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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)
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


This page was last updated on September 6, 2019. Questions, comments: please e-mail to mhidegkuti@ccc.edu.