Department of Mathematics and Statistics

Oakland University

146 Library Drive

Rochester, MI. 48309

Office: 546 Mathematics Science Center

E-mail: shaska[at]oakland.edu

Oakland University

146 Library Drive

Rochester, MI. 48309

Office: 546 Mathematics Science Center

E-mail: shaska[at]oakland.edu

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The course is ** fully online**.

- Chapter 12: Vectors and geometry of space
- 12.1 Three dimensional coordinate system
- 12.2 Vectors
- 12.3 The dot product
- 12.4 The cross product
- 12.5 Equations of lines and planes
- 12.6 Quadratic surfaces
- Chapter 13: Vector functions
- 13.1 Vector functions and space curves
- 13.2 Derivatives and integrals of vector functions
- 13.3 Arc length and curvature
- 13.4 Motion in space: velocity and acceleration
- Chapter 14: Functions of several variables, partial derivatives
- 14.1 Functions of several variables
- 14.2 Limits and continuity
- 14.3 Partial derivatives
- 14.4 Tangent planes and linear approximation
- 14.5 The chain rule
- 14.6 Directional derivatives and the gradient
- 14.7 Maximum and minimum values
- 14.8 Lagrange multipliers
- 14.9 Taylor series for functions of several variables* (not in the book)
- Chapter 15: Multiple integrals
- 15.1 Double integrals over rectangles
- 15.2 Iterated integrals
- 15.3 Double integrals over general regions
- 15.4 Double integrals in polar coordinates
- 15.5 Applications of double integrals
- 15.6 Surface area
- 15.7 Triple integrals
- 15.8 Triple integrals in cylinder coordinates
- 15.9 Triple integrals in spherical coordinates
- 15.10 Change of variables in multiple integrals
- Chapter 16: Vector Calculus
- 16.1 Vector fields
- 16.2 Line integrals
- 16.3 The fundamental theorem of line integrals
- 16.4 Green's theorem
- 16.5 Curl and divergence
- 16.6 Parametric surfaces and their areas
- 16.7 Surface integrals
- 16.8 Stoke's theorem
- 16.9 The divergence theorem