Limits and continuity: Rates of Change and Limits – Calculating Limits using Limiting Laws – The Precise definition of Limit – One-Sided Limits and Limits at Infinity – Continuity – Tangents and Derivatives.
Chapter-2 (Sections 2.3-2.7).
Differentiation: The Derivative as a Function – Differentiation Rules – The Derivative as a Rate of Change – Derivatives of Trigonometric Functions – The Chain Rule and Parametric Equations – Implicit Differentiation -nth derivatives of the functions: eax , (ax + b)n , log(ax + b), sin(ax + b) , cos(ax + b), eaxsin(bx+ c), eaxcos(bx + c) – Problems.
Chapter-3 (Sections 3.1-3.6).
Application of Derivatives: Extreme values of Functions – The Mean Value Theorem – Monotonic Functions and the First Derivative Test – Concavity and Curve Sketching.
Chapter-4 (Sections 4.1-4.4).
Integration: Estimating with Finite Sums – Sigma Notation and Limits of Finite Sums – The Definite Integral – The Fundamental Theorem of Calculus – Indefinite Integrals and the Substitution Rule – Substitution and Area between Curves.
Chapter-5 (Sections 5.1-5.6).
Techniques of Integration: Basic Integration Formulas – Integration by Parts – Integration of Rational Functions by Partial Fractions – Trigonometric Integrals – Trigonometric Substitutions– Improper Integrals.
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