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Lecture Notes and Sample Exams

Calculus and Analytic Geometry

Calculus 1


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 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

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

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

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

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
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

Graphing in Polar Coordinates

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