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MathTrackX

Special Functions

Dr. David Butler

This course is part two of the MathTrackX XSeries Program which has been designed to provide you with a solid foundation in mathematical fundamentals and how they can be applied in the real world.

Guided by experts from the School of Mathematics and the Maths Learning Centre at the University of Adelaide, this course will continue the study of functions initiated in the course Polynomials, Functions and Graphs by moving into trigonometric functions, exponential functions, and logarithmic functions.

This course is part two of the MathTrackX XSeries Program which has been designed to provide you with a solid foundation in mathematical fundamentals and how they can be applied in the real world.

Trigonometric functions are extremely important in applications of mathematics to study situations involving periodic phenomena such as tidal flow. Exponential and logarithmic functions have many uses in applications of mathematics to biology, business and economics, physics and other areas.

Join us as we provide opportunities to develop your skills and confidence in applying mathematical functions.

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What's inside

Learning objectives

Properties and graphing of trigonometric functions including sine, cosine and tangent
Exponential and logarithmic functions

Application of trigonometric, exponential and logarithmic functions.

Properties and graphing of trigonometric functions including sine, cosine and tangent
Exponential and logarithmic functions
Application of trigonometric, exponential and logarithmic functions.

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Designed for learners who want to build a solid foundation in the fundamentals of mathematics

Taught by experts from the School of Mathematics and the Maths Learning Centre at the University of Adelaide

Covers important mathematical functions including trigonometric, exponential, and logarithmic functions

Provides opportunities to develop skills and confidence in applying mathematical functions

Relevant for learners in various fields such as biology, business, economics, and physics

May require prerequisites in mathematics

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Reviews summary

Foundational special functions with real-world relevance

According to students, MathTrackX: Special Functions is a largely positive experience, particularly praised for its clarity of explanations and the effectiveness of its real-world applications, which make complex concepts digestible and highly relevant. Many learners found it an excellent refresher or a solid foundation-builder for essential trigonometric, exponential, and logarithmic functions. The instructor's clear teaching style and helpful exercises are frequently highlighted. While a few noted concerns about occasional lecture audio quality or the need for more diverse quiz problems, the course is generally well-received for its structured approach and practical insights.

Overall good, with minor inconsistencies in older lecture audio/video.

"Occasionally the audio quality in a few older lectures was slightly inconsistent."

"My only suggestion for improvement would be to update some of the older video lectures, as their resolution and audio quality are a bit dated..."

"The structure is logical, and the video lectures are well-produced."

Helpful exercises, but some quizzes could offer more problem variety.

"I sometimes felt the quizzes could have offered more diverse problem types to fully test application."

"The exercises were helpful for practice."

"I sometimes struggled with the difficulty jump between some lecture examples and the quiz questions. More worked examples or hints for the harder problems would be very helpful."

Pacing can vary, fitting refreshers but challenging true beginners.

"I found this course to be a bit too basic and repetitive for my needs. I already have a decent grasp of these functions..."

"Extremely disappointing. The course assumes too much prior knowledge and moves too quickly through complex derivations... Not for true beginners."

"As someone returning to mathematics after a long break, I found the pace just right – challenging enough to keep me engaged but not overwhelming."

Excellent for building a strong foundation or as a comprehensive refresher.

"This course was exactly what I needed to prepare for a higher-level math course. It reviews essential concepts thoroughly and effectively."

"Phenomenal course for anyone looking to build a strong math foundation."

"I came in rusty on these topics and now feel very confident."

Exceptionally clear lectures with highly relevant real-world applications.

"The explanations were incredibly clear, and the examples, especially those related to real-world phenomena like tidal flow, truly helped solidify my understanding."

"The way the concepts were tied to real-world scenarios made them much easier to grasp."

"This course provided a great structured review and filled in some gaps in my understanding. I use these functions daily in my engineering work."

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 MathTrackX: Special Functions with these activities:

Review prerequisites: Polynomials

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Strengthen your understanding of polynomials, which will help you better grasp the concepts of trigonometric, exponential, and logarithmic functions.

Browse courses on Polynomials

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Review the definition and properties of polynomials.
Practice factoring polynomials.
Complete exercises on simplifying polynomial expressions.

Graphing trigonometric functions

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Improve your ability to graph trigonometric functions, which is essential for visualizing and understanding their behavior.

Browse courses on Trigonometric Functions

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Plot points on the unit circle.
Use the unit circle to graph sine and cosine functions.
Practice graphing tangent, cotangent, secant, and cosecant functions.

Solving exponential and logarithmic equations

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Enhance your problem-solving skills by practicing solving exponential and logarithmic equations, which are essential in various applications.

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Review the properties of exponential and logarithmic functions.
Practice solving simple exponential equations.
Solve logarithmic equations using the change of base formula.

Three other activities

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Create a visual representation of trigonometric identities

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Deepen your understanding of trigonometric identities by creating a visual representation, such as a diagram or infographic, that illustrates their relationships.

Browse courses on Trigonometric Identities

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Research and understand different trigonometric identities.
Choose a visual format that effectively conveys the relationships.
Create a visually appealing and informative representation.

Explore online tutorials on advanced trigonometric concepts

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Enhance your knowledge by seeking out and following advanced tutorials that cover in-depth concepts related to trigonometric functions.

Browse courses on Trigonometric Identities

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Identify reputable online platforms or resources for tutorials.
Choose tutorials that align with your learning goals and skill level.
Actively engage with the tutorials, taking notes and practicing the concepts.

Develop a mathematical model using exponential functions

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Apply your understanding of exponential functions by creating a mathematical model that simulates a real-world phenomenon, such as population growth or radioactive decay.

Browse courses on Exponential Functions

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Choose a phenomenon that can be modeled using an exponential function.
Research and gather data related to the phenomenon.
Develop a mathematical model using an exponential function that fits the data.

Career center

Learners who complete MathTrackX: Special Functions will develop knowledge and skills that may be useful to these careers:

Mathematician

Mathematicians use mathematical techniques to study a wide range of topics, from abstract algebra to statistics. They may work in academia, government, or industry. This course can help you develop the skills you need to succeed as a Mathematician, including the ability to analyze data, solve problems, and communicate your findings.

See salaries and explore the career path for Mathematician

Operations Research Analyst

Operations Research Analysts use mathematical and analytical techniques to solve complex problems in a variety of industries. They may work in healthcare, finance, or manufacturing. This course can help you develop the skills you need to succeed as an Operations Research Analyst, including the ability to model systems, analyze data, and make recommendations.

See salaries and explore the career path for Operations Research Analyst

Financial Analyst

Financial Analysts use mathematical and analytical techniques to evaluate and make recommendations on investments. They may work in banks, investment firms, or insurance companies. This course can help you develop the skills you need to succeed as a Financial Analyst, including the ability to analyze financial data, build models, and make recommendations.

See salaries and explore the career path for Financial Analyst

Data Analyst

Data Analysts use mathematical and analytical techniques to collect, clean, and analyze data. They may work in a variety of industries, including healthcare, retail, and finance. This course can help you develop the skills you need to succeed as a Data Analyst, including the ability to collect and clean data, analyze data, and communicate your findings.

See salaries and explore the career path for Data Analyst

Software Engineer

Software Engineers design, develop, and maintain software applications. They may work in a variety of industries, including technology, healthcare, and finance. This course can help you develop the skills you need to succeed as a Software Engineer, including the ability to solve problems, design and implement algorithms, and test and debug software.

See salaries and explore the career path for Software Engineer

Actuary

Actuaries use mathematical and statistical techniques to assess risk and uncertainty. They may work in insurance companies, pension funds, or consulting firms. This course can help you develop the skills you need to succeed as an Actuary, including the ability to analyze data, build models, and make recommendations.

See salaries and explore the career path for Actuary

Quantitative Analyst

Quantitative Analysts use mathematical and statistical techniques to analyze financial data. They may work in investment banks, hedge funds, or asset management firms. This course can help you develop the skills you need to succeed as a Quantitative Analyst, including the ability to analyze data, build models, and make recommendations.

See salaries and explore the career path for Quantitative Analyst

Market Researcher

Market Researchers use mathematical and statistical techniques to collect and analyze data about consumer behavior. They may work in a variety of industries, including marketing, advertising, and retail. This course can help you develop the skills you need to succeed as a Market Researcher, including the ability to design and conduct surveys, analyze data, and communicate your findings.

See salaries and explore the career path for Market Researcher

Economist

Economists use mathematical and statistical techniques to study the economy. They may work in academia, government, or industry. This course can help you develop the skills you need to succeed as an Economist, including the ability to analyze data, build models, and make recommendations.

See salaries and explore the career path for Economist

Statistician

Statisticians use mathematical and statistical techniques to collect, analyze, and interpret data. They may work in a variety of industries, including healthcare, government, and finance. This course can help you develop the skills you need to succeed as a Statistician, including the ability to design and conduct studies, analyze data, and communicate your findings.

See salaries and explore the career path for Statistician

Data Scientist

Data Scientists use mathematical and statistical techniques to collect, clean, and analyze data. They may work in a variety of industries, including healthcare, retail, and finance. This course can help you develop the skills you need to succeed as a Data Scientist, including the ability to collect and clean data, analyze data, and communicate your findings.

See salaries and explore the career path for Data Scientist

Business Analyst

Business Analysts use mathematical and analytical techniques to solve problems in business. They may work in a variety of industries, including healthcare, finance, and manufacturing. This course can help you develop the skills you need to succeed as a Business Analyst, including the ability to analyze data, solve problems, and communicate your findings.

See salaries and explore the career path for Business Analyst

Risk Manager

Risk Managers use mathematical and statistical techniques to assess risk and uncertainty. They may work in a variety of industries, including finance, insurance, and healthcare. This course can help you develop the skills you need to succeed as a Risk Manager, including the ability to analyze data, build models, and make recommendations.

See salaries and explore the career path for Risk Manager

Teacher

Teachers use mathematical and analytical techniques to teach students about math and other subjects. They may work in a variety of settings, including schools, colleges, and universities. This course can help you develop the skills you need to succeed as a Teacher, including the ability to explain complex concepts clearly and effectively.

See salaries and explore the career path for Teacher

Professor

Professors use mathematical and analytical techniques to teach students and conduct research. They may work in a variety of settings, including colleges and universities. This course can help you develop the skills you need to succeed as a Professor, including the ability to explain complex concepts clearly and effectively and to conduct research.

See salaries and explore the career path for Professor

Reading list

We've selected 11 books that we think will supplement your learning. Use these to develop background knowledge, enrich your coursework, and gain a deeper understanding of the topics covered in MathTrackX: Special Functions.

Exploring Mathematics

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A detailed overview of mathematical functions, this text covers trigonometric functions, exponential and logarithmic functions, and applications to real-world situations.

MathTrackX

Special Functions

What's inside

Learning objectives

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Save this course

Reviews summary

Foundational special functions with real-world relevance

Activities

Career center

Reading list

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