Concise Modular Calculus 75 97

(1/6 on Integration of Multivariable Functions) Explains that double integrals are a method to compute volumes under graphs of ...

Illustrates the derivative as the formal concept behind instantaneous velocities, tangent lines and general instantaneous rates of ...

6/6 on Surfaces in 3-D Space) Visualizes the limiting behavior for functions of two variables. Explains how limits of multivariable ...

Explains what

(4/6 on Integration of Multivariable Functions) Justifies how the integration over regions other than boxes is accomplished with ...

(2/6 on Integration of Multivariable Functions) Introduces Fubini's Theorem as a much needed tool to avoid constant use of ...

(5/6 on Integration of Multivariable Functions) Derives the formula for integration in polar coordinates. Explains how to compute ...

(1/4 on Differentiation of Multivariable Functions) Explains partial derivatives as derivatives of a function's traces. Notes that partial ...

Explains the standard equations (vector, parametric and symmetric) of a line in three-dimensional space. Exhibits situations in ...

Visually illustrates the typical ways in which limits are used: Divisions by zero, defining derivatives, defining integrals and ...

Justifies how a derivative can be found implicitly when we cannot solve for y. Computes tangent lines via implicit differentiation ...

Explains limits at a point. Shows graphical, numerical and symbolic examples. Emphasizes computation that does not rely on ...

Defines sequences as, well, sequences of numbers. Explains how the limit of a sequence governs the sequence's long-term ...