![]() ![]() Stoke's Theorem as a 3D Analogues to 2D Green's Theorems in Circulation Form. Surface Integrals of Scalar Functions, Surface Area Elements in Spherical, Cylindrical, and Graph Casesįlux of a Vector Field through a Surface, Physical Examples Green's Theorem in the circulation and Flux Form Integrals of Fields, Circulation, Flux, Work of ForceĬonservative Fields, Finding Potentials, Independence of Path, FTC for those Fields Calculus 3 is a comprehensive Calculus course designed to cover the Calculus of Multivariable and Vector Calculus. ![]() Vector Fields, Radial, Gradient, Potential Plane Transformations, Jacobian, Change of Variables Triple Integrals in Spherical Coordinates Triple Integrals in Cylindrical Coordinates Triple Integrals in Cylindrical Coordinates, Emphasis on Examples Triple Integrals, Volumens and Masses of Solids ![]() The Method of Lagrange Multipliers, Optimization Problems, Extreme Distancesĭouble Integral as a Volume, Over Rectanglesĭouble Integrals over More General RegionsĬhanging Order of Integration, Volumes of Regions Between 2 Surfaces, Area of a Plane Region Using Double Integrals Calculus is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations. Local Extrema, Critical Points, 2nd Derivative Test Vectors differentiation and integration of vector valued functions multivariable calculus partial derivatives multiple integrals. Gradient, Directional Derivative, Applications* Partial First and Higher Order Derivatives, Clairaut Theorem, Differentiability Physical Concepts of Motion (Velocity, Acceleration, Speed) Using Vetor Calculusįunctions of 2 Variables, Graphs, Level CurvesĬalculus of Multivariable Functions, Limits, Two-Path Test Vector-Valued Functions and their Calculus Please follow instructions in your class pertaining to these topics. During the Summer sessions, the schedule is condensed into 8 weeks.Ī topic marked by * may be covered briefly for one or more of the following reasons: it is similar to another one covered previously it is of less importance for future development of the course material it is relatively simple and may be given as a reading assignment it is too advanced at the first reading. The following is a typical 15-week Fall or Spring semester schedule for MATH 210. Introduction to multivariable calculus: Vector valued functions and motion in the plane and in space, functions of several. ![]()
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