Calculus through Data & Modeling: Precalculus Review from Coursera

What's inside

Syllabus

Exponential and Logarithmic Functions

In this module, we will review some of the key concepts from Precalculus. Exponential and logarithmic functions arise often when modeling natural phenomena, and are important to Calculus. In applied settings, exponential functions model a relationship in which a constant change in the independent variable gives the same proportional change (i.e., percentage increase or decrease) in the dependent variable. This occurs widely in the natural and social sciences, as in a self-reproducing population, a fund accruing compound interest, or a growing body of manufacturing expertise. Thus, the exponential function also appears in a variety of contexts within physics, chemistry, engineering, mathematical biology, and economics.

Trigonometric Functions

Equally important are the trigonometric functions, some of the most well-known examples of periodic or cyclic functions. Common phenomena have an oscillatory, or periodic, behavior. This is observed through ocean waves, sound waves, or even the regular beating of your heart. All these phenomena can be modeled using equations based on the familiar sine and cosine functions. In this module, we will see how to apply and construct functions that permit us to model cyclic behavior.

Vectors in Space

In classical Euclidean geometry, vectors are an equivalence class of directed segments with the same magnitude (e.g., the length of the line segment (A, B)) and same direction (e.g., the direction from A to B). Vectors are used both in abstract sense as well as for applications, particularly in physics, Euclidean vectors are used to represent physical quantities that have both magnitude and direction, but are not located at a specific place, in contrast to scalars, which have no direction. For example, velocity, forces and acceleration are represented by vectors. In this module, we will study vectors specifically in the xy-plane and in "3D" space.

Equations of Lines and Planes

Continuing our study of multi-dimensional analytic geometry, vectors are now applied to create algebraic equations to describe common objects like lines and planes in space. This module will test your ability to visualize algebraic equations and to create movement and thus control of these objects in space by performing algebraic manipulations. This will create a solid foundation for our study of multivariable calculus on these higher dimensional objects.

Precalculus Review Final Exam

The assessment below will help to identify strengths as weaknesses in your foundational material in order to be successful in single and multivariable differentiable calculus. Use the assessment below as a guide as to where to follow up and seek out more resources and examples.

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Well-suited for novice learners seeking a strong foundation in mathematical functions

In-demand subject matter with applications across various disciplines

Prepares learners for advanced coursework in single and multivariable calculus

Leverages both theoretical and practical approaches to enhance understanding

Course materials include interactive elements like graphing calculators for hands-on learning

Taught by a qualified instructor with experience in the field

Reviews summary

Precalculus review for calculus through data & modeling

According to students, this intensive Precalculus Review course offers plenty of practice and serves as a great foundation for aspiring learners on how to process Data in Machine Learning and general concepts of Advanced Calculus by using common Mathematics. Learners say the course has great content, excellent lectures, and is well taught, but can be very difficult and challenging. Reviewers suggest taking Precalculus certification before attempting this one, and recommend completing the sample problems thoroughly.

Students get lots of practice.

"Great lecture and exercises"

"Good examples to demonstrate concepts."

"It provided excellent sample problems to understand the concepts, and it has an amazing professor. "

Concepts are explained clearly.

"Great way to refresh pre-calculus skills."

"A solid foundation for single and multivariable calculus courses."

"Excellent professor , excellent material , has helped me a lot to understand and revise some basics ."

The instructor is excellent.

"Great professor , excellent material"

"Instructor's lectures were concise and very clear."

"The lecture's quality is perfect"

Content is great.

"Great content."

"A super solid review of precalculus. Thank you!"

"Great content, great instructor, plenty of examples to practice throughout the course."

This course has a challenging difficulty level.

"very difficult for math rookies!"

"It was intensive and challenging."

"The last module turned out to be incredibly challenging for me."

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Calculus through Data & Modeling: Precalculus Review with these activities:

Watch video tutorials on the concepts of functions

Show steps

Watching video tutorials will help you understand the key concepts of functions and their applications.

Browse courses on Functions

Show steps

Find video tutorials on the concepts of functions
Watch the tutorials and take notes
Practice the concepts shown in the tutorials
Extend your learning by exploring additional resources

Review Precalculus concepts using online resources

Show steps

Establish a strong foundation by refreshing prior knowledge

Show steps

Identify areas of Precalculus needing review
Use websites like Khan Academy or Coursera to revisit core concepts
Solve practice problems or take quizzes

Review Precalculus Material

Show steps

Complete a review of high school Precalculus concepts to strengthen your foundational knowledge for this course.

Show steps

Review notes and materials from high school Precalculus courses.
Complete practice problems to test your understanding.
Seek support from a tutor or online forums if needed.

15 other activities

Expand to see all activities and additional details

Show all 18 activities

Review your notes and assignments from previous math courses

Show steps

Reviewing your previous knowledge will help you refresh your memory and identify areas where you need additional review.

Browse courses on Precalculus

Show steps

Gather your notes and assignments from previous math courses
Review the material, focusing on the topics covered in this course
Identify any areas where you need additional review

Create flashcards for key terms and formulas

Show steps

Enhance memory and recall through active learning

Show steps

Identify important terms, concepts, and formulas
Create physical or digital flashcards
Write the term or concept on one side and the definition or formula on the other
Review and quiz yourself regularly

Solve practice problems on equations of lines and planes

Show steps

Solving practice problems will help you develop your problem-solving skills and identify areas where you need additional practice.

Browse courses on Precalculus

Show steps

Find practice problems on equations of lines and planes
Solve the problems and check your answers
Identify any areas where you need additional practice

Join a study group to discuss the concepts of equations of lines and planes

Show steps

Discussing the concepts with peers will help you clarify your understanding and identify areas where you need further study.

Show steps

Find a study group or create your own
Meet regularly to discuss the concepts
Work together to solve problems and clarify concepts

Follow video tutorials on YouTube

Show steps

Supplement course materials with engaging video content

Show steps

Use search terms like '[topic name] tutorial' or '[skill name] tutorial'
Watch videos that provide clear explanations and examples
Take notes or pause the videos to practice
Explore playlists or channels for more comprehensive coverage

Utilize online graphing calculators

Show steps

Practice visualization and enhance problem-solving

Show steps

Access websites like Desmos or Wolfram Alpha
Input functions and equations
Graph results and analyze their properties
Use calculators to solve equations or perform calculations

Exponential and Logarithmic Practice Problems

Show steps

Engage in practice drills to reinforce your understanding of exponential and logarithmic functions and their applications in modeling.

Browse courses on Exponential and Logarithmic Functions

Show steps

Solve a set of practice problems on exponential and logarithmic equations.
Apply these functions to model real-world phenomena, such as population growth or decay.
Use graphing calculators or software to visualize and analyze these functions.

Practice graphing exponential, logarithmic, and trigonometric functions

Show steps

Practice graphing these functions will help you visualize their behavior and understand their properties.

Browse courses on Exponential Functions

Show steps

Find the domain and range of the functions
Plot points on the graph
Connect the points with a smooth curve

Trigonometric Function Applications

Show steps

Seek out tutorials to enhance your understanding of the applications of trigonometric functions in modeling periodic phenomena.

Browse courses on Trigonometric Functions

Show steps

Identify different types of periodic phenomena and their corresponding trigonometric models.
Learn to construct and analyze trigonometric functions to represent these phenomena.
Utilize graphing calculators or software to visualize and fit trigonometric functions to data.

Solve practice calculus problems from Khan Academy

Show steps

Strengthen understanding of calculus concepts through guided practice

Show steps

Create a free Khan Academy account
Access the Calculus section and choose the appropriate grade level or topics
Work through practice problems and watch video explanations
Attempt quizzes and review performance

Watch video tutorials on vector operations

Show steps

Watching video tutorials will help you understand the concepts of vector operations and how to perform them.

Show steps

Find video tutorials on vector operations
Watch the tutorials and take notes
Practice the vector operations shown in the tutorials

Visualizing Vectors in Space

Show steps

Create visual representations of vectors in 2D and 3D space to deepen your comprehension of their geometry and manipulation.

Browse courses on Vectors

Show steps

Use graphing software or online tools to plot vectors and visualize their directions and magnitudes.
Create animations or diagrams to demonstrate vector operations, such as addition, subtraction, and scalar multiplication.
Apply geometric principles to solve problems involving vectors in space.

Develop a cheat sheet or reference guide for the formulas and identities covered in the course

Show steps

Creating a cheat sheet or reference guide will help you organize and retain information throughout the course.

Browse courses on Functions

Show steps

Identify the key formulas and identities covered in the course
Organize and present the information in a clear and concise format
Use the cheat sheet or reference guide as a study tool throughout the course

Equations of Lines and Planes Project

Show steps

Embark on a project that involves applying your knowledge of equations of lines and planes to real-world scenarios, fostering a deeper understanding of their use in geometry and applications.

Show steps

Identify a real-world problem that can be modeled using equations of lines or planes.
Create mathematical models using equations of lines and planes to represent the problem.
Analyze and interpret the results of your models to solve the problem.
Present your findings and justify your solutions.

Create a poster or presentation on the applications of exponential and logarithmic functions

Show steps

Creating a poster or presentation will help you explore the applications of these functions and develop your communication skills.

Browse courses on Exponential Functions

Show steps

Choose a topic related to the applications of exponential and logarithmic functions
Research the topic and gather information
Create a poster or presentation that visually represents your findings
Present your findings to the class or a small group

Career center

Learners who complete Calculus through Data & Modeling: Precalculus Review will develop knowledge and skills that may be useful to these careers:

Data Analyst

Data Analysts collect, clean, and analyze large datasets to extract meaningful insights. They use their findings to help businesses make informed decisions. This course can help Data Analysts develop the skills they need to succeed, such as data modeling, data analysis, and data visualization. The course's emphasis on using functions to model and analyze data will be particularly helpful for Data Analysts, as they often need to use functions to represent complex relationships in data.

See salaries and explore the career path for Data Analyst

Statistician

Statisticians collect, analyze, and interpret data to help businesses and organizations make informed decisions. They use statistical methods to identify trends, patterns, and relationships in data. This course can help Statisticians develop the skills they need to succeed, such as data modeling, data analysis, and data visualization. The course's emphasis on using functions to model and analyze data will be particularly helpful for Statisticians, as they often need to use functions to represent complex relationships in data.

See salaries and explore the career path for Statistician

Financial Analyst

Financial Analysts evaluate the financial performance of companies and make recommendations to investors. They use financial data to forecast future performance and make investment decisions. This course can help Financial Analysts develop the skills they need to succeed, such as data modeling, data analysis, and data visualization. The course's emphasis on using functions to model and analyze data will be particularly helpful for Financial Analysts, as they often need to use functions to represent complex relationships in financial data.

See salaries and explore the career path for Financial Analyst

Operations Research Analyst

Operations Research Analysts use mathematical and analytical methods to improve the efficiency and effectiveness of organizations. They work in a variety of industries, including manufacturing, logistics, and healthcare. This course can help Operations Research Analysts develop the skills they need to succeed, such as data modeling, data analysis, and data visualization. The course's emphasis on using functions to model and analyze data will be particularly helpful for Operations Research Analysts, as they often need to use functions to represent complex relationships in operations.

See salaries and explore the career path for Operations Research Analyst

Actuary

Actuaries use mathematical and statistical methods to assess risk and uncertainty. They work in a variety of industries, including insurance, finance, and healthcare. This course can help Actuaries develop the skills they need to succeed, such as data modeling, data analysis, and data visualization. The course's emphasis on using functions to model and analyze data will be particularly helpful for Actuaries, as they often need to use functions to represent complex relationships in risk and uncertainty.

See salaries and explore the career path for Actuary

Data Scientist

Data Scientists use data and analysis to solve complex problems. They work in a variety of industries, including technology, finance, and healthcare. This course can help Data Scientists develop the skills they need to succeed, such as data modeling, data analysis, and data visualization. The course's emphasis on using functions to model and analyze data will be particularly helpful for Data Scientists, as they often need to use functions to represent complex relationships in data.

See salaries and explore the career path for Data Scientist

Business Analyst

Business Analysts use data and analysis to help businesses make informed decisions. They work in a variety of industries, including consulting, finance, and healthcare. This course can help Business Analysts develop the skills they need to succeed, such as data modeling, data analysis, and data visualization. The course's emphasis on using functions to model and analyze data will be particularly helpful for Business Analysts, as they often need to use functions to represent complex relationships in business data.

See salaries and explore the career path for Business Analyst

Market Researcher

Market Researchers study consumer behavior and trends to help businesses develop and market their products and services. They use a variety of methods to collect and analyze data, including surveys, interviews, and focus groups. This course can help Market Researchers develop the skills they need to succeed, such as data modeling, data analysis, and data visualization. The course's emphasis on using functions to model and analyze data will be particularly helpful for Market Researchers, as they often need to use functions to represent complex relationships in consumer behavior.

See salaries and explore the career path for Market Researcher

Computer Scientist

Computer Scientists conduct research on the theory and practice of computing. They work in a variety of industries, including technology, finance, and healthcare. This course may be useful for Computer Scientists who want to develop a deeper understanding of the mathematical foundations of computer science. The course's emphasis on using functions to model and analyze data will be particularly helpful for Computer Scientists who want to develop new algorithms and data structures.

See salaries and explore the career path for Computer Scientist

Software Engineer

Software Engineers design, develop, and maintain software applications. They work in a variety of industries, including technology, finance, and healthcare. This course may be useful for Software Engineers who want to develop a deeper understanding of the mathematical foundations of computer science. The course's emphasis on using functions to model and analyze data will be particularly helpful for Software Engineers who want to develop software applications that use data.

See salaries and explore the career path for Software Engineer

Physicist

Physicists study the laws of nature and the universe. They work in a variety of industries, including academia, government, and industry. This course may be useful for Physicists who want to develop a deeper understanding of the mathematical foundations of physics. The course's emphasis on using functions to model and analyze data will be particularly helpful for Physicists who want to develop new theories and models of the universe.

See salaries and explore the career path for Physicist

Chemist

Chemists study the composition, structure, and properties of matter. They work in a variety of industries, including academia, government, and industry. This course may be useful for Chemists who want to develop a deeper understanding of the mathematical foundations of chemistry. The course's emphasis on using functions to model and analyze data will be particularly helpful for Chemists who want to develop new theories and models of chemical reactions.

See salaries and explore the career path for Chemist

Geologist

Geologists study the structure and composition of the Earth. They work in a variety of industries, including academia, government, and industry. This course may be useful for Geologists who want to develop a deeper understanding of the mathematical foundations of geology. The course's emphasis on using functions to model and analyze data will be particularly helpful for Geologists who want to develop new theories and models of the Earth's structure and composition.

See salaries and explore the career path for Geologist

Engineer

Engineers design, develop, and maintain infrastructure and products. They work in a variety of industries, including construction, manufacturing, and transportation. This course may be useful for Engineers who want to develop a deeper understanding of the mathematical foundations of engineering. The course's emphasis on using functions to model and analyze data will be particularly helpful for Engineers who want to design and develop new infrastructure and products.

See salaries and explore the career path for Engineer

Biologist

Biologists study the structure, function, and development of living organisms. They work in a variety of industries, including academia, government, and industry. This course may be useful for Biologists who want to develop a deeper understanding of the mathematical foundations of biology. The course's emphasis on using functions to model and analyze data will be particularly helpful for Biologists who want to develop new theories and models of biological systems.

See salaries and explore the career path for Biologist