# MTH222 Calculus III

Lead Faculty: Dr. Igor Ya Subbotin

## Course Description

A study of sequences, Taylor Polynomials, infinite series, and tests for convergence, and the power series. An overview of ordinary differential equations; the initial-value Problem; exactness and integrating factors; and Bernoulli and higher-order equations with forcing functions. Graphing calculator is required.

## Learning Outcomes

• Clearly demonstrate an ability to employ vector operations and properties to include additive, scalar, and vector cross product operations. Using such fundamental properties, the student will provide evidence of employing vectors to define lines and planes in 3-space, and will demonstrate competence in extending such capability to conic surfaces.
• Show ability to define vector-valued functions in terms of the scalar functions as components to the basis vectors.
• Interpret resulting-properties correctly.
• Successfully differentiate and integrate the scalar components.
• Provide evidence of understanding and competence in differentiation and integration of functions of more than one variable.
• Demonstrate sufficient capability with partial derivatives so as to permit derivations of directional derivatives and gradient functions.
• Develop the elements of Jacobean Matrix.
• Display capability to incorporate change of variable and other associated applications as specified in the corresponding goal of this syllabus.
• Understand the comprehension of the classic theorems of mechanics will be evaluated by application to elementary surface.