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) Differentiationg Exponential Functions 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 Intermediate Value Theorem The Least Upper Bound Property and the Intermediate Value Theorem The Extreme Value Theorems 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