Stoke's Theorem as a 3D Analogues to 2D Green's Theorems in Circulation Form. The main concepts covered are generally partial derivatives. Surface Integrals of Scalar Functions, Surface Area Elements in Spherical, Cylindrical, and Graph Casesįlux of a Vector Field through a Surface, Physical Examples Calculus 3 is usually Multivariable Calculus, but differs through different universities/schools. Green's Theorem in the circulation and Flux Form Calculus 3 Lecture 11.1: An Introduction to Vectors: Discovering Vectors with focus on adding, subtracting, position vectors, unit vectors and magnitude. Integrals of Fields, Circulation, Flux, Work of ForceĬonservative Fields, Finding Potentials, Independence of Path, FTC for those Fields Vector Fields, Radial, Gradient, Potential Course Attributes: FA NSM AR NSM AS NSM AS AN. Prerequisite: Math 132 or score of 4 or 5 on Advanced Placement calculus BC, or permission of the department. Plane Transformations, Jacobian, Change of Variables Topics include differential and integral calculus of functions of two or three variables, and a brief introduction to differential equations. 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 Local Extrema, Critical Points, 2nd Derivative Test Math 2415 - Calculus III Perform calculus operations on vectorvalued functions, including derivatives, integrals, curvature, displacement, velocity. 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.
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