Duration of the online course: 14 hours and 52 minutes
New
Build real calculus skills fast with this free online course: master limits, derivatives, integrals, and exam-style practice to boost grades and confidence.
In this free course, learn about
Factor polynomials, find GCD factors, and simplify expressions
Interpret and graph functions (lines, parabolas, trig); understand function vs relation
Compute average rates of change and use linear models for real-world data
Convert degrees↔radians; know key trig graphs and periods (e.g., sine)
Understand limits, when they fail, and the epsilon-delta definition
Apply limit laws; resolve indeterminate forms (0/0) via algebraic simplification
Analyze continuity, classify discontinuities, and use the Intermediate Value Theorem
Find vertical/horizontal asymptotes and limits at infinity for rational functions
Define derivatives via tangent slopes; use power/product/quotient/chain rules
Differentiate trig, exponential, and logarithmic functions; use higher-order derivatives
Use implicit differentiation and related rates to model changing quantities
Do optimization and use linearization/differentials to estimate propagated/relative error
Understand integrals via Riemann sums; apply FTC, substitution, and ln/inverse trig integrals
Course Description
If you want calculus to feel logical instead of intimidating, this free online course is built to take you from essential algebra and graphing habits to the core ideas that power STEM, economics, and data-driven work. You will strengthen the foundations that typically slow students down, then learn how to read functions, interpret change, and connect equations to real meaning. Along the way, guided practice helps you turn common sticking points into routines you can rely on under exam pressure.
You will start by sharpening the prerequisites that make Calculus I much easier: factoring efficiently, recognizing patterns in graphs, and understanding how linear models describe rates of change. From there, you will develop a clear picture of what it means for a relation to be a function and how trig behavior shows up in graphs. These early skills become your toolkit for the first big calculus theme: limits. You will learn how limits answer questions about behavior near a point, why they sometimes fail to exist, and how the formal epsilon-delta idea supports the intuitive one. That naturally leads into continuity, where you learn to classify discontinuities and use powerful theorems that guarantee certain values must occur.
Next, you will shift to derivatives as a precise language for instantaneous change. You will understand the derivative from its definition, then gain fluency with the main rules used in problem solving, including product, quotient, chain, and implicit differentiation. You will also practice turning derivatives into modeling tools through related rates and optimization, so you can translate a word problem into an equation and make decisions using calculus rather than guessing.
Finally, you will build the bridge to integrals and accumulation. You will connect area ideas to sigma notation and Riemann sums, see how definite integrals are defined, and understand why the Fundamental Theorem of Calculus is the key link between rates of change and total change. You will also gain comfort with substitution and with logarithmic, exponential, and inverse trigonometric tools that commonly appear in later courses. A comprehensive review at the end helps you pull everything together and study with purpose.
Course content
Video class: Calculus I - 0.0 Review of Factoring13m
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 Graphs14m
Exercise: What determines the direction of a parabola's graph?
Video class: Calculus I - 0.2 Linear Models and Rates of Change12m
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 Graphs21m
Exercise: What condition must a relation meet to be classified as a function?
Video class: Calculus I - 0.4.1 Review of Trigonometric Functions16m
Exercise: Which of the following represents the correct conversion from 150 degrees to radians?
Video class: Calculus I - 0.4.3 Graphs of Trigonometric Functions06m
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 Calculus07m
Exercise: What do limits help solve in calculus?
Video class: Calculus I - 1.2.2 Limits That Fail to Exist07m
Exercise: When does a limit fail to exist?
Video class: Calculus I - 1.2.3 The Epsilon-Delta Limit Definition10m
Exercise: Which statement best describes the formal definition of a limit in calculus?
Video class: Calculus I - 1.3.1 Properties of Limits15m
Exercise: What is the limit of a constant function?
Video class: Calculus I - 1.3.2 Finding Limits of Indeterminant Form Functions14m
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 Continuity19m
Exercise: Identify the Discontinuity Type
Video class: Calculus I - 1.4.2 Properties of Continuity09m
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 Theorem13m
Exercise: What is the purpose of the Intermediate Value Theorem (IVT)?
Video class: Calculus I - 1.5.2 Vertical Asymptotes07m
Exercise: Identifying Vertical Asymptotes in Rational Functions
Video class: Calculus I - 2.1.1 The Slope of the Tangent Line Using the Definition of Slope18m
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 Derivative12m
Exercise: What is the derivative function?
Video class: Calculus I - 2.2.1 Basic Differentiation Rules10m
Exercise: Which of the following represents the correct derivative of the function f(x) = 5x⁴ using the power rule?
Video class: Calculus I - 2.2.2 Applying the Derivative to the Position Function11m
Video class: Calculus I -2.3.1 The Product and Quotient Rules for Derivatives16m
Exercise: Which of the following statements is true about the product and quotient rules for derivatives?
Video class: Calculus I - 2.3.2 Trigonometric and Higher-Order Derivatives09m
Video class: Calculus I - 2.4.1 The Chain Rule and General Power Rule13m
Exercise: What is the derivative of the function \( h(x) = (3x^2 - 5)^7 \) using the chain rule?
Video class: Calculus I - 2.4.2 Differentiation Strategies and Practice12m
Video class: Calculus I - 2.5.1 Implicit Differentiation13m
Exercise: Consider the equation 5x^2 + 3y^2 = 15. When using implicit differentiation to find dy/dx, which of the following results is correct?
Video class: Calculus I - 2.6.1 Related Rates - Modeling with Circles10m
Video class: Calculus I - 2.6.2 Related Rates - Modeling with Triangles12m
Exercise: An airplane flying at an altitude of 6 miles is approaching a radar station at a distance of 10 miles horizontally. If the distance between the airplane and the station is decreasing at a rate of 400 miles per hour, what is the horizontal speed of the airplane?
Video class: Calculus I - 3.1.1 Relative and Absolute Extrema10m
Video class: Calculus I - 3.1.2 Critical Numbers and Extrema20m
Exercise: What are the conditions under which a function can have critical numbers, where minima or maxima might occur?
Video class: Calculus I - 3.2.1 Rolle's Theorem11m
Video class: Calculus I - 3.2.2 The Mean Value Theorem13m
Exercise: Which of the following statements is true regarding the Mean Value Theorem?
Video class: Calculus I - 3.3.1 Increasing and Decreasing Functions13m
Video class: Calculus I - 3.3.2 The First Derivative Test13m
Exercise: Using the first derivative test, determine the nature of the critical point for the function f(x) = x^3 - 3x^2 + 2:
Video class: Calculus I - 3.4.1 Intervals of Concavity and Points of Inflection18m
Video class: Calculus I - 3.4.2 The Second Derivative Test11m
Exercise: What can you conclude about a critical point if the second derivative at that point is positive?
Video class: Calculus I - 3.5.1 Limits at Infinity07m
Video class: Calculus I - 3.5.2 Horizontal Asymptotes and Computational Techniques20m
Exercise: Which of the following statements about horizontal asymptotes for rational functions is true?
Video class: Calculus I - 3.6.1 Curve Sketching Using Graph Attributes10m
Video class: Calculus I - 3.6.2 Curve Sketching Using Derivatives14m
Exercise: When analyzing functions, which part primarily focuses on determining intervals of increase and decrease?
Video class: Calculus I - 3.7.1 Optimization16m
Video class: Calculus I - 3.7.2 Optimization Practice07m
Exercise: Consider a right circular cone with a volume of 9π cubic feet. What is the height of the cone if the radius of the base is 3 feet?
Video class: Calculus - 3.9.1 Tangent Line Approximation and Differentials18m
Video class: Calculus - 3.9.2 Propagated and Relative Error in Differentials08m
Exercise: A radius of a cylindrical object is measured to be 0.5 meters with a possible error of 0.02 meters. Estimate the relative error in calculating the area of its circular base, given the formula for the area of a circle is A = πr².
Video class: Calculus I - 4.1.1 Antiderivatives and the General Solution to a Differential Equation11m
Video class: Calculus I - 4.2.1 Sigma Notation and Summation Formulas11m
Video class: Calculus I - 4.2.2 Approximating the Area Under a Curve19m
Exercise: What is the effect of increasing the number of rectangles when approximating the area under a curve?
Video class: Calculus I - 4.2.3 Find the Area Under a Curve Using the Limit Definition15m
Video class: Calculus I - 4.3.1 Riemann Sums and Definite Integrals Defined08m
Exercise: Which of the following statements accurately describes the concept of a Riemann sum in the context of calculating the area under a curve?
Video class: Calculus I - 4.3.2 Evaluating Definite Integrals Without the FTC19m
Video class: Calculus I - 4.4.1 The Fundamental Theorem of Calculus19m
Exercise: How does the Fundamental Theorem of Calculus connect the concept of an antiderivative to finding the area under a curve?
Video class: Calculus I - 4.4.2 The Mean Value Theorem for Integrals and the Average Value of a Function13m
Video class: Calculus I - 4.4.3 The Second Fundamental Theorem of Calculus05m
Exercise: When applying the Second Fundamental Theorem of Calculus, if f(t) is continuous and X is used as the upper limit of integration, what is the derivative of the integral from 2 to X of f(t) dt?
Video class: Calculus I - 4.5.1 Integration by Substitution: Indefinite Integrals21m
Video class: Calculus I - 4.5.2 Integration by Substitution: Definite Integrals09m
Exercise: If we have an integral \( \int_{0}^{2} (x^2 + 4x + 5) \, dx \), what is the first step to simplify this using integration by substitution?
Video class: Calculus I - 5.1.1 Review: Logarithmic and Exponential Functions18m
Video class: Calculus I - 5.1.2 The Natural Logarithmic Function: Differentiation12m
Exercise: What is the result of differentiating the function f(x) = ln|cos(x)|?
Video class: Calculus I - 5.2.1 The Natural Logarithmic Function: Integration07m
Video class: Calculus I - 5.2.2 Natural Logarithmic Integration: Difficult Examples10m
Exercise: When performing integration using natural logarithmic integration, which technique is typically employed when the degree of the numerator polynomial is equal to or greater than the degree of the denominator polynomial?
Video class: Calculus I - 5.3.1 The Inverse of a Function14m
Video class: Calculus I - 5.3.2 The Derivative of The Inverse of a Function08m
Exercise: If the function f is differentiable and has an inverse function g, what is the relationship between the derivative of the inverse function g and the derivative of the original function f?
Video class: Calculus I - 5.5.1 Logarithmic and Exponential Functions: Derivatives and Integrals (Base not e)16m
Exercise: What is the derivative of the function f(x) = 5^(3x) using the rules for derivatives of exponential functions with bases other than e?
Video class: Calculus I - 5.7.1 Review: Inverse Trigonometric Functions15m
Exercise: What is the range of the arc sine function?
Video class: Calculus I - 5.7.2 Inverse Trigonometric Functions: Differentiation10m
Video class: Calculus I - 5.8.1 Inverse Trigonometric Functions: Integration18m
Exercise: If you want to integrate the function \( \int \frac{dx}{x^2 + 1} \), which inverse trigonometric function form should you apply?
Video class: Calculus I Final Exam Review53m
This free course includes:
14 hours and 52 minutes of online video course
Digital certificate of course completion (Free)
Exercises to train your knowledge
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