Calculus Home
Explore our developing collection of Calculus topics, from foundational concepts to typical applications. Our chapters are designed to be active and engaging, with detailed explanations, interactive Desmos calculators to illustrate key ideas, examples, and practice problems (each with a complete solution a click away) to help you learn Calculus well and excel.
Introductory Ideas
Let's build from everyday thinking to develop basic concepts and lay the groundwork we need.
View Introductory Ideas Home Page→Chapter Content
A. First Calculations; Linear Approximations, Differentials
- A. First Calculations; Linear Approximations, Differentials
- A.1 First Calculations
- A.2 Generalizing to Other Rates of Change
- A.3 Introducing Linear Approximations
- A.4 Practice Problems: Linear Approximations
- A.5 Differentials; Steps Toward Determining
𝑑 𝑓 𝑑 𝑥 𝑥 = 𝑎 - A.6 Estimating
𝑑 𝑓 𝑑 𝑥 𝑥 = 𝑎
B. Average Rate of Change; Better Estimate for 𝑑 𝑓 𝑑 𝑥 𝑥 = 𝑎
Limits & Continuity
A deep dive into limits and continuity, which are foundational to all of Calculus. Lots of practice problems, all with complete solutions.
View Limits & Continuity Home Page→Chapter Content
A. Limits Concepts
B. Calculating Limits
C. Limits at Infinity
- C. Limits at Infinity
- C.1 Introduction to Limits at Infinity
- C.2 The Epsilon Strip
- C.3 Some Limits at Infinity That Exist; Some That Do Not
- C.4 Some Limits at Negative Infinity That Exist; Some That Do Not
- C.5 Limits of Polynomials
- C.6 Limits of Rational Functions
- C.7 Limits of Exponential and Logarithmic Functions
- C.8 Limits at Infinity with Square Roots
Calculating Derivatives
Being able to calculuate derivatives quickly is key to proceeding in the course. Let's learn the rules we need, and then practice to become completely comfortable using them.
View Calculating Derivatives Home Page→Chapter Content
A. Derivatives of Polynomials, Exponential, and Trig Functions
B. Derivatives of the Product and Quotient of Functions
C. The Chain Rule
D. Implicit Differentiation
E. Inverse Functions
F. Derivative of l n ( 𝑥 )
Just PRACTICE PROBLEMS & Solutions
Derivative Applications
Time to put those derivatives to use! Let's work through typical application problems step-by-step.
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Integration
Learn and practice some initial techniques of integration.
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