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Calculus

Limits, derivatives, integrals, and vector calculus.

Chapters

17 chapters · 17 problem sets

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1 Functions and ModelsFunctions are the central objects of calculus. Problems ›

2 Limits and DerivativesThe limit is the foundation on which all of calculus is built. Problems ›

3 Differentiation RulesComputing derivatives straight from the limit definition is slow and error-prone. Problems ›

4 Applications of DifferentiationWith the differentiation rules in hand, the derivative becomes a tool for understanding the behavior of functions: where they rise and fall, where… Problems ›

5 IntegralsWhere differential calculus grew from the tangent and velocity problems, integral calculus grows from the area and distance problems. Problems ›

6 Applications of IntegrationThe definite integral is more than an antiderivative bookkeeping tool — it is a machine for summing infinitely many infinitesimal contributions. Problems ›

7 Techniques of IntegrationDifferentiation follows fixed rules; integration does not. Problems ›

8 Further Applications of IntegrationBeyond areas, volumes, and work, the definite integral measures a much wider range of quantities. Problems ›

9 Differential EquationsA differential equation is an equation relating an unknown function to its own derivatives. Problems ›

10 Parametric Equations and Polar CoordinatesUntil now, plane curves have been described as a graph of a function or by an implicit relation between x and y . Problems ›

11 Infinite Sequences and SeriesMany functions central to physics and engineering — among them the exponential, the trigonometric functions, and the Bessel functions of vibrating… Problems ›

12 Vectors and the Geometry of SpaceThis chapter sets up coordinate systems and vectors for three-dimensional space — the working stage for multivariable calculus. Problems ›

13 Vector FunctionsUp to now the functions we worked with returned numbers. Problems ›

14 Partial DerivativesSingle-variable calculus handles quantities that depend on one input. Problems ›

15 Multiple IntegralsThe definite integral extends naturally from a single variable to two or three. Problems ›

16 Vector CalculusThis chapter studies the calculus of vector fields — functions that attach a vector to every point of space. Problems ›

17 Second-Order Differential EquationsBuilding on the first-order equations of Chapter 9, this chapter develops second-order linear differential equations — how to solve them, and how t… Problems ›

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