Math 31A Differential and Integral Calculus

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Introduction – Limit Laws, Limits and Continuity – Evaluating Limits Algebraically – Trigonometric Limits, Limits at Infinity – Intermediate Value Theorem – Definition of the Derivative – The Derivative as a Function – Product and Quotient Rules – Higher Derivatives, Trig Functions – The Chain Rule – Implicit Differentiation – Related Rates – Midterm – Linear Approximation, Extreme Values

Extreme Values continued – Mean Value Theorem – The Shape of a Graph – Graph Sketching – Applied Optimization – Newton’s Method, Area – The Definite Integral – Midterm – The Indefinite Integral – Fundamental Theorem – The Substitution Method – Areas Between Curves, Average Value – Volumes of Revolution – Method of Cylindrical Shells

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