Free online courseCalculus 1
Duration of the online course: 44 hours and 56 minutes
4.63
(59)
Enroll in this free online Calculus 1 course. Learn about functions, limits, derivatives, integrals, and more through comprehensive lectures. Perfect for beginners in calculus.
Course Description
Are you ready to dive deep into the fascinating world of calculus? "Calculus 1" offers a comprehensive introduction to calculus over an engaging 44 hours and 56 minutes of instruction. Highly rated with an average score of 5 out of 5, this course is perfect for those embarking on their basic studies journey, particularly in the subcategory of calculus.
The course starts by laying a strong foundation, exploring fundamental concepts related to lines, angles of inclination, and the distance formula. It then proceeds to the essential topic of functions and provides a thorough review of trigonometry, ensuring that students are well-prepared for the more advanced subjects that follow.
Students will encounter a variety of intriguing topics as they navigate through the curriculum. Combining and composing functions, understanding limits, and grasping the crucial concept of continuity form the building blocks for more complex ideas. The course delves deeply into the principles of differentiation, from basic techniques to the application of product and quotient rules, ensuring that learners can find derivatives with ease.
Further exploration into the world of derivatives involves practical applications. Students will understand how to use derivatives to analyze the behavior of functions, including discussions on related rates and implicit differentiation. By examining increasing and decreasing functions, concavity, and essential theorems like Rolle's Theorem and the Mean-Value Theorem, students gain a robust understanding of these fundamental concepts.
To make the learning process even more engaging, the course dives into graphing functions, finding optimization solutions, and addressing limits of functions at infinity. Each concept is intricately connected, providing students with a holistic view of calculus.
The course doesn't stop at differentiation; it also offers a detailed introduction to integral calculus. Starting with indefinite integrals and advancing through techniques like integration by substitution, students are guided step-by-step through the intricacies of finding areas under curves using Riemann Sums and evaluating definite integrals.
The program culminates with a comprehensive exploration of the fundamental theorem of calculus, bridging the gap between differentiation and integration. Practical applications extend to finding areas between curves and calculating volumes of solids using various methods, including disks, washers, and cylindrical shells. Finally, students learn how to find the length of a curve on a plane, rounding out their understanding.
With a detailed curriculum designed to take learners from foundational principles to advanced applications, "Calculus 1" is an exceptional choice for anyone seeking to master the fundamentals of calculus. Whether preparing for advanced studies or looking to strengthen mathematical skills, this course ensures a well-rounded, in-depth understanding of calculus.
Conteúdo do Curso
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Video class: Calculus 1 Lecture 0.1: Lines, Angle of Inclination, and the Distance Formula
0h48m
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Exercise: _What is the slope of a line and how is it defined?
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Video class: Calculus 1 Lecture 0.2: Introduction to Functions.
1h37m
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Video class: Calculus 1 Lecture 0.3: Review of Trigonometry and Graphing Trigonometric Functions
1h20m
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Exercise: _What is the relationship between radians and degrees?
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Video class: Calculus 1 Lecture 0.4: Combining and Composition of Functions
0h15m
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Video class: Calculus 1 Lecture 1.1: An Introduction to Limits
1h27m
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Video class: Calculus 1 Lecture 1.2: Properties of Limits. Techniques of Limit Computation
3h00m
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Video class: Calculus 1 Lecture 1.4: Continuity of Functions
1h26m
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Exercise: _What is the layman's term definition of continuity for a function?
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Video class: Calculus 1 Lecture 1.5: Slope of a Curve, Velocity, and Rates of Change
1h50m
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Video class: Calculus 1 Lecture 2.1: Introduction to the Derivative of a Function
1h16m
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Exercise: _What is the derivative?
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Video class: Calculus 1 Lecture 2.2: Techniques of Differentiation (Finding Derivatives of Functions Easily)
1h12m
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Video class: Calculus 1 Lecture 2.3: The Product and Quotient Rules for Derivatives of Functions
1h02m
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Exercise: _What is the product rule in calculus?
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Video class: Calculus 1 Lecture 2.4: Applications of the Derivative
0h40m
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Video class: Calculus 1 Lecture 2.5: Finding Derivatives of Trigonometric Functions
0h48m
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Video class: Calculus 1 Lecture 2.6: Discussion of the Chain Rule for Derivatives of Functions
1h34m
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Video class: Calculus 1 Lecture 2.7: Implicit Differentiation
1h08m
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Exercise: _What is the difference between an explicit and implicit function?
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Video class: Calculus 1 Lecture 2.8: Related Rates
0h53m
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Video class: Calculus 1 Lecture 3.1: Increasing/Decreasing and Concavity of Functions
1h34m
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Video class: Calculus 1 Lecture 3.2: A BRIEF Discussion of Rolle's Theorem and Mean-Value Theorem.
0h06m
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Video class: Calculus 1 Lecture 3.3: The First Derivative Test for Increasing and Decreasing
0h26m
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Exercise: _What does the first derivative test tell us about a curve?
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Video class: Calculus 1 Lecture 3.4: The Second Derivative Test for Concavity of Functions
0h36m
This free course includes:
44 hours and 56 minutes of online video course
Exercises to train your knowledge
Certificate of course completion
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