
Students will learn about the tangent line, one of the reasons for the importance of limits.
Students will learn about velocity, another reason for the importance of limits.
Practice problems for The Tangent Line and Velocity.
Solutions to problem set The Tangent Line and Velocity
Students will learn the intuitive definition of the limit of a function.
Students will learn how to find one-sided limits.
In this lecture, the notion of infinite limit is explained.
Practice problems for The Limit of a Function
Solutions to problem set The Limit of a Function
Students will learn how to apply the limit laws.
Practice problems for Limit Laws.
Solutions to problem set Limit Laws
Students will learn the precise definition of a limit and learn how to prove limit statements.
Practice problems for Precise Definition of Limit
Solutions to problem set Precise Definition of Limit
In this lecture, students will learn about continuity and examples of discontinuity.
Practice problems for Continuity
Solutions to problem set Continuity
This lecture explains the Intermediate Value Theorem, and we will look at an application of the theorem.
Practice problems for Intermediate Value Theorem
Solutions to problem set Intermediate Value Theorem
Students will learn the definition of derivative and how the derivative relates to tangent lines and velocities.
In this lecture, students will learn how to calculate derivatives using the definition of derivative.
Practice problems for Derivatives
Solutions to problem set Derivatives
Students will learn the definition of the derivative of a function at a variable x.
Students will learn what it means for a function to be differentiable at x=a.
Students will learn about a corner, a case where differentiability fails.
Students will learn about a cusp, another case where differentiability fails.
Students will learn about the relationship between differentiability and continuity.
Practice problems for Differentiability
Solutions to problem set Differentiability
In this lecture, students will learn how to apply the differentiation rules.
Practice problems for Differentiation Rules
Solutions to problem set Differentiation Rules
Students will learn what the derivatives of the six trigonometric functions are.
Practice problems for Derivatives of Trigonometric Functions
Solutions to problem set Derivatives of Trigonometric Functions
Students will learn how to apply the chain rule to find the derivative of composite functions.
Practice problems for Chain Rule
Solutions to problem set Chain Rule
Students will learn how to apply implicit differentiation when a function is expressed implicitly as a function of x.
In this lecture, we explore an example of implicit differentiation that involves an intriguing curve.
Practice problems for Implicit Differentiation
Solutions to problem set Implicit Differentiation
In this lecture, we look at some applications of rates of change in economics and physics.
Students will learn how to solve related rates problems.
In this lecture, we see how related rates are used in finding marginal profit.
Practice problems for Related Rates
Solutions to problem set Related Rates
The definitions of absolute maximum and minimum values are provided, and the definition of critical number is provided.
Students will learn a procedure for finding absolute maximum and minimum values.
Practice problems for Finding Absolute Maximum and Minimum Values
Solutions to problem set Finding Absolute Maximum and Minimum Values
Students will learn how to apply the First Derivative Test to find local maximum and minimum values.
An additional example of finding local maximum and minimum values is provided.
Practice problems for Finding Local Maximum and Minimum Values
Solutions to problem set Finding Local Maximum and Minimum Values
Students will learn how to solve optimization problems.
An additional optimization problem is explored.
Practice problems for Optimization.
Solutions to problem set Optimization.
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Brought to you by the instructor of the successful courses Linear Algebra for Beginners: Open Doors to Great Careers and Linear Algebra for Beginners: Open Doors to Great Careers 2!
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"Awesome foundation!" -- Michael Sinegar
"Clearly delivered in digestible chunks" -- Herman Leung
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Would you like to learn a mathematics subject that is crucial for many high-demand lucrative career fields such as:
If you're looking to gain a solid foundation in Differential Calculus, allowing you to study on your own schedule at a fraction of the cost it would take at a traditional university, to further your career goals, this online course is for you. If you're a working professional needing a refresher on calculus or a complete beginner who needs to learn Calculus for the first time, this online course is for you.
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Why you should choose this instructor: I earned my PhD in Mathematics from the University of California, Riverside. I have extensive teaching experience: 6 years as a teaching assistant at University of California, Riverside, over two years as a faculty member at Western Governors University, #1 in secondary education by the National Council on Teacher Quality, and as a faculty member at Trident University International.
In this course, I cover the core concepts such as:
After taking this course, you will feel CARE-FREE AND CONFIDENT. I will break it all down into bite-sized no-brainer chunks. I explain each definition and go through each example STEP BY STEP so that you understand each topic clearly. I will also be AVAILABLE TO ANSWER ANY QUESTIONS you might have on the lecture material or any other questions you are struggling with.
Practice problems are provided for you, and detailed solutions are also provided to check your understanding.
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