Instructor:

Michael W. Bermel

Materials:

Text: Calculus Early Transcendentals Sixth Addition
James Stewart (2008) Thomson Brooks/Cole

Course Content:

Vectors and the Geometry of Space: Vectors in the Plane, Space Coordinates and Vectors in Space, Dot Product of Two Vectors, Cross Product of Two Vectors, Lines and Planes in Space, Surface in Space, Cylindrical and Spherical Coordinates

Vector -Valued Functions: Differenatiation and Integration of Vector Value Functions, Velocity and Acceleration, Tangent Vectors and Normal Vectors, Arc Length and Curvature

Functions of Several Variables: Limits and Continuity, Partial Derivatives, Differentials, Chain Rule for Functions of Several Variables, Directional Derivatives and Gradients, Applications of Functions of Two Variables, Optimization (Including Lagrange Multipliers)

Multiple Integration: Interated Integrals and Area in the Plane, Double Integrals and Volume, Change of Variables (Polar Coordinates), Center of Mass and Moments of Inertia, Surface Area, Triple Integrals and Applications, Triple Integrals in Cylindrical Spherical Coordinates, Change of Variables (Jacobians)

Vector Analysis: Vector Fields, Line Integrals, Conservative Vector Fields and Independence of Path, Green's Theorem, Surface Integrals, Divergence Theorem, Stokes Theorem

Differential Equations: Separable Differential Equations, First Order Linear Differential Equations, Second Order Linear Differential Equations (Homogeneous and Non-Homogeneuous)

Year Outline:

Quarter1 (4 Exams)
Unit Q101: Three Dimensional Systems (CH12)
Unit Q102: Partial Differentiation (CH 14A)
Unit Q103: Double Integrals and Change of Variable (CH 15A)
Unit Q104: Triple Integrals (include cylindrical and spherical coordinates) (CH 15B)

Quarter2 (4 Exams)
Unit Q201: Vector-Valued Functions (CH 13)
Unit Q202: Vector Fields, Line Integrals, FTC, and Green's Theorem (CH 16A)
Unit Q203: Parametric Surfaces, Surface Integrals, Stokes Theorem and The Divergence Theorem(CH 16B)
Unit Q204: Partial Differentiation - Application (Optimization) (CH 14B)

Quarter3 (2 Exams and 7 Review Assignments)
Unit Q301: Differential Equations (100 points)
Unit Q302: Cumulative Review Group Assignments (100 points)
Unit Q303: Calculus 3 - Vector Calculus Cumulative Exam (300 points)

Quarter4 (3 Exams/Assignments/Projects)
Unit Q401: Additional Topic 1 (TBD)
Unit Q402: Additional Topic 2 (TBD)
Unit Q403: Additional Topic 3 (TBD)

Additional
Topics List:

EDE: Extended Differential Equations
LAF: Linear Algebra Foundation
CBP: Calculus Based Probability
GLM: Statistics - ANOVA and Generalized Linear Models
DMV: Discrete Mathematics (Voting)
DMD: Discrete Mathematics (Fair Division)
DMA: Discrete Mathemtics (Apportionment)
DMG: Discrete Mathematics (Graphy Theory)