This course helps to build the foundational material to use mathematics as a tool to model, understand, and interpret the world around us. This is done through studying functions, their properties, and applications to data analysis. Concepts of precalculus provide the set of tools for the beginning student to begin their scientific career, preparing them for future science and calculus courses. This course is designed for all students, not just those interested in further mathematics courses. Students interested in the natural sciences, computer sciences, psychology, sociology, or similar will genuinely benefit from this introductory course, applying the skills learned to their discipline to analyze and interpret their subject material. Students will be presented with not only new ideas, but also new applications of an old subject. Real-life data, exercise sets, and regular assessments help to motivate and reinforce the content in this course, leading to learning and mastery.
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課程信息
Some familiarity with algebraic expressions and function basics at the high school level.
您將學到的內容有
Model data with both single and multivariable functions
Visualize and analyze data using different technologies.
Understand properties of different types of functions to apply them accordingly to model different situations.
Perform vector operations, such as addition, scalar multiplication, dot product, and cross product, to analyze geometry in space.
Some familiarity with algebraic expressions and function basics at the high school level.
提供方
约翰霍普金斯大学
The mission of The Johns Hopkins University is to educate its students and cultivate their capacity for life-long learning, to foster independent and original research, and to bring the benefits of discovery to the world.
授課大綱 - 您將從這門課程中學到什麼
Module 1: Basics and Common Functions
Functions help to study the relationship between two or more variables. They are the basic quantitative tool used to visualize, analyze, and interpret these relationships. Studying functions is the first step in developing analytics skills for mathematical modeling. In this module, we develop the concept of a function and review important algebraic operations on functions used later in this course. We will also study the important features, like domain, range, and end behavior of graphs.
Module 2: Equations of Lines, Quadratics, and More Functions
In this module, we will study two common types of functions: linear and quadratic. We will learn how to identify common features of their graphs, and see how they can be used to model real world situations, particularly those involving revenue and cost. We will also further explore function compositions, and learn how to find the inverse of a function.
Module 3: Exponential and Logarithmic Functions
In this module, we expand our catalog of functions to study two new functions that arise when modelling natural phenomena: the exponential and logarithmic functions. In the last module, we saw that one-to-one functions have inverses, which reverse the function process. For example, the function f(x) = x^3 has as its inverse the function g(x) = x^(1/3). We now want to expand this process to find inverses for exponential functions - those of the form f(x) = a^x, where a is a positive number not equal to one.
Module 4: Properties of Logarithms
Understanding the logarithm as an exponent allows for important algebraic properties of the logarithm. In this module, we will explore these properties and their uses as we apply logarithms to real world examples.
審閱
- 5 stars78.57%
- 4 stars14.28%
- 3 stars3.17%
- 2 stars0.79%
- 1 star3.17%
來自PRECALCULUS: RELATIONS AND FUNCTIONS的熱門評論
Great course if you have forgtten the basic functions such as log starts here !!!s
It will be nice to see more applications of the the material.
Great course explained everything concisely. However the sample problems and test of week 1 had certain sums which were not covered in the video
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t course!The explanations are really very clear and the exercises very useful! Loved the lecturer's style of teaching
關於 Precalculus through Data and Modelling 專項課程
This specialization helps to build the foundational material to use mathematics as a tool to model, understand, and interpret the world around us. This is done through studying functions, their properties, and applications to data analysis. Concepts of precalculus provide the set of tools for the learner to begin their scientific career, preparing them for future science and calculus courses.
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