calculus

Notes

calculus 1. Preliminaries (Review) Functions and graphs Polynomial, rational, exponential, logarithmic functions Trigonometric functions Coordinate geometry Goal: Refresh algebra and function skills needed for calculus. 2. Limits and Continuity The concept of a limit One-sided limits Limits at infinity Continuity and discontinuities The Intermediate Value Theorem Key idea: Understanding behavior of functions near a point. 3. Derivatives Definition of the derivative Derivatives as rates of change Tangent lines Basic differentiation rules Higher-order derivatives Key idea: Measuring change. 4. Differentiation Techniques Product rule Quotient rule Chain rule Implicit differentiation Derivatives of inverse functions Logarithmic differentiation Key idea: Efficiently computing derivatives. 5. Applications of Derivatives Related rates Optimization problems Mean Value Theorem Curve sketching Motion (velocity & acceleration) Key idea: Using derivatives to solve real-world problems. 6. Integrals Antiderivatives Definite and indefinite integrals Riemann sums Fundamental Theorem of Calculus Key idea: Accumulation and area. 7. Techniques of Integration ...