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Topics ·
Review: Functions. Intuitive approach to limits. ·
Computing limits. Rigorous definition of limit. Trigonometric functions, continuity. Rate of change, tangent lines. ·
Techniques of differentiation. Derivatives of trigonometric functions. Chain rule. ·
Related rates. Local linear approximation.
Implicit differentiation. Increase, decrease, concavity. ·
Relative extrema. Graphing curves. ·
Absolute extrema. Applied problems. Rolle's theorem. Mean Value theorem. ·
Indefinite integral, anti derivative. Area and definite integral
as the limit of a sum. ·
Fundamental theorem of calculus. Substitution. Area between two
curves. ·
Volumes. Arc length.
Surfaces of revolution. Average value. ·
Transcendental functions: logarithm, exponential, inverse trigonometric functions. L'hopital's rule. ·
Integration by parts.
Trigonometric integrals and substitutions. ·
Partial fractions. ·
Improper integrals. Sequences. Infinite series. ·
Convergence tests. Alternating series. ·
Taylor polynomials. Taylor and power series. Convergence
of power series.
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