## Lecture Notes

### Calculus

Much part of these lecture notes came from calculus classes I taught.

#### Lecture Notes

#### Differential Calculus

Some Important Formulas from College Algebra and Trigonometry for Freshmen Calculus#### Integral Calculus

#### Sequences, Series, and Vector-Valued Functions

#### Multi-Variable Calculus

#### References and Further Reading

Click on linked topics to view lecture notes.

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

The Chain Rule

The Proof of the Chain Rule

Implicit Differentiation

Linear Approximations and Differentials

Maximum and Minimum

Mean Value Theorem

The First and Second Derivative Test

Not in particular order.

Tom M. Apostol, Calculus, Volum I. One-VAriable Calculus, with an Introduction to Linear Algebra, 2nd Edition, John Wiley & Sons, 1967Tom 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 Alan Weinstein, Calculus I, II, III, Second Edition, Springer, 1984

Jerrold Marsden and Alan Weinstein, Calculus Unlimited, The Benjamin/Cummings Publishing Company, Inc., 1981

Jerrold Marsden and Anthony Tromba, Vector Calculus, 5th Edition, W. H. Freeman and Company, 2003

Ivan S. Sokolnikoff, Advanced Calculus, McGraw-Hill Book Company, Inc., 1939