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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.
Good to know
Good to know
Know what's good ,
what to watch for , and
possible dealbreakers
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
Save this course
Save Math Fundamentals: Integrals to your list so you can find it easily later:
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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
Show steps
Stay organized and ensure you have easy access to the materials you need for the course.
Show steps
-
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
Show steps
Strengthen your foundation in algebra and trigonometry, which are essential prerequisites for calculus.
Browse courses on
Algebra
Show steps
-
Review the concepts of functions, equations, and inequalities.
-
Practice solving trigonometric equations and identities.
Form a Study Group
Show steps
Collaborate with peers to discuss concepts, work on problems, and provide support.
Show steps
-
Find classmates who are interested in forming a study group.
-
Establish regular meeting times and a study schedule.
Four other activities
Expand to see all activities and additional details
Show all seven activities
Explore Khan Academy's Calculus Tutorials
Show steps
Supplement your understanding with interactive tutorials and practice exercises.
Show steps
-
Visit the Khan Academy Calculus section.
-
Work through the tutorials on derivatives and integrals.
Review Apostol's Calculus, Volume I (2nd Edition)
Show steps
Familiarize yourself with the foundational concepts of calculus, such as limits, derivatives, and integrals, which will be essential for this course.
Show steps
-
Read through the first three chapters of the book.
-
Work through the practice problems at the end of each chapter.
Practice Derivative Problems
Show steps
Reinforce your understanding of derivatives through practice problems.
Show steps
-
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
Show steps
Organize your understanding of integral concepts visually to strengthen your comprehension.
Show steps
-
Identify the main concepts related to integrals.
-
Create a visual representation of these concepts, connecting them with branches and sub-branches.
Organize Course Notes and Resources
Show steps
Stay organized and ensure you have easy access to the materials you need for the course.
Show steps
Show steps
Show steps
- 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
Show steps
Strengthen your foundation in algebra and trigonometry, which are essential prerequisites for calculus.
Browse courses on
Algebra
Show steps
Show steps
Show steps
- Review the concepts of functions, equations, and inequalities.
- Practice solving trigonometric equations and identities.
Form a Study Group
Show steps
Collaborate with peers to discuss concepts, work on problems, and provide support.
Show steps
Show steps
Show steps
- Find classmates who are interested in forming a study group.
- Establish regular meeting times and a study schedule.
Four other activities
Expand to see all activities and additional details
Show all seven activities
Explore Khan Academy's Calculus Tutorials
Show steps
Supplement your understanding with interactive tutorials and practice exercises.
Show steps
Show steps
Show steps
- Visit the Khan Academy Calculus section.
- Work through the tutorials on derivatives and integrals.
Review Apostol's Calculus, Volume I (2nd Edition)
Show steps
Familiarize yourself with the foundational concepts of calculus, such as limits, derivatives, and integrals, which will be essential for this course.
Show steps
Show steps
Show steps
- Read through the first three chapters of the book.
- Work through the practice problems at the end of each chapter.
Practice Derivative Problems
Show steps
Reinforce your understanding of derivatives through practice problems.
Show steps
Show steps
Show steps
- 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
Show steps
Organize your understanding of integral concepts visually to strengthen your comprehension.
Show steps
Show steps
Show steps
- 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
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.
Statistician
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.
Quantitative Analyst
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.
Economist
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.
Financial Risk Manager
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.
Data Scientist
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.
Actuary
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.
Investment Analyst
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.
Financial Analyst
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.
Business Analyst
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.
Data Analyst
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.
Market Research Analyst
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.
Operations Research Analyst
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.
Computer Programmer
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.
Software Engineer
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.
For more career information including salaries, visit:
OpenCourser.com/course/2puj4g/math
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.
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.
Offers a comprehensive exploration of integral calculus, extending the understanding gained in this course. It provides a detailed analysis of measure theory and its applications in integration.
Dives into the applications of integration in convex functions. It provides an in-depth examination of convex functions and their applications, extending the knowledge gained through this course.
Offers an in-depth exploration of integral calculus, extending the understanding gained in this course. It provides a detailed analysis of measure theory and its applications in integration.
Introduces diverse integration applications, ensuring a thorough exploration of calculus. It offers an extensive examination of the subject, covering advanced topics in analysis.
Introduces advanced integral theory, which is essential for a deeper understanding of calculus. It provides a comprehensive analysis of measure theory and its significance in the field.
Graduate-level textbook on real analysis, which provides a comprehensive treatment of the foundations of calculus. It good choice for students who want a deeper understanding of the mathematical theory behind calculus.
Save
Provides a rigorous and comprehensive treatment of the foundations of calculus. It good choice for students who want a deeper understanding of the mathematical theory behind calculus.
Provides a comprehensive overview of the concepts covered in the course, including derivatives, integrals, and their applications. It valuable reference tool for students who want to deepen their understanding of the material.
Save
Provides a comprehensive and rigorous treatment of the material covered in the course. It good choice for students who want a more in-depth understanding of the theory behind calculus.
This popular calculus textbook used by many universities and colleges. It is known for its clear and concise explanations, as well as its wide range of examples and exercises. The book covers all the topics that are covered in the course, and it good resource for students who want to learn more about integral calculus.
Is designed for students in the physical sciences who need to understand the basics of calculus. It covers the same topics as a traditional calculus course, but with a focus on applications in physics and engineering.
Is designed for students in business, economics, and the social sciences who need to understand the basics of calculus. It covers the same topics as a traditional calculus course, but with a focus on applications in those fields.
Save
Is designed for students in the life sciences who need to understand the basics of calculus. It covers the same topics as a traditional calculus course, but with a focus on applications in biology and medicine.
Provides a rigorous and comprehensive treatment of integration. It covers all the topics that are typically covered in a first-year calculus course, as well as more advanced topics such as improper integrals and multiple integrals. It valuable resource for students who want to learn more about integration.
This book, which is commonly used as an alternative to traditional textbooks, provides a rigorous and in-depth treatment of calculus. It covers all the topics that are typically covered in a first-year calculus course.
Provides a comprehensive and applied treatment of calculus. It covers all the topics that are typically covered in a first-year calculus course.
Save
Provides a rigorous and in-depth treatment of mathematical analysis. It covers all the topics that are typically covered in a first-year calculus course.
Save
Provides a rigorous and in-depth treatment of real analysis. It covers all the topics that are typically covered in a first-year calculus course.
Provides a rigorous and in-depth treatment of measure and integral. It covers all the topics that are typically covered in a first-year calculus course.
Save
Provides a modern and rigorous treatment of classical analysis. It covers all the topics that are typically covered in a first-year calculus course.
For more information about how these books relate to this course, visit:
OpenCourser.com/course/2puj4g/math
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Effort
4 to 5 hours per week for 5 weeks
Level
Introductory
Via
edX
Institution
Universitat Politècnica de València
Instructor
Antonio José Guirao Sánchez
Language
English
Transcript
English
Good to know
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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