Lecture Notes
Calculus
Much part of these lecture notes came from calculus classes I taught.
Lecture Notes
Differential Calculus
Integral Calculus
Sequences, Series, and Vector-Valued Functions
Multi-Variable Calculus
Free Online Textbooks
References and Further Reading
Click on linked topics to view lecture notes.
Some Important Formulas from College Algebra and Trigonometry for Freshmen Calculus
Limits of Functions
Examples of Non-Existing Limits
The Precise Definition of a Limit
How to Calculate Limits I
How to Calculate Limits II
How to Calculate Limits III
Continuity
Limits Involving Infinity and Asymptotes
Finding a Line Tangent to a Curve
Derivatives
A Physical Meaning of Derivative: Velocity and Acceleration
Basic Differentiation Formulas
Continuity versus Differentiability
The Product and Quotient Rule
Derivatives of Trigonometric Functions
The Chain Rule
The Proof of the Chain Rule
Implicit Differentiation
Related Rates
Derivatives of Logarithmic and Exponential Functions
Inverse Trigonometric Functions
Linear Approximations and Differentials
Maximum and Minimum
Mean Value Theorem
The First and Second Derivative Test
Optimization Problems
Optimization Problems II: Business and Economic Optimization Problems
L'Hôpital's Rule
Newton’s Method
Antiderivatives
Areas under Curves
Definite Integral
The Fundamental Theorem of Calculus
Substitution Rule
Areas Between Curves
Applications of Definite Integrals: Volumes by Slicing
Applications of Definite Integrals: Solids of Revolution (The Disk Method)
Applications of Definite Integrals: Solids of Revolution (The Washer Method)
Applications of Definite Integrals: Volumes by Cylindrical Shells
Applications of Definite Integrals: Arc Length
Applications of Definite Integrals:Surfaces of Revolution
Integration by Parts
Trigonometric Integrals
Trigonometric Substitution
Inverse Trigonometric Functions
Integration of Rational Functions by Partial Fractions
Improper Integrals
Sequences
Infinite Series
Cauchy-Maclaurin Integral Test
The Ratio, Root and Comparison Tests
Alternating Series, Absolute and Conditional Convergence
Approximating Functions with Polynomials
Properties of Power Series
Taylor Series
Vectors
The Dot Product
The Cross Product
Lines and Planes in Space
Derivatives and Integrals of Vector-Valued Functions
Arc Length and Reparametrization
Calculus
Benjamin Crowell, Calculus
Michael Spivak, Calculus
Gilbert Strang, Calculus
Ellery Williams Davis and William Charles Brenke, The Calculus
Advanced Calculus
George A. Gibson, Advanced Calculus. An alternative copy is available here.
Francis B. Hildebrand, Advanced Calculus for Applications
David V. Widder, Advanced Calculus. An alternative copy is available here. (Much better scanned copy!)
Robert Wrede and Murray R. Spegel, Advanced Calculus, Schaum's Outlines
Ivan S. Sokolnikoff, Advanced Calculus
Tom M. Apostol, Calculus, Volum I. One-Variable Calculus, with an Introduction to Linear Algebra, 2nd Edition, John Wiley & Sons, 1967
Tom M. Apostol, Calculus, Volume II. Multi-Variable Calculus and Linear Algebra, with Applications to Differential Equations and Probability, 2nd Edition, John Wiley & Sons, 1969
Jerrold Marsden and Anthony Tromba, Vector Calculus, 5th Edition, W. H. Freeman and Company, 2003
Jerrold Marsden and Alan Weinstein, Calculus I, II, III, Second Edition, Springer, 1984
Jerrold Marsden and Alan Weinstein, Calculus Unlimited, The Benjamin/Cummings Publishing Company, Inc., 1981
Ivan S. Sokolnikoff, Advanced Calculus, McGraw-Hill Book Company, Inc., 1939