MATH 1013: Applied Calculus I

This undergraduate course presents a thorough academic investigation into the foundational theories, conceptual models, and methodological frameworks of Applied Calculus I. Specifically, students examine introduction to the theory and applications of both differential and integral calculus. Limits. Derivatives of algebraic and trigonometric functions. Riemann sums, definite integrals and the Fundamental Theorem of Calculus. Logarithms and exponentials, Extreme value problems, Related rates, Areas and Volumes. Instruction focuses on building core critical thinking, quantitative problem-solving, and disciplinary competencies necessary for upper-level studies and professional applications.

• Limits and continuity: formal epsilon-delta definitions, one-sided limits, and indeterminate forms via L'Hôpital's Rule in MATH 1013
• Differential calculus techniques: product, quotient, chain rules, and implicit differentiation
• Applications of derivatives: critical points, extreme value theorem, concavity, inflection points, and curve sketching
• Applied optimization and related rates: geometric rate modeling, profit maximization, and Mean Value Theorem in Applied Calculus I