直接就业的很好的准备。此外，数学课程是许多相关科学、技术、工程和数学(STEM)项目的基础。

数学-艺术助理俄勒冈转学(AAOT)

https://catalog.cocc.edu/programs/mathematics/mathematics-aaot/

学习数学可以培养分析和量化的能力，这在当今数据驱动的经济中是很有价值的。俄勒冈州艺术学院转校的重点是数学，包括数学专业通常要求的课程，并满足俄勒冈州所有公立大学的低级别通识教育要求。

向量微积分2

https://catalog.cocc.edu/course-outlines/mth-255/

成绩单标题向量微积分II学分4评分模式标准信件评分总接触时数60讲座时数30实验时数30推荐准备MTH 254。课程描述为理工科学生继续学习矢量分析。包括二重积分和三重积分，应用于面积、体积和质心;介绍向量分析，包括散度，旋度，线积分和功，曲面积分;保守场和格林和斯托克斯定理。使用绘图技术。课程学习成果分析二重积分和三重积分在矩形，极坐标，圆柱，和球坐标系下的各种应用。2.分析各种向量场。 3. Evaluate line integrals in scalar and vector fields. 4. Analyze parametric surfaces in scalar and vector fields. Content outline Evaluate double and triple integrals in rectangular, polar, cylindrical, spherical coordinate systems, and by using the Jacobian Applications of double and triple integrals for finding volume, surface area, mass and center of mass Vector fields: curl, gradient, divergence, and determine if the field is conservative or not Line integrals in scalar and vector fields The fundamental theorem of line integrals Parametric surfaces: in a scalar field, in a vector field, and area Green’s and Stokes’ theorems Required materials This class requires a textbook and access to graphing technology. General education/Related instruction lists Mathematics