Instructor:

Michael W. Bermel

Materials:

Text: Calculus Early Transcendentals Sixth Addition
James Stewart (2008) Thomson Brooks/Cole
Calculator: TI 89 Software: MATLAB

Assessment:

Quarter grades are based on the overall total from the following.

Tests (3/4 @ 100 points each) :	3/400 points
Projects and Alternate Assessments	100 points

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

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 (3 Exams and 1 Alt. Assignment)
Unit Q101: Basic Vectors Fundamentals (CH12)
Unit Q102: Partial Differentiation (CH 14A)
Unit Q103: Partial Differentiation - Application (Optimization) (CH 14B)

Quarter2 (4 Exams and 1 Alt. Assignment)
Unit Q201 : Double Integrals and Change of Variable (CH 15A)
Unit Q202: Double Integrals - Application (CH 15B | Probability Supplement)
Unit Q203: Triple Integrals (include cylindrical and spherical coordinates) (CH 15C)
Unit Q204: CH 14 and 15 (Multivariable Calculus Cumulative)

Quarter3 (3 Exams and 1 Alt. Assignment)
Unit Q301: Vector-Valued Functions (CH 13)
Unit Q302: Line Integrals (CH 16A)
Unit Q303: Green's Theorem (CH 16B)

Quarter4 (3 Exams and 1 Cumulative Endterm Exam)
Unit Q401: Parametric Surfaces (CH16C)
Unit Q402: Stoke's and The Divergence Theorem (CH16D)
Unit Q403: CH 16 (Vector Calculus Cumulative)
Unit Q404: Differential Equations