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Math Fundamentals

Integrals

Antonio José Guirao Sánchez

This course is conceived as a review of the basic concepts of differential calculus, necessary for the first courses of those university studies where mathematics is taught. Our objective is to provide a basic course on functions and derivatives, including their applications.

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What's inside

Learning objectives

The concept of primitive, its properties and the concept of immediate primitive.
Pseudo-immediate primitives.
Primitives of arcotangent type.

Primitives of rational functions.
The definite integral and area calculus.
Change of variable and integration by parts.

The concept of primitive, its properties and the concept of immediate primitive.
Pseudo-immediate primitives.
Primitives of arcotangent type.
Primitives of rational functions.
The definite integral and area calculus.
Change of variable and integration by parts.

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In-depth analysis of the fundamental ideas of differential calculus

Suitable for university students majoring in mathematics or related fields

Covers important concepts like derivatives, primitives, and integration

Provides a strong foundation for further studies in mathematics

Taught by instructors with expertise in the subject matter

Recommended for those seeking to enhance their mathematical skills

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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 Math Fundamentals: Integrals with these activities:

Organize Course Notes and Resources

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Stay organized and ensure you have easy access to the materials you need for the course.

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Create a dedicated folder for the course.
File your lecture notes, assignments, and other resources in an organized manner.

Review High School Algebra and Trigonometry

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Strengthen your foundation in algebra and trigonometry, which are essential prerequisites for calculus.

Browse courses on Algebra

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Review the concepts of functions, equations, and inequalities.
Practice solving trigonometric equations and identities.

Form a Study Group

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Collaborate with peers to discuss concepts, work on problems, and provide support.

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Find classmates who are interested in forming a study group.
Establish regular meeting times and a study schedule.

Four other activities

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Explore Khan Academy's Calculus Tutorials

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Supplement your understanding with interactive tutorials and practice exercises.

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Visit the Khan Academy Calculus section.
Work through the tutorials on derivatives and integrals.

Review Apostol's Calculus, Volume I (2nd Edition)

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Familiarize yourself with the foundational concepts of calculus, such as limits, derivatives, and integrals, which will be essential for this course.

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Read through the first three chapters of the book.
Work through the practice problems at the end of each chapter.

Practice Derivative Problems

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Reinforce your understanding of derivatives through practice problems.

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Find the derivative of the following functions:
f(x) = x^2 + 2x - 3
g(x) = sin(x) + cos(x)

Create a Mind Map of Integral Concepts

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Organize your understanding of integral concepts visually to strengthen your comprehension.

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Identify the main concepts related to integrals.
Create a visual representation of these concepts, connecting them with branches and sub-branches.

Career center

Learners who complete Math Fundamentals: Integrals will develop knowledge and skills that may be useful to these careers:

Mathematician

Mathematicians are experts in the field of mathematics, and they are able to apply mathematical techniques to solve problems and create new knowledge. This course provides core concepts of differential calculus, which is the type of mathematics that underpins much of modern science, including integral calculus. This course could be useful for someone looking to understand this core field of mathematics.

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Statistician

Statisticians collect, analyze, interpret, and present data, which can help organizations make informed decisions. This course provides a foundation in the type of mathematics that is needed in this field, particularly in differential calculus. This course may be useful for someone who wants to begin a career as a statistician.

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Quantitative Analyst

Quantitative Analysts use mathematical and statistical techniques to analyze financial data, which can help investment firms make informed decisions. This course in Math Fundamentals: Integrals provides a basis for understanding the mathematics that is needed in this field, particularly in differential calculus. This course may be useful for someone who wants to begin a career as a Quantitative Analyst.

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Economist

Economists study how societies use resources to produce goods and services, and how individuals make decisions in the face of scarcity. This course in Math Fundamentals: Integrals can provide a foundation in the mathematics that is needed in this field, particularly in differential calculus. This course may be useful for someone who wants to begin a career as an Economist.

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Financial Risk Manager

Financial Risk Managers identify and assess financial risks, and develop strategies to mitigate those risks. This course in Math Fundamentals: Integrals can provide a foundation in the mathematics that is needed in this field, particularly in differential calculus. This course may be useful for someone who wants to begin a career as a Financial Risk Manager, but it should be noted that this role typically requires an advanced degree.

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Data Scientist

Data Scientists use scientific methods, processes, algorithms, and systems to extract knowledge and insights from data. This course in Math Fundamentals: Integrals can provide a foundation in the mathematics that is needed in this field, particularly calculus. This course may be useful for someone who wants to begin a career as a Data Scientist.

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Actuary

Actuaries use mathematical and statistical methods to assess risk and uncertainty, which can help insurance companies, pension funds, and other organizations make informed decisions. This course in Math Fundamentals: Integrals provides a foundation in the type of mathematics that is needed in this field, particularly in differential calculus. This course may be useful for someone who wants to begin a career as an actuary, although it may not be essential knowledge for the role.

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Investment Analyst

Investment Analysts study and evaluate businesses, industries, and economies to make recommendations to investors. This course, while not directly related to finance, can provide some of the core mathematics for understanding the markets and underlying factors that influence investment decisions. This course may be useful for someone who wants to begin a career as an Investment Analyst, but it should be noted that this role typically requires an advanced degree.

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Financial Analyst

Financial Analysts examine financial data and other information to identify investment opportunities, which can help maximize returns for their clients. The knowledge of integral calculus from this course may be useful for someone who wants to begin a career as a Financial Analyst, because it can help someone to understand the underlying mathematics of their field.

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Business Analyst

Business Analysts use their knowledge of business and technology to analyze business processes and make recommendations for improvement. This course may be useful for someone who wants to begin a career as a Business Analyst, particularly if they hope to work in a technology-focused company. The course can help to develop the mathematical skills needed for data analysis.

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Data Analyst

Data Analysts turn datasets into knowledge, which can lead to actionable insights for organizations. This course on Math Fundamentals: Integrals provides a basis for understanding how to approach some of the mathematics that is needed in this field, such as integrals and other necessary concepts of differential calculus. This course may be useful for someone who wants to begin a career as a Data Analyst.

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Market Research Analyst

Market Research Analysts collect and analyze data about consumer behavior, which can help organizations develop more effective marketing campaigns. This course provides core functions of differential calculus that can help someone understand aspects of consumer behavior. This course may be useful for someone who wants to begin a career as a Market Research Analyst, although it may not be essential knowledge for the role.

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Operations Research Analyst

Operations Research Analysts use mathematical and analytical methods to solve complex business problems, such as optimizing supply chains or predicting demand. This course on Math Fundamentals: Integrals provides a basis for understanding the mathematics that is needed in this field, especially in differential calculus. This course may be useful for someone who wants to begin a career as an Operations Research Analyst.

See salaries and explore the career path for Operations Research Analyst

Computer Programmer

Computer Programmers write and maintain computer programs, which can include designing, coding, testing, and debugging. This course on Math Fundamentals: Integrals may be useful for someone who wants to begin a career as a Computer Programmer, as it can help to develop the mathematical skills needed for programming.

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Software Engineer

Software Engineers develop and maintain computer software, which can include designing, coding, testing, and debugging. This course on Math Fundamentals: Integrals may be useful for someone who wants to begin a career as a Software Engineer, as it can help to develop the mathematical skills needed for programming.

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Reading list

We've selected 21 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 Math Fundamentals: Integrals.

Introduction to Infinite Dimensional Stochastic...

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Classic text on calculus, providing a rigorous and in-depth treatment of the subject. It good choice for students who want a deeper understanding of the mathematical foundations of calculus.

Math Fundamentals

Integrals

What's inside

Learning objectives

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