Precalculus: Mathematical Modeling

Go to Course: https://www.coursera.org/learn/precalculus-mathematical-modelling

Introduction

### Course Review: Precalculus: Mathematical Modeling on Coursera In an era where data and mathematical information shape decisions across various sectors, the need for a strong foundational understanding of mathematical modeling cannot be overstated. Coursera’s course, **Precalculus: Mathematical Modeling**, stands out as an excellent choice for learners who wish to leverage mathematics as a tool for understanding and interpreting the world around them. Whether you are a novice planning to embark on a scientific career or someone who merely wants to enhance your analytical skills, this course is tailored for all. #### Course Overview The **Precalculus: Mathematical Modeling** course aims to equip students with essential precalculus concepts essential for further studies in science and calculus. It dives into a range of topics, focusing on functions, their properties, and their applications in data analysis. More than a mere academic endeavor, this course empowers students to model real-world scenarios using mathematics, ensuring they are well-prepared for future studies and careers. #### Syllabus Breakdown Let’s explore the syllabus, which is structured into four comprehensive modules: **Module 1: Linear Modeling** Data is an integral part of our daily lives, generated from countless activities, including smartphone usage and financial transactions. In this module, students learn how to collect, analyze, and visualize data. The focus on linear modeling helps students understand how to create and modify models based on real data, ensuring they grasp the significance of statistical validation. This foundational knowledge is crucial for anyone looking to interpret complex data sets and communicate findings effectively. The emphasis on common pitfalls encourages students to think critically and responsibly about their conclusions. **Module 2: Exponential Modeling** This module introduces students to exponential functions, a cornerstone of many natural phenomena such as population dynamics and pharmacokinetics. Through realistic examples, students will not only understand how to work with this critical function but also apply it to various scenarios, including financial calculations involving interest and present value. Understanding exponential growth and decay is vital for anyone venturing into biology, economics, or any field reliant on data trends. **Module 3: Modeling with Other Functions** While linear and exponential functions are prominent, this module broadens the learning experience by exploring polynomial, periodic, and power functions. By understanding the diverse capabilities of different functions, students will be better equipped to choose the right mathematical tool for their specific modeling needs. This knowledge is particularly advantageous for fields where complex behavior must be modeled accurately. **Module 4: Dimensional Analysis** Dimensional analysis is a practical skill that is often overlooked in mathematics courses. This module focuses on the relationships between physical quantities and their respective units, teaching students how to perform accurate conversions and comparisons. The real-world application of analyzing the strength of a hypothetical explosion through dimensional analysis makes the learning both practical and engaging. #### Personal Reflection and Recommendation Having walked through the course content, I can confidently recommend **Precalculus: Mathematical Modeling** for anyone interested in strengthening their mathematical skills and applying them to real-world problems. The clarity of the modules, combined with the focus on practical applications, sets this course apart. The engaging teaching methods, inclusive of visualizations and interactive problem-solving, make it an enjoyable learning experience. Whether aiming to enter a scientific field or simply wanting to enhance your analytical capabilities, this course provides the foundational skills necessary to excel in more advanced studies. In conclusion, if you are seeking to demystify the world of data and gain a robust mathematical foundation that will serve you in various disciplines, I wholeheartedly endorse Coursera’s **Precalculus: Mathematical Modeling** as an essential addition to your personal and professional development. Enroll today and start transforming data into meaningful insights!

Syllabus

Module 1: Linear Modeling

Data is all around us, Trillions of terabytes of data are generated and recorded daily by just using a smartphone, driving a car, or using a credit card. In this course, students examine how data is created, obtained, examined, and used to shape everyday life. To understand an analyze this data, researchers in diverse fields conjecture models based on their data. With more data, they modify and update the model accordingly. The model is then tested to validate results and conclusions. This module will help you to visualize large data sets, present different models for data, and statistics to measure how good the model is to the data. We will also focus on how to communicate the results of the models and common pitfalls to avoid overreaching or overstating your conclusions.

Perhaps the most important function of this course and your future courses in calculus, the exponential function is introduced to model many natural phenomena. For example, this function is used to measure population growth, the spread of a disease, and the elimination of drug from the body. Types of interest and present value calculations will require the understanding and use of the exponential functions. We will allow the exponential to have any positive base, but the natural exponential, that with e = 2.718.. will be our main object of study.

In this module, we will use other functions to model specific behavior, such as polynomial, periodic and power functions.

In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantities (such as length, mass, time, and electric charge) and units of measure (such as miles vs. kilometres, or pounds vs. kilograms) and tracking these dimensions as calculations or comparisons are performed. In this module, we will study dimensional analysis, or more specifically the factor-label method and apply it to measure the strength of an explosion.