MM 365: Calculus I

Introduces single-variable differential and integral calculus. Topics include limits and continuity, definition of the derivative, differentiation rules (product, quotient, chain rule), implicit differentiation, applications of derivatives (optimization and related rates), Riemann sums, and the Fundamental Theorem of Calculus.

• Limits and continuity: epsilon-delta definitions, one-sided limits, and indeterminate forms using L'Hopital rule in MM 365
• Differentiation rules: product rule, quotient rule, chain rule, and implicit differentiation techniques for Calculus I
• Applications of derivatives: Mean Value Theorem, curve sketching, optimization problems, and related rates in MM 365
• Integral calculus foundations: definite integrals as Riemann sums, substitution method, and the Fundamental Theorem of Calculus at Purdue Global