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所在平台: Udemy |
课程主页: https://www.udemy.com/course/math-150-precalculus/
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课程名称：数学150（预备微积分） 课程概述： 本课程旨在帮助学生理解并掌握一系列数学概念，特别是与函数和方程相关的内容。以下是各章节的重点： 第2章：函数 在这一章节中，将介绍函数的基本概念，重点包括函数的定义、定义域及其组合。函数是输入与输出之间的关系，每个输入对应一个唯一输出。定义域指的是所有可能输入值的集合，而函数的组合则是将两个或多个函数结合在一起，其中一个函数的输出成为另一个函数的输入。 第3章：线性函数及应用 本章讨论线性函数及其实际应用。线性方程的形式为y=mx+b，其中m为斜率，b为y截距。线性函数在现实生活中广泛应用，包括商业和物理问题。此外，本章还涉及二次函数（形式为y=ax²+bx+c）和线性方程组的解法，以及非线性系统及其应用。 第4章：指数与对数函数 这一章节集中于指数函数和对数函数。指数函数展示了随时间增长或衰减的现象，在生物学和金融领域中至关重要。对数函数是指数函数的反函数，用于求解指数方程。同时，本章还将探讨如何解答指数和对数方程。 第5章：复利与现值 本章讨论了在金融领域中重要的概念，包括复利和现值。复利是指在初始本金及其上产生的利息上再计利息的过程，而现值则帮助确定未来某一金额的当前价值。 本课程将为学生打下坚实的数学基础，为后续更高级的数学学习做好准备。
Content Ch 2 Functions, Domain, Composition of functionsCH 3.1 LinesCH 3.2 Applications of Linear Functions CH 3.3 Quadratic FunctionsCH 3.4. systems of linear equationsCH 3.5 Non-Linear SystemsCH 3.6 Applications of Non-Linear SystemsCH 4.1 Exponential and Logarithmic FunctionsCH 4.2 Logarithmic Functions CH 4.3 Exponential Equations CH 4.4. Logarithmic EquationsCh5 Compounded Interest & Present ValueChapter 2 introduces the concept of functions, focusing on their definitions, domains, and compositions. A function is a relation between inputs and outputs where each input has a unique output. The domain of a function refers to the set of all possible input values. Composition of functions involves combining two or more functions where the output of one function becomes the input of another.Chapter 3 covers linear functions and their applications. Lines are represented by equations of the form y=mx+by = mx + by=mx+b, where m is the slope and b is the y-intercept. Linear functions are widely used in real-world situations, as discussed in Applications of Linear Functions. The chapter also explores quadratic functions, which are represented by equations of the form y=ax2+bx+cy = ax^2 + bx + cy=ax2+bx+c, and systems of linear equations, which involve solving multiple equations simultaneously. Non-linear systems are also addressed, along with their real-life applications.Chapter 4 focuses on exponential and logarithmic functions. Exponential functions involve growth or decay over time and are essential in fields like biology and finance. Logarithmic functions are the inverses of exponential functions and are used to solve exponential equations. This chapter also explores solving both exponential and logarithmic equations.Chapter 5 discusses compounded interest and present value, critical concepts in finance. Compounded interest involves earning interest on both the initial principal and previously earned interest, while present value helps determine the current worth of a future sum of money.
