MATH 621 Selected Topics in Advanced Calculus II

SELECTED TOPICS INADVANCED CALCULUS IIMa 6211. Course DescriptionThis course studies: vector, multiple integrals, curves and surfaces, theory ofintegration, and infinite and power series.Pre-requisite: MA 620 Selected Topics in Advances Calculus I2. Goals of the Course1. To provide a foundation for the calculus that is both rigorous and significant toteachers of secondary-school mathematics.2. To provide insight into the fundamental concepts of the calculus. (e.g. sequence,limit, continuity, derivative, integral, etc.)3. To extend and apply further the concepts of undergraduate calculus.3. Instructional Procedures1. Lecture/discussion2. Small group and independent study3. Use of computer software and graphing calculators4. Course Content1. Elements of Partial Differentiationa. Partial Derivativesb. Implicit Functionsc. Geometrical Significance of Partial Derivativesd. Maxima and Minimae. Composite Functions and the Chain Rulef. Second Derivatives by the Chain Ruleg. Homogeneous Functions and Euler’s Theoremh. Derivatives of Implicit Functionsi. Extremal Problems with Constraintsj. Lagrange’s Methodk. Sufficient Conditions for Differentiability2. Implicit-Function Theoremsa. Implicit Functionsb. Fundamental Theorem and its Generalizations

Olmstead, John M.H., Advanced Calculus, Prentice Hall, 1961Simmons, George, Calculus Gems, McGraw-Hill, 1992Spiegel, Murray R., Schaum’s Outline Series; Theory and Problems ofAdvanced Calculus, McGraw Hill, 1968D. Relevant Periodical SourcesNoneE. Relevant SoftwareDeriveF. OtherTI-82 or TI-83 Graphing Calculator