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Learn fundamental calculus concepts through this comprehensive 11-hour video course covering limits, derivatives, and integrals. Master the introduction to calculus by exploring average and instantaneous rates of change, understanding function limits using various methods including the sandwich theorem and one-sided limits, and working with continuous functions and limits involving infinity. Develop proficiency in finding derivatives using the power rule, product rule, quotient rule, and chain rule, while applying these concepts to real-world scenarios involving position, velocity, acceleration, and marginal cost. Study trigonometric derivatives, implicit differentiation, logarithmic differentiation, and inverse function derivatives. Progress to integration techniques including u-substitution, integration by parts, and tabular integration, then apply these skills to calculate volumes using circular slices and shell methods, determine arc lengths, and find surface areas. Practice using graphing calculators (TI-83, TI-84, TI-89) for limit estimation and derivative calculations throughout the course, and gain experience with both indefinite and definite integrals while exploring triple integrals and exponential function derivatives.
