Lecture Notes and Sample Exams

Calculus and Analytic Geometry

 Calculus 1 Preliminary Guide to Review Are you ready for calculus? - Answers Complete Analysis of a Function - Part 1 Complete Analysis of a Function - Part 2 Complete Analysis of a Function - Part 3 Limits Limits at infinity - Part 1 Limits at infinity - Part 2 Properties of limits at infinity Two-sided limits Properties of limits Limits involving logarithms Limits involving e Trigonometric Limits Instantaneous Velocity Average Velocity - Part 1 Average Velocity - Part 2 Instantaneous Velocity Differentiation Differentiating by Finding Limits Proving the Rules Practice 1 (generalized polynomials) Differentiating sinx and cosx (proofs) Antiderivatives (practice) Proving the Product Rule Differentiating Logarithmic Functions Practice 2 (after product rule, sinx, cosx, lnx) Proving the quotient rule Practice 3 Chain Rule (practice) Practice 4 (after chain rule) Practice 5 (after exponential functions) Antiderivatives 2 (practice) Differentiating Trigonometric Functions Practice 6 (after inverse trig functions) Implicit Differentiation Applications of Derivative Relative Extrema (polynomials only) Tangent Lines (generalized polynomials only) Optimization 2 (Polynomials) Optimization 3 (Generalized Polynomials) Optimization 4 (After Chain Rule) The Second Derivative Test More Optimization (after chain rule) Related Rates Hyperbolic Functions Complete analysis of a function l'Hôpital's Rule Integration Riemann Sums The Fundamental Theorem Definite Integrals (practice) Integration by substitution Trigonometric Differentiation and Integration Formulas Applications of the Integral - 1 (practice) Applications of the Definite Integral - 2 Improper integrals Integration by parts Other Leibniz notation Graphing in Polar Coordinates Graphing the antiderivative (Practice) Proving the Mean Value Theorem Calculus 2 Preliminary Are you ready for calculus 2? - Some Solutions Review of Differentiation (practice) Exponential and Logarithmic Functions Basic Differentiation and Integration Formulas Review of Differentiation 2 (practice) Techniques of Integration Integration by substitution Trigonometric Integrals 1 Integration by Parts Trigonometric Substitutions Hyperbolic Functions Partial Fractions Integrating Hyperbolic Functions Numerical Integration Improper Integrals Applications of Integration Applications of the Definite Integral - 1 (Areas) Volumes 1 (Cross-sections) Volumes 2 (disk method) Volumes 3 (washer method) Volumes 4 (shell method) Arc Length Work Center of Mass Sequences and Series The Real Number System Sequences - Part 1 Sequences - Part 2 Sequences - Part 3 Sequences - Part 4 Limits of Sequences Fractions and decimals (review) Geometric Series Series 1 (definition, telescoping, geometric, integral test) Series 2 (comparison test) Series 3 (ratio test and root tests) Series 4 (alternating test) Power Series Taylor Series Other Parametrization Graphing in Polar Coordinates