Free online courseCalculus I entire course
Duration of the online course: 16 hours and 1 minutes
New course
Master core concepts of Calculus I with our comprehensive free online course. Topics include limits, derivatives, integrals, optimization, and more. Perfect for beginners!
Course Description
Embark on a comprehensive journey through the essential concepts of calculus with "Calculus I," an extensive course that spans 16 hours and 1 minute. Tailored for those venturing into the core principles of calculus, this course is nestled within the Basic Studies category and falls specifically under Calculus. As of now, it awaits its first review, presenting an uncharted opportunity for students to gain a fresh perspective on the intricate world of calculus.
The course begins with a preliminary review of foundational topics such as factoring, graphing, and understanding linear models and rates of change. These initial lessons lay the groundwork for delving into the heart of calculus, ensuring that students are well-prepared to tackle more complex concepts. A significant emphasis is placed on functions and their graphs, alongside a detailed review of trigonometric functions and how to solve trigonometric equations.
Advancing into the crux of calculus, students are introduced to the concept of limits, which serve as the cornerstone of calculus. Through numerical and graphical approaches, the course elucidates how to determine limits, including those that do not exist, and delves into the epsilon-delta definition. Properties of limits and techniques for finding limits of indeterminate form functions are thoroughly explored, ensuring students grasp the underpinnings of continuity and its properties. The Intermediate Value Theorem, infinite limits, vertical asymptotes, and the fundamental principles surrounding them are analyzed in detail.
The course progresses to the study of derivatives, beginning with an introduction to the derivative using the slope of the tangent line and the definition of a derivative. Basic differentiation rules are rigorously covered, followed by practical applications of derivatives, such as the product and quotient rules, trigonometric and higher-order derivatives, and the essential Chain Rule. Differentiation strategies, implicit differentiation, and real-world applications in related rates are thoroughly discussed, providing students with a solid understanding of how derivatives function in various contexts.
Students then explore the critical concepts of extrema, Rolle's Theorem, and the Mean Value Theorem, which are pivotal for understanding the behavior of functions. The first and second derivative tests, along with techniques for determining intervals of concavity and points of inflection, are explained in depth. Detailed exploration of curve sketching, using both graph attributes and derivatives, prepares students to tackle optimization problems and understand tangent line approximation, differentials, and propagated errors.
The final section of the course introduces antiderivatives and differential equations, including sigma notation, summation formulas, and approximating the area under curves. The course meticulously covers Riemann Sums, definite integrals, and the Fundamental Theorems of Calculus, ensuring a holistic understanding of integration techniques, including integration by substitution.
Concluding with logarithmic, exponential, and inverse functions, the course provides a robust review of their properties, differentiation, and integration techniques, including the challenging applications of L'Hopital's Rule in resolving indeterminate forms.
Designed to provide a deep, foundational understanding of calculus, "Calculus I" is the optimal choice for students seeking to master this critical mathematical discipline. This course's meticulously structured content bridges essential pre-calculus concepts with the sophisticated intricacies of calculus, paving the way for academic and professional success in mathematics and related fields.
Conteúdo do Curso
-
Video class: Calculus I - 0.0 Review of Factoring
0h13m
-
Exercise: What is the greatest common divisor (GCD) that you can factor out of the polynomial 10x^3 - 15x^2 + 5x?
-
Video class: Calculus I - 0.1 Graphs
0h14m
-
Video class: Calculus I - 0.2 Linear Models and Rates of Change
0h12m
-
Exercise: What is the average rate of change for a population that increased from 800,000 in the year 2018 to 840,000 in the year 2021?
-
Video class: Calculus I - 0.3 Functions and Their Graphs
0h21m
-
Video class: Calculus I - 0.4.1 Review of Trigonometric Functions
0h16m
-
Exercise: Which of the following represents the correct conversion from 150 degrees to radians?
-
Video class: Calculus I - 0.4.2 Solving Trigonometric Equations
0h08m
-
Video class: Calculus I - 0.4.3 Graphs of Trigonometric Functions
0h06m
-
Exercise: What is the period of the function y = sin(x) according to the video transcript?
-
Video class: Calculus I - 1.1.1 A Preview of Calculus
0h07m
-
Video class: Calculus I - 1.2.1 Finding Limits Numerically and Graphically
0h11m
-
Exercise: What is the limit of the function g(x) = (x^2 - 4)/(x - 2) as x approaches 2?
-
Video class: Calculus I - 1.2.2 Limits That Fail to Exist
0h07m
-
Video class: Calculus I - 1.2.3 The Epsilon-Delta Limit Definition
0h10m
-
Exercise: Which statement best describes the formal definition of a limit in calculus?
-
Video class: Calculus I - 1.3.1 Properties of Limits
0h15m
-
Video class: Calculus I - 1.3.2 Finding Limits of Indeterminant Form Functions
0h14m
-
Exercise: What happens when you have a rational function and you try to find the limit by direct substitution but end up with an indeterminate form such as 0/0?
-
Video class: Calculus I - 1.4.1 Continuity
0h19m
-
Video class: Calculus I - 1.4.2 Properties of Continuity
0h09m
-
Exercise: Which of the following functions is guaranteed to be continuous for all real numbers?
-
Video class: Calculus I - 1.4.3 The Intermediate Value Theorem
0h13m
-
Video class: Calculus I - 1.5.1 Infinite Limits and Their Properties
0h10m
-
Exercise: When analyzing the function f(x) = 1/x, what is the behavior of the limit as x approaches 0 from the left?
-
Video class: Calculus I - 1.5.2 Vertical Asymptotes
0h07m
-
Video class: Calculus I - 2.1.1 The Slope of the Tangent Line Using the Definition of Slope
0h18m
-
Exercise: What is the process used to find the slope of the tangent line at a specific point using the definition of a slope?
-
Video class: Calculus I - 2.1.2 The Derivative Using the Definition of a Derivative
0h12m
This free course includes:
16 hours and 1 minutes of online video course
Exercises to train your knowledge
Certificate of course completion
100% free, from content to certificate
This online course can only be accessed through the Cursa App. Download it using the QR code or the links below:
This online course can only be accessed through the Cursa app. Install it using the links below:
-
Study for free!
Here you never pay! Not even for the certificate, because everything in the app is 100% free!
-
Improve your resume!
There are more than 4,000 free courses for you to study anything that interests you!
-
Free Digital Certificate!
Complete the course and issue your internationally recognized Digital Certificate free of charge.
More free courses at Calculus
Free CourseIntroductory Calculus
5
(1)
40h09m
38 exercises
Free CourseCalculus 1 for beginners
5
(1)
10h40m
6 exercises
Free CourseCalculus 3
4.8
(15)
75h24m
1 exercises
Free CourseCalculus 2
4.75
(8)
50h03m
6 exercises
Free CourseCalculus 1
4.63
(60)
44h56m
8 exercises
Free CourseCalculus 1
New course
7h37m
19 exercises
Free CourseCalculus basics
New course
2h42m
17 exercises
Free CourseCalculus
New course
33h57m
34 exercises
Free CourseCalculus 1 lectures
New course
22h27m
22 exercises
Free CourseIntroductory Calculus
5
(1)
40h09m
38 exercises
Free CourseCalculus 1 for beginners
5
(1)
10h40m
6 exercises
Free CourseCalculus 3
4.8
(15)
75h24m
1 exercises
Free CourseCalculus 2
4.75
(8)
50h03m
6 exercises
Free CourseCalculus 1
4.63
(60)
44h56m
8 exercises
Free CourseCalculus 1
New course
7h37m
19 exercises
Free CourseCalculus basics
New course
2h42m
17 exercises
Free CourseCalculus
New course
33h57m
34 exercises
Free CourseCalculus 1 lectures
New course
22h27m
22 exercises
Download the App now to have access to + 3300 free courses, exercises, certificates and lots of content without paying anything!
-
100% free online courses from start to finish
Thousands of online video courses, audio or text courses.
-
More than 48 thousand free exercises
To test your knowledge during online courses
-
Valid free Digital Certificate with QR Code
Generated directly from your cell phone's photo gallery and sent to your email
Download our app via QR Code or the links below::.
