Advanced Calculus

Catalog description

Advanced Calculus builds on prior calculus concepts to provide a rigorous and comprehensive exploration of advanced topics in calculus and analysis. The course begins with an introduction to writing proofs, using definitions and theorems, to analyze the real number system. The course progresses to using definitions and theorems to analyze the properties of functions, focusing on continuity, differentiability, integrability, and convergence. Then, it examines the rigorous treatment of advanced vector calculus operations, including the differentiation and integration of vector functions, and applies these skills to solve real-world problems in physics and engineering. Finally, students will synthesize and apply advanced integration and topological techniques to solve complex problems. This course solidifies the mathematical foundation needed for specialized and research-focused applications in mathematics and related fields.