BASIC CALCULUS
A Journey Through Limits, Derivatives, and Integrals
Calculus
Limits and Continuity
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Understanding limits and their role in calculus.
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One-sided, infinite, and limits at infinity.
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Continuity and types of discontinuities (removable, jump, infinite).
Derivatives
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Definition and interpretation of the derivative as a rate of change.
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Rules of differentiation (power, product, quotient, chain rules).
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Applications of derivatives in optimization and motion analysis.
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Higher-order derivatives and concavity analysis.
Integration
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Understanding integration as accumulation and area under a curve.
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Indefinite integrals and basic antiderivative rules.
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Definite integrals and their applications in physics and geometry.
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Techniques of integration (substitution and integration by parts).
Fundamental Theorem of Calculus
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Connection between differentiation and integration.
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Practical use of the theorem in solving real-world problems.
Applications of Calculus
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Motion: Velocity and acceleration analysis using derivatives.
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Area and volume: Finding areas under curves and volumes of solids.
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Growth and decay: Modeling population and radioactive decay.
