Vectors, multivariable functions, partial derivatives, multiple integration, and theorems of Green and Stokes. (Offered each semester)

MATH 112 Calculus II

1. Understand and use the fundamental theorem of calculus.
2. Familiarity with various techniques of integration.
3. Understand the Calculus of functions of a single variable.
4. Familiarity with the polar coordinate system.

Larson, Hostetler and Edwards, Calculus, 9^th edition, Brooks/Cole, 2010 (ISBN: 9780547209982)

Lamarr C. Widmer, Ph.D., Associate Professor of Mathematics

Students majoring in computer science, engineering, mathematics, physics, or chemistry.

1. To develop a rigorous understanding of the geometry of space and functions of several variables including partial differentiation and multiple integration.
2. To develop a rigorous understanding of vectors and vector-valued functions with an introduction to vector analysis.
3. To enhance learning by examining geometric, numerical, and algebraic aspects of each problem.
4. To acquire an understanding of the breadth of mathematics by introducing applications in a wide variety of scientific fields.
5. To use the tools of Calculus to formulate and solve multi-step problems, and to interpret the numerical results.
6. To enhance the ability to communicate mathematical concepts through a series of written laboratory assignments and classroom discussions.
7. To select and use technology when appropriate in problem solving.
8. To develop an ability to recognize calculus concepts in the context of written problems and implement the corresponding processes.
9. To develop the process of making appropriate conjectures, finding suitable means to test those conjectures, and drawing conclusions about their validity.

1. Vectors and space: a) space coordinates, b) dot product, c) cross product, and d) lines and planes in space.
2. Vector-valued functions: a) differentiation and integration of vector-valued functions, b) velocity and acceleration, c) tangent and normal vectors, d) arclength, and e) curvature.
3. Functions of several variables: a) limits and continuity, b) partial derivatives, c) differentials, d) chain rule, e) directional derivatives and gradient, f) tangent planes, g) extrema, and h) LaGrange multipliers.
4. Multiple integration: a) iterated integrals, b) double and triple integrals, c) surface area, d) cylindrical and spherical coordinates, and e) center of mass and moments of inertia.
5. Vector Analysis: a) vector fields, b) line integrals, c) independence of path, d) Green's Theorem, e) surface integrals, f) Divergence Theorem, and g) Stoke's Theorem.