Calculus 1: Introduction to Calculus for Scientists & Engineers ( 4 sessions per month)

This course is the first in the calculus curriculum and introduces the central concepts of calculus. Topics include limits, continuity, derivatives of algebraic and transcendental functions of one variable, applications of these concepts, and a brief introduction to the integral of a function.

Introduction to Limits
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• Limit of a Function and Limit Laws
• One-Sided Limits
• Function Continuity
• Infinite limits & Limits Involving Infinity; Asymptotes of Graphs
• Tangent Lines and the Derivative at a Point using limitsThe Derivative as a Function by using
• limits

Derivative Rules (Differentiation Rules)
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• The Derivative as a Rate of Change
• Derivatives of Trigonometric Functions
• The Chain Rule
• Implicit Differentiation
• Derivatives of Inverse Functions and Logarithms
• Inverse Trigonometric Functions
• Related Rates

Application of Derivatives
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• Extreme Values of Functions on Closed Intervals
• The Mean Value Theorem
• Monotonic Functions and the First Derivative Test
• Concavity and Curve Sketching
• Indeterminate Forms and L’Hôpital’s Rule
• Applied Optimization
• Antiderivatives & Derivatives

Introduction to Integration
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• Area and Estimating with Finite Sums
• Sigma Notation and Limits of Finite Sums
• The Definite Integral
• The Fundamental Theorem of Calculus