Course Material
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Limits of sequences. Basic limits are studied, as well as basic properties of limits. More complicated limits are evaluated using properties of limits and basic limits.
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Limits of functions, continuity, intermediate value theorem. Definition of the derivative, basic derivatives and properties of derivatives with proofs. Local maxima and minima, concavity, points of inflexion. Graphs of rational functions. Rolle’s theorem, mean value theorems, L’ Hopital’s rule, Taylor expansion.
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Word problems involving derivatives. Problems involving maxima and minima and problems involving related rates.
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Integrals. Indefinite and definite integrals. Fundamental theorem of calculus. Techniques of integration. Use of definite integrals for the evaluation of areas between curves.
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Improper integrals of first and second kind. Comparison test.
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Introduction to first order differential equations. Separable first order differential equations. Linear first order differential equations, technique of integrating factor.