Where to find a free course about Calculus 1 lectures ?

Free online course Calculus 1 lectures

Duration of the online course: 22 hours and 27 minutes

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Build strong Calculus 1 skills with a free online course: master limits, derivatives, optimization, and integrals through clear lectures and practice.

In this free course, learn about

Evaluate limits graphically, numerically, and by formal definition
Determine continuity and one-sided limits at a point
Analyze infinite limits and vertical asymptotes
Compute derivatives from first principles; tangent lines and instantaneous rates
Apply product, quotient, and chain rules to differentiate functions
Use implicit differentiation to find dy/dx for relations
Solve related rates problems (e.g., balloon radius vs volume change)
Find absolute/relative extrema on intervals; apply critical point analysis
Use Rolle’s Theorem and the Mean Value Theorem and interpret conclusions
Analyze monotonicity, concavity, and use 1st/2nd derivative tests
Perform curve sketching using intercepts, asymptotes, extrema, and concavity
Set up and solve optimization problems with constraints
Use Newton’s Method to approximate roots
Differentiate/integrate ln and exponential functions; separable growth/decay ODEs

About the free online course

Strengthen your foundation in Calculus 1 with a free online course designed to turn intimidating concepts into tools you can use with confidence. If limits, derivatives, and integrals have felt like a collection of rules to memorize, this course helps you connect ideas, understand why procedures work, and recognize which technique fits a problem. It is ideal for high school and college students, self-learners preparing for exams, or anyone who needs calculus for STEM pathways.

You will begin by developing real intuition for limits using graphical and numerical reasoning, then refine that understanding with formal definitions, continuity, one-sided limits, and infinite limits. From there, the focus shifts to derivatives: interpreting them as slopes, instantaneous rates of change, and tangible answers to real questions about motion, change, and sensitivity. As you progress, you will learn to differentiate efficiently and accurately, including product, quotient, and chain rules, as well as implicit differentiation for relationships that cannot be solved neatly for one variable.

To move beyond computation, you will apply derivatives to decision-making. You will analyze increasing and decreasing behavior, extrema on intervals, and concavity, using key theorems that power curve sketching and justify results. You will also practice optimization and numerical approximation with Newton’s method, gaining problem-solving habits that transfer to physics, economics, engineering, and data-driven fields.

The course continues with exponential and logarithmic functions, building comfort with common forms seen in applications. You will also see how calculus models change over time through introductory differential equation ideas like growth and decay. Reviews placed throughout help you consolidate what you learned and prepare strategically for major exams. With lecture support and targeted exercises, you can study at your own pace and leave with a clearer, more reliable grasp of Calculus 1.

Course content

Video class: Calculus 1: Lecture 1.2 Finding Limits Graphically and Numerically 35m
Exercise: What is the definition of a limit in calculus?
Video class: Calculus 1: Lecture 1.4 Continuity and One-Sided Limits 1h25m
Exercise: What does it mean for a function to be continuous at a point C?
Video class: Calculus 1: Lecture 1.5 Infinite Limits 1h07m
Exercise: What does it mean if the limit of f(x) as x approaches c equals infinity?

Video class: Calculus 1: Lecture 2.1 The Derivative and the Tangent Line Problem 1h03m
Exercise: What is the slope variable in the equation of a line y = mx + b?
Video class: Calculus 1: Lecture 2.2, 2.3, 2.4 Differentiation, Rates of Change, Product, Quotient, Chain Rules 2h23m
Exercise: What is the derivative of f(x) = 7x^6 + 3sin(x)?
Video class: Calculus 1: Lecture 2.5 Implicit Differentiation 57m
Exercise: Consider the function y = x² + sin(x). What is the derivative of y with respect to x?

Video class: Calculus 1: Lecture 2.6 Related Rates 53m
Exercise: A spherical balloon is inflated with gas at a rate of 700 cubic centimeters per minute. How fast is the radius of the balloon changing when the radius is 15 centimeters?
Video class: Calculus 1: Lecture 3.1 Extrema on an Interval 51m
Exercise: What is the absolute maximum value of a continuous function on a closed interval?
Video class: Calculus 1: Lecture 3.2 Rolle's Theorem and the Mean Value Theorem 1h07m
Exercise: Consider a function f that is continuous on the closed interval [a, b] and differentiable on the open interval (a, b). According to Rolle's theorem, if f(a) = f(b), which of the following must be true?

Video class: Calculus 1: Lecture 3.3 Increasing and Decreasing Functions and the First Derivative Test 39m
Exercise: Which of the following is true about a function whose first derivative is negative on an interval?
Video class: Calculus 1: Lecture 3.4 Concavity and The Second Derivative Test 1h27m
Exercise: Consider the function f(x) = x^3 - 6x^2 + 8. At which x-value does the function have a relative minimum?
Video class: Calculus 1: Exam 2 Review 1h08m
Exercise: What is the derivative of the function f(x) = 3x^2 + cos(x) - sec(x)?

Video class: Calculus 1: Lecture 3.5 Limits at Infinity 59m
Exercise: Given a function f(x) that approaches a number L as x approaches infinity, what does this imply about f(x)?
Video class: Calculus 1: Lecture 3.6 A Summary of Curve Sketching 31m
Exercise: To find the x-intercept of a function, what must you do?
Video class: Calculus 1: Lecture 3.7 Optimization Problems 34m
Exercise: Given a rectangle with a fixed perimeter of 90 units, what is the maximum area that can be achieved?

Video class: Calculus 1: Lecture 3.8 Newton's Method 41m
Exercise: Which of the following statements about Newton's Method is correct?
Video class: Calculus 1: Lecture 5.1 The Natural Logarithmic Function Differentiation 40m
Exercise: Find the derivative of the function f(x) = ln(9x). Use the chain rule to simplify your answer.
Video class: Calculus 1: Lecture 5.2 The Natural Logarithmic Function Integration 37m
Exercise: What is the integral of 1/x dx?

Video class: Calculus 1: Lecture 5.4 Exponential Functions Differentiation and Integration 1h15m
Exercise: What is the integral of the function e^(7x - 4) with respect to x?
Video class: Calculus 1: Lecture 6.2 Growth and Decay(Separable Differential Equations Only in This Video) 42m
Exercise: Which of the following statements correctly describes a property of differential equations?
Video class: Calculus 1: Exam 4 Review 1h16m
Exercise: Using the Mean Value Theorem for integrals, find the value of C on the interval [1, 3] for the function f(x) = 9/x^3.

Video class: Calculus 1: Final Exam Review 1h26m
Exercise: Which of the following describes how to find the velocity of an object at the moment it strikes the ground when dropped from a height, given the position function s(t) = -16t^2 + s_0?