预微积分概论:一种创造性和连通性的方法

Discovery Precalculus: A Creative and Connected Approach

Strengthen your critical thinking skills in this inquiry-based Pre-calculus course.

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德州大学奥斯汀分校
edX
  • 完成时间大约为 15
  • 初级
  • 英语
注:因开课平台的各种因素变化,以上开课日期仅供参考

你将学到什么

How to make conjectures, construct logical arguments, and justify your reasoning

The concept of function in mathematics, function characteristics and properties, and rate of change of functions

Modeling of common relations and functions such as linear, power, exponential, and logarithmic functions using statistical regression and matrix methods

An exploration of algebra and geometry, and the connections between the two in analytic geometry

Properties and applications of exponential and logarithmic functions including exponential growth and decay and The Logistic Function

The development of the trigonometric functions and identities along with applications of trigonometry

Limits and rate of change of functions as a precursor to Calculus

Other Coordinates Systems – an investigation of parametrization of the plane and the polar coordinate system along with exploration and use of vectors

Sequences and Series including The Method of Induction

Basic probability and combinatorics used in an investigation and development of the Binomial Theorem and its connections to Pascal’s Triangle

课程概况

In this interactive pre-Calculus course, you will deepen and extend your knowledge of functions, graphs, and equations from high school algebra and geometry courses so you can successfully work with the concepts in a rigorous university-level calculus course. This course is designed to engage learners in the “doing” of mathematics, emphasizing conceptual understanding of mathematical definitions and student development of logical arguments in support of solutions. The course places major emphasis on why the mathematics topics covered work within the discipline, as opposed to simply the mechanics of the mathematics.

课程大纲

The course is organized around the following seven units:

Functions, Rates, and Patterns
Algebra and Geometry
Exponential and Logarithmic Functions
Trigonometry
Limits and Rate of Change of Functions
Exploring Other Coordinate Systems
Sequences and Series

预备知识

A mastery of mathematics up through the Algebra II or College Algebra level. 

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